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<hr />
<div>==<span id="LFIDescription">Instrument description</span>==<br />
The Low-Frequency Instrument (see Fig. 1 in the [[LFI overview]]) consists of a 20 K focal plane unit hosting the corrugated feed horns, the orthomode transducers (OMTs) and the receiver front-end modules (FEMs). Forty-four composite waveguides {{BibCite|darcangelo2009a}} are interfaced with three conical thermal shields and connect the front-end modules to the warm (roughly 300 K) back-end unit (BEU) containing a further radio frequency amplification stage, detector diodes, and all the electronics for data acquisition and bias supply. <br />
<br />
Best LFI noise performance is obtained with receivers based on InP High Electron Mobility Transistor (HEMT) low noise amplifiers (LNAs) for minimal power dissipation and best performance. To further minimize power consumption in the focal plane, the radiometers are split into two sub-assemblies connected by waveguides, one located at the telescope focal area, the other on the 300 K portion of the Planck satellite. These design features allow the entire front-end LNA dissipation to be <0.55 W, which enables the active cooling of the focal assembly. This is achieved with a vibration-less hydrogen sorption cooler, which also provides 18 K pre-cooling to the HFI helium J-T cooler. Two sorption cooler units are included in the flight hardware.<br />
<br />
As shown schematically in Fig. 1 below, the LFI consists of the following subsystems:<br />
* Radiometer Array Assembly (RAA);<br />
* Sorption Cooler Subsystem (SCS);<br />
* Radiometer Electronics Box Assembly (REBA).<br />
<br />
The RAA includes the Front End Unit (FEU) and the Back End Unit (BEU), connected via waveguides. The FEU is located at the focus of the telescope, as one component of the joint LFI/HFI focal assembly (see sections below). The BEU is mounted on the top of the Planck service module (SVM).<br />
The REBA (Radiometer Electronics Box Assembly) and the warm parts of the Sorption Cooler System (SCS) are located on one of the lateral panels of the SVM. The FEU and the Sorption Cooler Compressor (SCC) are connected by concentric stainless steel tubes. The smaller tube carries hydrogen at approximately 60 atmospheres from the cooler compressors to the FEU, while the larger tube returns the hydrogen at about 0.3 atmospheres. These units are described in following sections and in the [[LFIAppendix|Annexes]], while the SCS is described in details in the [[LFI design, qualification, and performance#The Sorption Cooler|Sorption Cooler]] section.<br />
All LFI units are linked together by the LFI harness, which also connects to the spacecraft interface.<br />
<br />
[[File:schema.jpg|thumb|center|500px|'''Figure 1. Block Diagram of LFI.''']]<br />
<br />
=== ''Radiometer Array Assembly (RAA)'' ===<br />
<br />
The Radiometer Array Assembly (RAA) consists of two main units (the front end unit, FPU and the Back End Unit, BEU), connected by a set of waveguides.<br />
The Focal Plane Unit (FPU) is the heart of the LFI instrument; it contains the feed array and associated orthomode transducers (OMTs) and FEMs, all cooled to 20 K by the sorption cooler. The FPU comprises a set of 11 modules, which are mounted on a mechanical support which meets the thermo-mechanical requirements of the instrument and adds thermal inertia.<br />
The BEU comprises the radiometer Back End Modules (BEM) and the Data Acquisition Electronics (DAE), which are connected by an internal harness.<br />
The HFI Unit is located inside the LFI FPU and supported by the LFI structure. The LFI structure gives the mechanical and thermal interface to the HFI unit with the proper stiffness and thermal de-coupling. The LFI structure also guarantees the proper alignment of the HFI detector with the telescope focal plane.<br />
<br />
The timescale of the stability of the receiverS is driven by the 1 rpm rotation speed of the spacecraft, which requires a very low 1/<i>f</i>-noise or gain variation of the low noise amplifiers and other components.<br />
The LFI uses a pseudo-correlation receiver concept (Fig. 2 below). This radiometer concept is chosen to maximize the stability of the instrument by reducing the effect of non-white noise generated in the radiometer itself. In this scheme, the difference between the inputs to each of the chains (the signal from the telescope and that from a reference blackbody, respectively) is continuously being observed. To remove the effect of instability in the back-end amplifiers and detector diodes, it is necessary to switch the signal detected at the diodes at a high rate.<br />
The signals from the sky and from a reference load are combined by a hybrid coupler, amplified in two independent amplifier chains, and separated out by another hybrid. The sky and the reference load power can then be measured and differenced. Since the reference signal has been subject to the same gain variations in the two amplifier chains as the sky signal, the true sky power can be recovered.<br />
The differencing receiver greatly improves the stability if the two input signals are almost equal, at<br />
a cost of a factor of &radic;2 in sensitivity, compared to a perfectly stable total-power radiometer with the same noise temperature and bandwidth. This radiometer concept is also capable of greatly reducing the knee frequency.<br />
A single Radiometer Chain Assembly (RCA; see Fig. 2) consists of each functional unit from the feed horn to the BEM. The RAA therefore includes a set of 11 RCAs and the Data Acquisition Electronics (see also Fig. 1 above), all mounted on a suitable mechanical structure. Although there are differences in the details of the radiometer chains at different frequencies, their overall configuration is similar, and a general description of their design is provided in this section.<br />
Planck LFI has 11 Radiometer Chain Assemblies (RCAs). Each RCA is constituted by a feed horn and FEM in the FEU (at 20 K), BEM (at 300 K) in the BEU, and four waveguides that connect each FEM-BEM couple. The frequency distribution of the RCA is the following:<br />
* 2 RCAs at 30 GHz;<br />
* 3 RCAs at 44 GHz;<br />
* 6 RCAs at 70 GHz.<br />
<br />
[[File:rca_schematic.jpg|thumb|center|640px|'''Figure 2. A complete RCA from feed-horn to analogue voltage output. The insets show the OMT, the details of the 20 K pseudo-correlator and of the back-end radio-frequency amplification, low-pass filtering, detection, and DC amplification.''']]<br />
<br />
==== ''Radiometer Chain Assembly (RCA)''====<br />
<br />
Every RCA consists of two radiometers, each feeding two diode detectors (see Fig. 2 above), for a total of 44 detectors. The 11 RCAs are labelled by a number from 18 to 28, as outlined in Fig. 1 of the [[LFI overview]], right panel.<br />
<br />
Fig. 2 provides a more detailed description of each radiometric receiver. In each RCA, the two perpendicular linear polarization components split by the OMT propagate through two independent pseudo-correlation differential radiometers, labelled as ''M'' or ''S,'' depending on the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2).<br />
<br />
In each radiometer the sky signal coming from the OMT output is continuously compared with a stable 4 K blackbody reference load mounted on the external shield of the HFI 4-K box (Valenziano et al. 2009{{BibCite|valenziano2009}}). After being summed by a first hybrid coupler, the two signals are amplified by approximately 30 dB (see upper-left inset of Fig. 2). The amplifiers were selected for best operation at low drain voltages and for gain and phase match between paired radiometer legs, which is crucial for good balance. Each amplifier is labelled with codes ''1'' or ''2'' so that the four outputs of the LNAs can be named with the sequence: ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). <br />
Tight mass and power constraints called for a simple design of the Data Acquisition Electronics (DAE) box so that power bias lines were divided into five common-grounded power groups with no bias voltage readouts; only the total drain current flowing through the front-end amplifiers is measured and is available to the house-keeping telemetry (this design has important implications for front-end bias tuning, which depends critically on the satellite electrical and thermal configuration and was repeated at all integration stages during on-ground and in-flight satellite tests).<br />
A phase shift (or phase switch) alternating between 0&deg; and 180&deg; at the frequency of 4096 Hz is applied in one of the two amplification chains and then a second hybrid coupler restores the sky and reference load components, which are further amplified and detected in the warm BEU, with a voltage output ranging from -2.5 V to +2.5 V.<br />
<br />
Each radiometer has two output diodes which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence ''M-00'', ''M-01'', ''S-10'', ''S-11''.<br />
<br />
After detection, an analogue circuit in the DAE box removes a programmable offset in order to obtain a nearly null DC output voltage and a programmable gain is applied to increase the signal dynamics and optimally exploit the ADC input range. After the ADC, data are digitally down-sampled, re-quantized and compressed in the REBA according to a scheme described in (Herreros et al. 2009{{BibCite|herreros2009}}, Maris et al. 2009{{BibCite|maris2009}}), before being combined in telemetry packets. On the ground, telemetry packets are converted to time ordered data for both the sky and reference load, after calibrating the ADU (Analog-to-Digital Unit) samples into volts. The calibration takes into account the applied offset and gain factors.<br />
<br />
To first order, the mean differential power output for each of the four receiver diodes can be written as follows (Seiffert et al. 2002{{BibCite|seiffert2002}}, Mennella et al. 2003{{BibCite|mennella2003}}, {{PlanckPapers|bersanelli2010}}):<br />
<br />
<math> \label{eq:power}<br />
P_{\rm out}^{\rm diode} = a\, G_{\rm tot}\,k\,\beta \left[ T_{\rm sky} + T_{\rm noise} - r\left(<br />
T_{\rm ref} + T_{\rm noise}\right) \right]<br />
</math><br />
<br />
where <i>G</i><sub>tot</sub> is the total gain, <i>k</i> is the Boltzmann constant, <i>&beta;</i> the receiver bandwidth, and <i>a</i> is the diode constant. <i>T</i><sub>sky</sub> and <i>T</i><sub>ref</sub> are the average sky and reference load antenna temperatures at the inputs of the first hybrid and <i>T</i><sub>noise</sub> is the receiver noise temperature.<br />
<br />
The gain modulation factor (Mennella et al. 2003{{BibCite|mennella2003}}, {{PlanckPapers|planck2011-1-6 }}), <i>r</i>, is defined by<br />
<br />
<math> \label{eq:erre1} <br />
r = \frac{T_{\rm sky} + T_{\rm noise}}{T_{\rm ref} + T_{\rm noise}} ,<br />
</math><br />
<br />
and is used to balance (in software) the temperature offset between the sky and reference load signals and minimize the residual 1/<i>f</i> noise in the differential data stream. This parameter is calculated from the average uncalibrated total power data using the relationship<br />
<br />
<math> \label{eq:erre2}<br />
r = \langle V_{\rm sky} \rangle/ \langle V_{\rm ref}\rangle,<br />
</math><br />
<br />
where <<i>V</i><sub>sky</sub>> and <<i>V</i><sub>ref</sub>> are the average sky and reference voltages calculated in a defined time range.<br />
The white noise spectral density at the output of each diode is essentially independent of the reference-load absolute temperature and is given by<br />
<br />
<math> \label{eq:dt1}<br />
\Delta T_0^{\rm diode} = \frac{2\,(T_{\rm sky}+T_{\rm noise})}{\sqrt{\beta}}.<br />
</math><br />
<br />
If the front-end components are not perfectly balanced, then the separation of the sky and reference load signals after the second hybrid is not perfect and the outputs are mixed. First-order deviations in white noise sensitivity from the ideal behaviour are caused mainly by noise temperature and phase-switch amplitude mismatches. Following the notation used in (Seiffert et al. 2002 {{BibCite|seiffert2002}}), we define &epsilon;<sub><i>T</i><sub>n</sub></sub>, as the imbalance in front end noise temperature, and &epsilon;<sub><i>A</i><sub>1</sub></sub> and &epsilon;<sub><i>A</i><sub>2</sub></sub>, the imbalance in signal attenuation in the two states of the phase switch. Equation above for the two diodes of a slightly imbalanced radiometer then becomes<br />
<br />
<math> \label{eq:dt2} (\Delta T^{\rm diode} )^2 ≈ (\Delta T_0^{\rm diode})^2 ( 1± \frac{\epsilon_{A1}- \epsilon_{A2}}{2} <br />
+ \alpha \epsilon_{T{\rm n}}),<br />
</math><br />
<br />
which is identical for the two diodes apart from the sign of the term &epsilon;<sub><i>A</i><sub>1</sub></sub> − &epsilon;<sub><i>A</i><sub>2</sub></sub>, representing the phase switch amplitude imbalance. This indicates that the isolation loss caused by this imbalance generates an anti-correlation between the white noise levels of the single-diode data streams.<br />
For this reason, the LFI scientific data streams are obtained by averaging the voltage outputs from the two diodes in each radiometer:<br />
<br />
<math> \label{eq:v1} <br />
V^{\rm rad}_{\rm out} = w_1 V^{\rm diode\,1}_{\rm out} +w_2 V^{\rm diode\,2}_{\rm out} </math>,<br />
<br />
where &omega;<sub>1</sub> and &omega;<sub>2</sub> are inverse-variance weights calculated from the data as discussed in ({{PlanckPapers|planck2011-1-6}}). This way, the diode-diode anti-correlation is cancelled, and the radiometer white noise becomes<br />
<br />
<math> \label{eq:dt3}<br />
\Delta T^{\rm rad} ≈ \frac{ T_0^{\rm diode}}{\sqrt{2}} (1+\alpha \epsilon_{T{\rm n}})^{1/2}.<br />
</math><br />
<br />
In the equations above, &epsilon;&laquo;1, while &alpha; (a term &asymp;1) is given by<br />
<br />
<math> \label{eq:alpha} <br />
\alpha = \frac{ T_{\rm noise} (2 \; T_{\rm noise} + T_{\rm sky} + T_{\rm ref} }<br />
{2 (T_{\rm sky} + T_{\rm noise} )(T_{\rm ref} + T_{\rm noise})}.<br />
</math><br />
<br />
See the [[TOI processing LFI|Diode Combination]] section for the details of the diode combination procedure. <br />
<br />
In Fig. 3 below we show a close-up of the two front end modules of an RCA with the four phase switches, which are labelled with the four letters ''A'' and ''B'' (main arm), and ''C'' and ''D'' (side arm). Each phase switch is characterized by two states: state 0 (no phase shift applied to the incoming wave); and state 1 (180&deg; phase shift applied) and can either stay fixed in a state or switch at 4 kHz between the two states.<br />
<br />
Phase switches are clocked and biased by the DAE and their configuration can be programmed via telecommand. In order to simplify the instrument electronics, phase switches are configured and operated in pairs, by convention they are labelled ''A/C'' (corresponding to the first LNA both of main and side arm) and ''B/D'' (corresponding to the second LNA both of main and side arm). This means that if phase switches ''A'' and ''C'' are switching at 4 kHz then ''B'' and ''D'' are fixed, both in the same state (either 0 or 1); and viceversa. This simplification, required during the design phase to comply with mass and power budgets, comes at the price of losing some setup redundancy.<br />
<br />
[[File:phase_switch_operation.jpg|thumb|center|460px|'''Figure 3. Close-up of the two front-end modules of an RCA. There are four phase switches, labelled A, B, C, and D. Each switch can be fixed in one of its two positions (labelled as 0, 1) or switched at 4 kHz between 0 and 1. Phase switches are clocked and biased by the DAE in pairs: A/C and B/D.''']]<br />
<br />
==== ''Feed Horns (FHs)''====<br />
<br />
Dual profiled corrugated horns have been selected at all LFI frequencies as the best design in terms of the shape of the main lobe, level of the side lobes, control of the phase centre, and compactness. <br />
Details of the design, flight model and tests of Planck-LFI feed horns can be found in (Villa et al. 2009{{BibCite|villa2009}}) and in the corresponding [[LFIAppendix#Feed Horns (FH)|Annex]] section.<br />
<br />
==== ''Ortho-Mode Transducers (OMTs)''====<br />
<br />
The Ortho–Mode Transducer (OMTs) separates the radiation collected by the feedhorn into two orthogonal polarization components. It consists of a circular to square waveguide transition (directly connected to the FH), a square waveguide section and two separate rectangular waveguides (the main and side arms, which separate and pick up the orthogonal polarizations, connected with the FEU). A 90&deg; bend is always present on the side arm, while a twist is also necessary on the main (30 and 44 GHz) and side (70 GHz) arms, in order to match the FEU polarization.<br />
<br />
The details of the flight models and measurements of the Planck LFI ortho-mode transducers can be found in (D'Arcangelo et al. 2009{{BibCite|darcangelo2009b}}) and in the corresponding [[LFIAppendix#OrthoMode Transducers (OMT)|Annex]] section.<br />
<br />
==== ''Front End Modules (FEMs)''====<br />
<br />
Front End Modules are located in the FPU, just behind the Feed Horn and the Ortho Mode Transducers. The 70 GHz FEMs are mounted onto the inner wall of the main frame (the wall facing HFI instrument) from the HFI side. The 44 and 30 GHz FEMs are inserted into the main frame from the waveguide (WG) side and fixed to the bottom plate. Screws to the bottom plate are inserted from the WG side.<br />
The LFI FEMs are the first active stage of amplification of the radiometer chain. Each FEM contains four amplification paths, each of which is composed of several cascaded LNAs followed by a phase switch. Two passive hybrids, at the input and output of the FEM, are used to mix pairs of signals of the same radiometer (see Fig. 3). This cuases the instabilities of each chain to be applied to both the sky and load signals.<br />
<br />
The passive hybrid coupler ("magic-tee") combines the signals from the sky and cold load with a fixed phase offset of either 90&deg; or 180&deg; between them. It has a 20% bandwidth, low loss, and amplitude balance needed at the output to ensure adequate signal isolation.<br />
<br />
The details of the design, development and verification of the 70 GHz front-end modules for the Planck Low Frequency Instrument can be found in (Varis et al. 2009{{BibCite|varis2009}}) and in the corresponding [[LFIAppendix#Front End Modules (FEM)|Annex]] section.<br />
<br />
==== ''Waveguides (WGs)''====<br />
<br />
The LFI Front End Unit (FEU) is connected to the Back End Unit (BEU) by 44 rectangular waveguides approximately 1.5-2.0 m long. Each waveguide exhibits a low voltage standing wave ratio, low thermal conductivity, low insertion loss, and low mass. In addition, the waveguide path permits the LFI/HFI integration and the electrical bonding between the FPU and the BEU. Because of the Focal Plane Unit arrangement, the waveguides are in general twisted and bent in different planes and with different angles, depending on the particular waveguide. From the thermal point of view the waveguides have to connect two systems (the BEM and FEM) that are at very different temperatures. At BEM level the waveguides are at a temperature of 300 K, while at FEM level the temperature is 20 K. The waveguides have to reduce the thermal flow from 300 K to 20 K. In Fig. 1 in the [[LFI overview]] (left panel) a conceptual sketch of the LFI configuration is shown. <br />
<br />
Details of the Planck-LFI flight model of the composite waveguides can be found in (D'Arcangelo et al. 2009{{BibCite|darcangelo2009a}}) and in the corresponding [[LFIAppendix#Waveguides|Annex]] section.<br />
<br />
==== ''Back End Modules (BEMs)''====<br />
<br />
The BEMs are composed of four identical channels each made of Low Noise Amplifiers (LNAs), an RF bandpass Filter, RF to DC diode detector, and DC amplifiers.<br />
The FEM output signals are connected by waveguides from the Focal Plane Unit (FPU) assembly to the Back End Modules (BEMs) housed adjacent to the Data Acquisition Electronics (DAE) assembly. To maintain compatibility with the FEMs, each BEM accommodates four receiver channels from the four waveguide outputs of each FEM. The BEM internal signal routes are not cross-coupled and can be regarded as four identical parallel circuits.<br />
Each BEM is constructed as two mirror halves. The two amplifier/detector assemblies each contain two amplifier/detector circuits. Each is supplied from one of a pair of printed circuit boards, which also house two DC output amplifiers.<br />
<br />
The details of the design, development and verification of the 30 and 44 GHz back-end modules for the Planck Low Frequency Instrument can be found in (Artal et al. 2009{{BibCite|artal2009}}). <br />
Details of the design, development and verification of the 70 GHz back-end modules for the Planck Low Frequency Instrument can be found in (Varis et al. 2009{{BibCite|varis2009}}).<br />
Details are also reported in the corresponding [[LFIAppendix#Back End Modules (BEM)|Annex]] section.<br />
<br />
==== ''4K Load'' ====<br />
<br />
The purpose of the 4K reference load is to provide the radiometer with a stable reference signal. Reducing the input offset (the radiometric temperature difference between the sky and the reference load) reduces the minimum achievable radiometer 1/<i>f</i> noise knee frequency for a given amplifier fluctuation spectrum. A reference load temperature that matches the sky temperature (approximately 2.7 K) would be ideal. <br />
<br />
Details of the design, characteristics, and performance of the LFI 4-K reference load units are given in (Valenziano et al. 2009{{BibCite|valenziano2009}}) and in the corresponding section of the [[LFIAppendix#4K Load|Annexes]].<br />
<br />
=== Naming Convention ===<br />
<br />
The naming of all the LFI elements has been described in the previous sections, but here is summarized again for clarity. <br />
<br />
The 11 RCAs are labelled by numbers from 18 to 28, as outlined in Fig. 1 in the [[LFI overview]] (right panel). In each RCA, the two perpendicular linear polarization components are labelled as ''M'' or ''S'' according to the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2). <br />
<br />
Each front-end amplifier (see upper-left inset of Fig. 2) is labelled with the codes ''1'', ''2'', so that the four outputs of the FEM LNAs can be named with the sequence ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). <br />
<br />
Each radiometer has two output diodes (see upper-right inset of Fig. 2), which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence ''M-00'', ''M-01'', ''S-10'', and ''S-11''.<br />
<br />
=== ''REBA'' ===<br />
<br />
The Radiometer Electronics Box Assembly (REBA) is the electronics unit that processes the digitized scientific data and manages the overall instrument. It is also in charge of communication with the spacecraft.<br />
There are two REBA boxes, one nominal and one redundant. The redundancy concept is cold, which means that both boxes are never ON at the same time; the operation of each unit is managed by the spacecraft switching on the corresponding unit. The REBA ASW (Application SoftWare) is the same in each REBA box.<br />
<br />
A detailed description of the Planck LFI REBA can be found in (Herreros et al. 2009{{BibCite|herreros2009}}) and in the corresponding section of the [[LFIAppendix#REBA|Annexes]].<br />
<br />
=== ''Instrument On-board Software'' ===<br />
<br />
The REBA software is the on-board software of LFI. It is installed in the two computing subunits of REBA: the DPU (Digital Processing Unit), responsible of the control and monitoring of the instrument and the interface with the spacecraft; and the SPU (Signal Processing Unit), responsible for the data reduction and compression.<br />
<br />
Details can be found in the corresponding section of the [[LFIAppendix#Instrument On-board Software|Annexes]]. <br />
<br />
==== ''Reduction and Compression of Science Data'' ====<br />
<br />
To assess stability against 1/<i>f</i> noise, the Low Frequency Instrument (LFI) on board the Planck mission acquired data at a rate much higher than the data rate allowed by the science telemetry bandwidth of 35.5 kbps. The data were processed by an on-board pipeline, followed on the ground by a decoding and reconstruction step, to reduce the volume of data to a level compatible with the bandwidth, while minimizing the loss of information. The on-board processing of the scientific data used by Planck/LFI to fit the allowed data-rate is an intrinsically lossy process which distorts the signal in a manner that depends on a set of five free parameters (<i>N</i><sub>aver</sub>, <i>r</i><sub>1</sub>, <i,>r</i><sub>2</sub>, <i>q</i>, <i>O</i>) for each of the 44 LFI detectors.<br />
A brief description of the characteristics of this algorithm and the level of distortion introduced by the on-board processing as a function of these parameters can be found in the corresponding section of the [[LFIAppendix#Reduction and Compression of Science Data|Annexes]], while a full description of the Planck LFI on-board data handling system and the tuning and optimization method of the on-board processing chain can be found in (Maris et al. 2009{{BibCite|maris2009}}).<br />
<br />
The strategy adopted to fit into the telemetry bandwidth relies on three on-board processing steps: downsampling; pre-processing the data to ensure loss-less compression; and loss-less compression itself. To demonstrate these steps, a model of the input signal was used. Note that while the compression is loss-less, the pre-processing is not, due to the need to rescale the data and convert them to integers (a process named data re-quantization). However, the whole strategy is designed to keep strict control over the way in which lossy operations are done, and to quantify the amount of information loss in order to assess the optimal compression rate with minimal information loss.<br />
<br />
=== ''Instrument Operations'' ===<br />
<br />
==== ''Operational Modes'' ====<br />
<br />
The operations of the LFI are designed to be automatic and require little if any intervention from the ground. A small number of commands are required for operating the instrument and eventually for diagnostic and reconfiguration purposes.<br />
Each sky survey is conducted by the LFI with the instrument in the Normal Operations Mode. No deployable elements, or mechanically moving parts are included in the instrument. The scanning of the sky is achieved by progressive repointing of the satellite spin axis, with the Sun direction always within a cone 10&deg; from the spin axis.<br />
Within the Normal Science Mode the instrument can be configured in order to fit with different science or diagnostic needs without changing the power consumption and thus the temperature in the FPU. <br />
<!-- <br />
Changes in power consumption in the FPU are minimized and should occur only in the case that failures in the radiometers that could create interference problems require an RCA to be switched off. Power adjustments on the first stage of the HEMT amplifiers (which were contemplated), require extremely small power level variations.--><br />
<br />
A brief summary of the LFI Operational Modes and the transitions between them is given in the corresponding section of the [[LFIAppendix#LFI Operational Modes|Annexes]].<br />
<br />
<!--<br />
==== ''In-flight Operations'' ====<br />
<br />
TBW<br />
<br />
<br />
==== ''Anomalies'' ====<br />
<br />
TBW<br />
--><br />
<br />
==<span id="LFITests">Ground Tests</span>==<br />
During its development, the LFI flight model was calibrated and tested at various integration levels from sub-systems (Davis et al. 2009{{BibCite|davis2009}}) to individual integrated receivers ({{PlanckPapers|villa2010}}) and the whole receiver array ({{PlanckPapers|mennella2010}}). In every campaign we performed tests according to the following classification:<br />
<br />
* ''functionality tests'', performed to verify the instrument functionality;<br />
* ''tuning tests'', to tune radiometer parameters (biases, DC electronics gain and offset, digital quantization and compression) for optimal performance in flight-like thermal conditions;<br />
* ''basic calibration and noise performance tests'', to characterize instrument performance (photometric calibration, isolation, linearity, noise and stability) in tuned conditions;<br />
* ''susceptibility tests'', to characterize instrument susceptibility to thermal and electrical variations.<br />
<br />
Where possible, the same tests were repeated in several test campaigns, in order to ensure enough redundancy and confidence in the repeatability of the instrument behaviour. A matrix showing the instrument parameters measured in the various test campaigns is provided in Table 1 of ({{PlanckPapers|mennella2010}}).<br />
<br />
The ground test campaign was developed in three main phases: cryogenic tests on the individual RCAs; cryogenic tests on the integrated receiver array (the so-called radiometer array assembly, RAA); and system-level tests after the integration of the LFI and HFI instruments onto the satellite. The first two phases were carried out at the Thales Alenia Space - Italia laboratories located in Vimodrone (Milano, Italy) (note that receiver tests on 70 GHz RCAs were carried out in Finland, at Yilinen laboratories), while system level tests (SLTs) were conducted in a dedicated cryofacility at the Centre Spatiale de Li&egrave;ge (CSL) located in Liege, Belgium. <br />
<br />
In Table 1 below we list the temperature of the main cold thermal stages during ground tests compared to in-flight nominal values. These values show that system-level tests were conducted in conditions that were as flight-representative as possible, while results obtained during RCA and RAA tests need to be extrapolated to flight conditions to allow comparison. Details of the RCA test campaign are discussed in ({{PlanckPapers|villa2010}}), while the RAA tests and the extrapolation methods are presented in ({{PlanckPapers|mennella2010}}).<br />
<br />
{| border="1" cellspacing="0" cellpadding="2" align="center"<br />
|+ '''<small>Table 1. Temperatures of the main cold stages during the various ground test campaigns compared to in-flight nominal values.</small>'''<br />
|-<br />
!scope="col"| Temperature <br />
!scope="col"| Nominal<br />
!scope="col"| RCA tests<br />
!scope="col"| RAA tests<br />
!scope="col"| System-level<br />
|-<br />
|width="120" | Sky<br />
|width="100" | ~ 3 K<br />
|width="100" | ≳ 8 K<br />
|width="100" | ≳ 18.5 K<br />
|width="100" | ~ 4 K<br />
|-<br />
|width="120" | Ref. load<br />
|width="100" | ~ 4.5 K<br />
|width="100" | ≳ 8 K<br />
|width="100" | ≳ 18.5 K<br />
|width="100" | ~ 4.5 K<br />
|-<br />
|width="120" | Front-end unit<br />
|width="100" | ~ 20 K<br />
|width="100" | ~ 20 K<br />
|width="100" | ~ 26 K<br />
|width="100" | ~ 20 K<br />
|-<br />
|}<br />
<br />
During the various test campaigns the instrument was switched off and moved several times in a time period of about three years. A series of functional tests were always repeated at each location and also in-flight, in order to verify the instrument functionality and the response repeatability. No failures or major problems have been identified due to transport and integration procedures.<br />
<br />
The expected Planck LFI scientific performance, resulting mainly from cryogenic system level tests, are described in ({{PlanckPapers|mennella2010}}).<br />
<br />
== <span id="LFICalibration">In-flight Calibration</span>==<br />
<br />
The LFI Commissioning and Calibration and Performance Verification (CPV) phases started on 4 June 2009 and lasted until 12 August 2009 when Planck started scanning the sky in nominal mode. At the onset of CPV, the active cooling started when the radiating surfaces on the payload module reached their working temperatures (approximately 50 K on the third V-groove, and 40 K on the reflectors) by passive cooling. This was achieved during the transfer phase. Nominal temperatures were achieved on 3 July 2009, when the dilution cooler temperature reached 0.1 K ({{PlanckPapers|planck2011-1-3}}, Meinhold et al. 2009 {{BibCite| meinhold2009}}). The cooldown of the HFI 4-K stage (see Fig. 4 below), was key during CPV for the LFI, because it provided a variable input signal that was exploited during bias tuning.<br />
<br />
The LFI Commissioning and CPV was carried out in four phases: <br />
* LFI switch-on and basic functionality verification (Commissioning);<br />
* tuning of front-end biases and back-end electronics (CPV);<br />
* preliminary calibration tests (CPV);<br />
* thermal tests (CPV). <br />
<br />
[[File:FUNCT_tests_schedule_vs_K-eps-converted-to.jpg|thumb|center|460px|'''Figure 4. Functional tests performed during CPV against timeline. Curves from thermal sensors monitoring the 4-K stage and the FPU temperature are superimposed.''']]<br />
<br />
Details of the LFI Commissioning and CPV test campaign are given in (Gregorio et al. 2013{{BibCite|gregorio2013}}).<br />
<br />
==<span id="LFIPerformance">Performance Summary</span>==<br />
<br />
A summary of the LFI performance parameters is given in Table 1 of the section titled [[Summary LFI|Summary of LFI data characteristics]]. <br />
<br />
=== Instrument scientific performance ===<br />
<br />
==== ''Optical parameters''====<br />
<br />
The most accurate measurements of the LFI main beams were made with Jupiter, the most powerful unresolved (to Planck) celestial source in the LFI frequency range. Since the LFI feedhorns point to different positions on the sky, they detect the signal at different times. <br />
To map the beam, each sample in the selected timelines was projected in the (<i>u</i>, <i>v</i>) plane perpendicular to the nominal line-of-sight (LOS) of the telescope (and at 85&deg; to the satellite spin axis). The <i>u</i> and <i>v</i> coordinates are defined in terms of the usual spherical coordinates (&theta;, &phi;) :<br />
<br />
: <math> u = \sin θ \, \cos φ, </math> <br />
: <math> v = \sin θ \, \sin φ. </math> <br />
<br />
To increase the signal-to-noise ratio, data were binned in an angular region of 2′ for the 70 GHz channels and 4′ for the 30 and 44 GHz channels. We recovered all beams down to −25 dB from the peak. An elliptical Gaussian was fit to each beam for both M and S radiometers. Differences between the M and S beams caused by optics and receiver non-idealities are inevitable at some level, but they appear to be well within the statistical uncertainties, and for the purposes of point-source extraction, the beams may be considered identical. For the details of the typical FWHM and ellipticity averaged over each frequency channel, refer to ({{PlanckPapers|planck2011-1-4 }}) and ({{PlanckPapers|planck2014-a05||Planck-2015-A05}}). Exhaustive details on all LFI beam parameters are presented in the LFI data processing section entitled [[Beams LFI|Beams]].<br />
<br />
==== ''Photometric Calibration''====<br />
<br />
Photometric calibration, i.e., conversion from voltage to antenna temperature, is performed for each radiometer after total power data have been cleaned of 1 Hz frequency spikes (see the LFI data processing section [[TOI processing LFI#Spikes Removal|Spikes Removal]] page and ({{PlanckPapers|planck2011-1-6 }}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}})), and differenced. Here we report a brief overview of the photometric calibration; for details see the LFI data processing section [[TOI processing LFI#Photometric Calibration|Photometric Calibration]].<br />
<br />
Our calibrator is the well-known dipole signal induced by spacecraft motion with respect to the CMB rest frame. The largest calibration uncertainty comes from the presence of the Galaxy and of the CMB anisotropies in the measured signal. We therefore use an iterative calibration procedure in which the dipole is fitted and subtracted, producing a sky map that is then removed from the original data to enhance the dipole signal for the next iteration. Typically, convergence is obtained after a few tens of iterations.<br />
<br />
In our current calibration model we use as a calibration signal the sum of the solar dipole &Delta;T<sub>Sun</sub> and the orbital dipole &Delta;T<sub>orb</sub>, which is the contribution from Planck’s orbital velocity around the Sun,<br />
<br />
<math> \label{eq:cal1} \Delta T= ( \Delta T_{\rm Sun} + \Delta T_{\rm orb} ) \sin \theta_{\rm axis} </math>,<br />
<br />
where &theta;<sub>axis</sub> is the angle between the spacecraft axis and the overall dipole axis (solar + orbital).<br />
In this equation, the absolute calibration uncertainty is dominated by the uncertainty in the solar dipole, which is known to about 0.2%. The modulation of the orbital dipole by Earth's motion around the Sun is known with an uncertainty almost three orders of magnitude smaller; however, at least one complete Planck orbit is needed for its measurement. We employ the orbital dipole as an absolute calibration.<br />
The accuracy of our current calibration can be estimated by taking into account two components: 1) the statistical uncertainty in time periods when the dipole signal is weak; and 2) the systematic uncertainty caused by neglecting gain fluctuations that occur on periods shorter than the smoothing window. In our calibration procedure the gain is estimated for every pointing period; if we call <i>G<sub>i</sub></i> the gain estimate from the <i>i</i>th pointing period, we have that the associated uncertainty is<br />
<br />
<math> \label{eq:cal2} \delta G = \sqrt{\frac{ \Sigma_{i=1}^N (G_i-< G>)^2 }{N-1} } </math>,<br />
<br />
where <i>N</i> is the overall number of pointing and <<i>G</i>> is the average of the <i>N</i> gains.<br />
We then approximate the effect of the smoothing filter as an average over <i>M</i> consecutive pointings, so that the overall uncertainty can be estimated as<br />
<br />
<math> \label{eq:cal3} \delta G |_{\rm stat} = \frac{\delta G}{\sqrt{M}} = \frac{1}{\sqrt{M}} <br />
\sqrt{\frac{ \Sigma_{i=1}^N (G_i-< G>)^2 }{N-1} } </math>.<br />
<br />
==== ''Noise Properties''====<br />
<br />
The noise characteristics of the LFI data streams are closely reproduced by a simple (white + 1/<i>f</i> ) noise model,<br />
<br />
<math> \label{eq:p1} P(f)= \sigma^2 \left[1+ \left(\frac{f}{f_{\rm knee}}\right)^\alpha \right] </math>,<br />
<br />
where <i>P</i>(<i>f</i>) is the power spectrum and &alpha;&asymp;−1.<br />
In this model, noise properties are characterized by three parameters, the white noise limit &sigma;, the knee frequency <i>f</i><sub>knee</sub>, and the exponent of the 1/<i>f</i> component &alpha;, also referred to as the slope. Here we give noise performance estimates based on one year of operations; details of the analysis are given in LFI data processing section ([[TOI processing LFI#Noise|Noise estimation]]) and in <br />
({{PlanckPapers|planck2011-1-6}}, {{PlanckPapers|planck2011-1-4 }}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}).<br />
<br />
Noise properties have been calculated following two different and complementary approaches: 1) fitting the equation above to time-ordered data for each radiometer; and 2) building normalized noise maps by differencing data from the first half of each pointing period with data from the second half of that pointing period to remove the sky signal (“jackknife” data sets).<br />
<br />
Typical uncertainties are 0.5% for the white noise, between 5 and 10% for the slope, and between 10 and 20% for the knee frequency.<br />
<br />
==== ''White Noise Sensitivity''====<br />
<br />
Details of the white noise sensitivity can be found in ({{PlanckPapers|planck2011-1-4}}). <br />
<br />
Table 2 summarizes the sensitivity numbers calculated during the first year of operations using methods and procedures described in detail in ({{PlanckPapers|planck2011-1-6}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}), compared with scientific requirements. The measured sensitivity is in very good agreement with pre-launch expectations. While the white noise moderately exceeds the design specification, this performance is fully in line with the LFI science objectives.<br />
<br />
{| border="1" cellspacing="0" cellpadding="2" align="center"<br />
|+ '''<small>Table 2. White noise sensitivity of the LFI frequency channels compared with requirements.</small>'''<br />
|-<br />
!scope="col"| Channel <br />
!scope="col"| Measurement [&mu;K<sub>CMB</sub> s<sup>1/2</sup>]<br />
!scope="col"| Requirement [&mu;K<sub>CMB</sub> s<sup>1/2</sup>]<br />
|-<br />
|width="120" | 70 GHz<br />
|width="100" | 152.0<br />
|width="100" | 119<br />
|-<br />
|width="120" | 44 GHz<br />
|width="100" | 174.2<br />
|width="100" | 119<br />
|-<br />
|width="120" | 30 GHz<br />
|width="100" | 148.1<br />
|width="100" | 119<br />
|-<br />
|}<br />
<br />
=== Instrument technical performance ===<br />
<br />
<br />
==== ''Spectral response''====<br />
<br />
The in-band receiver response was thoroughly modelled and measured for all the LFI detectors during ground tests. The complete set of bandpass curves was published in (Zonca et al. 2009{{BibCite|zonca2009}}, {{PlanckPapers|planck2014-a06||Planck-2015-A06}}) where all the details of the LFI radiometer's spectral response are given. From each curve we have derived the effective centre frequency according to:<br />
<br />
<math> \label{eq:spectr} <br />
\nu_0 = \frac{ \int_{\nu_{\rm min}}^{\nu_{\rm max}} \nu g(\nu) \; d \nu}<br />
{\int_{\nu_{\rm min}}^{\nu_{\rm max}} g(\nu)\; d\nu }<br />
</math> <br />
<br />
where &Delta;&nu; = &nu;<sub>max</sub> − &nu;<sub>min</sub> is the receiver bandwidth and <i>g</i>(&nu;) is the bandpass response. <br />
Details about colour corrections, <i>C</i>(&alpha;), needed to derive the brightness temperature of a source with a power-law spectral index &alpha;, are provided in <br />
<br />
Some details are also given in the corresponding section of the [[LFIAppendix#Spectral Response|Annexes]].<br />
<br />
<br />
===== ''Bandpass estimation''=====<br />
<br />
As detailed in (Zonca et al. 2009{{BibCite|zonca2009}}, {{PlanckPapers|planck2014-a06||Planck-2015-A06}}), our most accurate method to measure the LFI bandpasses is based on measurements of individual components integrated into the LFI Advanced RF Model (LARFM) to yield a synthesized radiometer bandpass.<br />
The LARFM is a software tool based on the open-source Quasi Universal Circuit Simulator (QUCS). The measured frequency responses of the various subsystems (feed-OMT, FEM, BEM) are considered as lumped S-parameter components. <br />
Measurements of single components are obtained with standard methods and provide highly reliable results, with precision of order 0.1-0.2 dB over the entire band.<br />
Waveguides are simulated with an analytical model, in order to reproduce the effect of their temperature gradient and the effect of standing waves caused by impedance mismatch at the interfaces between the FEM and BEM. This is because the 1.8-m long waveguides were not measured at unit level in cryogenic conditions. The model provides accurate agreement with the measured waveguide response in the conditions of the test measurements (300 K).<br />
The composite bandpasses are estimated to have a precision of about 1.5 to 2 dB.<br />
<br />
Some details are also given in the corresponding section of the [[LFIAppendix#Bandpass Estimation|Annexes]].<br />
<br />
==== ''Stability''====<br />
<br />
Thanks to its differential scheme, the LFI is insensitive to many effects caused by 1/<i>f</i> noise, thermal fluctuations, or electrical instabilities.<br />
As detailed in ({{PlanckPapers|planck2011-1-4}}), one effect detected during the first survey was the daily temperature fluctuation in the back-end unit induced by the downlink transponder, which was powered on each day for downlinks during the first 258 days of the mission. As expected, the effect is highly correlated between the sky and reference load signals. In the difference, the variation is reduced by a factor around (1 − <i>r</i>), where <i>r</i> is the gain modulation factor defined above (see <i>r</i> definition in [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section).<br />
<br />
A particular class of signal fluctuations occasionally observed during operations was due to electrical instabilities that appeared as abrupt increases in the measured drain current of the front-end amplifiers, with a relaxation time variable from few seconds to some hundreds of seconds. Typically, these events caused a simultaneous change in the sky and reference load signals. Because they are essentially common-mode, their residual on the differenced data is negligible, and the data are suitable for science production. In a few cases the residual fluctuation in the differential output was large enough (a few millikelvin in calibrated antenna temperature units) to be flagged, and the data were not used. The total amount of discarded data for all LFI channels until Operational Day 389 was about 2000s per detector, or 0.008%.<br />
<br />
A further peculiar effect appeared in the 44 GHz detectors, where single isolated samples, either on the sky or the reference voltage output, were clear outliers compared with the rest. Over a reference period of four months, 15 occurrences of single-sample spikes (out of 24 total anomaly events) were discarded, an insignificant loss of data.<br />
<br />
==== ''Thermal susceptibility''====<br />
<br />
As mentioned in the section [[LFI design, qualification, and performance#LFI In-flight Calibration|LFI In-flight Calibration]] above, and detailed in (Gregorio et al. 2013{{BibCite|gregorio2013}}), during the CPV campaign, susceptibility tests were performed in order to characterize the LFI instrument susceptibility to thermal and electrical variations.<br />
<br />
The effect of temperature fluctuations on the LFI radiometers originates in the Planck cold end interface of the hydrogen sorption cooler to the instrument focal plane. The temperature is actively controlled through a dedicated stage, the Thermal Stabilization Assembly (TSA), providing a first reduction of the effect. The thermal mass of the focal plane strongly contributes to reduce residual fluctuations.<br />
The physical temperature fluctuations propagated at the front end modules cause a correlated fluctuation in the radiometer signal, degrading the quality of scientific data. The accurate characterization of this effect is crucial for attempts to remove it from raw data by exploiting the housekeeping information on thermal sensors.<br />
<br />
The propagation of the temperature oscillations through the focal plane and the instrument response to thermal changes were characterized through two main tests: <br />
* the thermal dynamic response, aimed at measuring the dynamic thermal behaviour of the LFI Focal Plane;<br />
* the thermal susceptibility of the radiometers.<br />
<br />
Further details are also given in the corresponding section of the [[LFIAppendix#Thermal Susceptibility|Annexes]].<br />
<br />
==== Instrument budgets ====<br />
<br />
LFI power, mass and telemetry budgets are given in the corresponding section of the [[LFIAppendix#Instrument Budgets|Annexes]].<br />
<br />
== <span id="LFISystematics">Systematic Effects </span>==<br />
<br />
The LFI design was driven by the need to suppress systematic effects well below instrument white noise. The differential receiver scheme, with reference loads cooled to 4 K, greatly minimizes the effect of 1/<i>f</i> noise and common-mode fluctuations, such as thermal perturbations in the 20-K LFI focal plane. The use of a gain modulation factor (see <i>r</i> definition in the [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section above) largely compensates for spurious contributions from input offsets. Furthermore, diode averaging (see <i>V</i><sup>rad</sup><sub>out</sub> definition in the [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section above) allows us to cancel second-order correlations, such as those originating from phase switch imbalances.<br />
<br />
We have developed an error budget for systematic effects ({{PlanckPapers|bersanelli2010}}, {{PlanckPapers|planck2011-1-4}}{{PlanckPapers|planck2013-p02a}} and {{PlanckPapers|planck2014-a04||Planck-2015-A04}}) as a reference for both instrument design and data analysis. Our goal is to ensure that each systematic effect is rejected to the specified level, either by design or by robust removal in software. At this stage, the following effects are relevant:<br />
<br />
[[File:Selection_258.png|500px]]<br />
<br />
For each of these effects we used flight data and information from ground tests to build timelines, maps, and angular power spectra that represent our best knowledge of their impact on the scientific analysis.<br />
The details of the systematic effect analysis are given in the section entitled LFI data processing section ([[LFI systematic effect uncertainties|Systematic Effects uncertainties]]).<br />
<br />
== <span id="SCS">The Sorption Cooler</span> ==<br />
The Planck H2 Sorption Cooler is the first stage of the active cryogenic chain. Its task is to maintain the LFI down to the operating temperature while providing a pre-cooling stage for the HFI refrigerators. The system performs a simple thermodynamic cycle based on hydrogen compression, gas pre-cooling by three passive radiators, further cooling due to the heat recovery by the cold low pressure gas stream, expansion through a J-T valve, and evaporation at the cold stage ({{PlanckPapers|planck2011-1-3}}). A schematic of the Planck Sorption Cooler System (SCS) is shown in Fig. 5. The engine of the cryocooler is the compressor. It serves two main functions: to produce the high-pressure hydrogen gas flow; and to maintain a stable gas recovery rate, which keeps the return pressure, hence the liquid temperature, constant. The high pressure gas flowing to the cold end is pre-cooled by exchanging heat with the three passive stages at the V-Grooves and with the evaporated cold gas returning back to the compressor. The gas then expands at the cold end through a J-T valve, producing approximately 1 Watt of cooling power at a temperature of <20K: most of this heat lift is used at the LVHX2 (Liquid Vapour Heat eXchanger 2, see Fig. 5) interface to absorb the LFI heat load at a temperature around 20K. The remaining heat lift is used at the LVHX1 as a pre-cooling stage, at a temperature lower than 19 K, for the two HFI refrigerators. The cooler and its performance are described in detail in (Morgante et al. 2009{{BibCite|morgante2009}}). <br />
<br />
[[File:SCS_CAD_Figure.jpg|thumb|center|480px|'''Figure 5. Planck Sorption Cooler CAD view with labels of the main sub-systems.''']]<br />
<br />
Both LVHXs provide a temperature of around 18 K, with fluctuations driven by the cooler instabilities (compressor element variations, cycling, two-phase flow dynamics, etc.). Stabilization of the HFI interface (LVHX1) temperature is not necessary, since thermal control of the subsequent colder stages is more efficient and very effective. To reduce cold end fluctuations directly transmitted to the LFI radiometers, a copper block, designated as the Temperature Stabilization Assembly (TSA), is inserted, as an intermediate stage, between LVHX2 and the LFI Focal Plane Unit (FPU). The TSA comprises a temperature sensor and a heater, controlled by a PID-type feedback loop, working in combination with the passive thermal inertia. The set-point temperature of the TSA is an adjustable parameter of the sorption cooler system, chosen to provide dynamic range for control during mission: as the compressor elements age, the return gas pressure and thus the temperature of LVHX2 rise slowly. To keep the LFI temperature reference stable during operations the set point must be periodically adjusted to maintain the level of oscillations within the required range (Fig. 6).<br />
<br />
[[File:TSA_LVHX2_mission.jpg|thumb|center|480px|'''Figure 6. LVHX2 (black, HK parameter name SD029540) and TSA (red, HK parameter name SD030540) temperature profile from 125 to 563 days after launch.''']]<br />
<br />
Two sorption cooler units were integrated on-board the Planck spacecraft. Both units were used to cover the mission lifetime, with one cooler operated for the first two sky surveys. At the end of its lifetime a switchover operation, performed on August 11th 2010 (455 days after launch), activated the second unit that ran since then. The LVHX2 temperature change due to the new cooler start, and the subsequent re-adjustment of the LFI temperature stabilization stage, is clear in Fig. 6.<br />
<br />
<!--<br />
== Acronyms ==<br />
<br />
: ADC Analog-to-Digital Converter<br />
: ADU Analog-to-Digital Unit<br />
: BEM Back End Module <br />
: BEU Back End Unit <br />
: CCE Central Check-out Equipment<br />
: CDMS Command and Data Management Subsystem<br />
: CDMU Central Data Management Unit<br />
: CoG Centre of Gravity<br />
: CPV Calibration and Performance Verification<br />
: CSL Centre Spatiale de Liege<br />
: DAE Data Acquisition Electronics <br />
: DC Direct Current<br />
: DPC Data Processing Centre<br />
: DPU Digital Processing Unit<br />
: EMC Electro-Magnetic Compatibility<br />
: EMI Electro-Magnetic Interference<br />
: FEM Front End Module <br />
: FEU Front End Unit<br />
: FH Feed Horn<br />
: FOV Field Of View<br />
: FPU Focal Plane Unit<br />
: HK House Keeping<br />
: ILT Instrument Level Test<br />
: IST Integrated System Test<br />
: JFET Junction Field Effect Transistor<br />
: LEOP Launch and Early Orbit Phase<br />
: MLI Multilayer Insulation<br />
: MoI Moment of Inertia<br />
: MOS Margin Of Safety<br />
: OMT Ortho Module Transducer <br />
: PCS Power Control Subsystem<br />
: PSF Point Spread Function<br />
: RAA Radiometer Array Assembly <br />
: RAM Random Access Memory<br />
: RCA Radiometer Chain Assembly <br />
: REBA Radiometer Electronics Box Assembly <br />
: S/C Spacecraft<br />
: SCC Sorption Cooler Compressor assembly <br />
: SCCE Sorption Cooler Cold End <br />
: SCE Sorption Cooler Electronics <br />
: SCOS Spacecraft Control and Operations System<br />
: SCP Sorption Cooler Piping <br />
: SCS Sorption Cooler Subsystem <br />
: SLT System Level Test<br />
: SPU Signal Processing Unit<br />
: SS Stainless Steel<br />
: SVM Service Module<br />
: TCS Thermal Control System<br />
: TM Telemetry<br />
: TSA Thermal Stabilization Assembly<br />
: TTC Telemetry, Tracking and Command<br />
: VSWR Voltage Standing Wave Ratio <br />
: WG Waveguide<br />
<br />
== Glossary ==<br />
<br />
: Feed Horns xxx <br />
: REBA Radiometer Electronics Box Assembly<br />
--><br />
<br />
== References ==<br />
<br />
<References /><br />
<br />
<br />
[[Category:LFI design, qualification and performance|001]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=LFI_design,_qualification,_and_performance&diff=11317LFI design, qualification, and performance2015-02-04T21:26:16Z<p>Agregori: /* Operational Modes */</p>
<hr />
<div>==<span id="LFIDescription">Instrument description</span>==<br />
The Low-Frequency Instrument (see Fig. 1 in the [[LFI overview]]) consists of a 20 K focal plane unit hosting the corrugated feed horns, the orthomode transducers (OMTs) and the receiver front-end modules (FEMs). Forty-four composite waveguides {{BibCite|darcangelo2009a}} are interfaced with three conical thermal shields and connect the front-end modules to the warm (roughly 300 K) back-end unit (BEU) containing a further radio frequency amplification stage, detector diodes, and all the electronics for data acquisition and bias supply. <br />
<br />
Best LFI noise performance is obtained with receivers based on InP High Electron Mobility Transistor (HEMT) low noise amplifiers (LNAs) for minimal power dissipation and best performance. To further minimize power consumption in the focal plane, the radiometers are split into two sub-assemblies connected by waveguides, one located at the telescope focal area, the other on the 300 K portion of the Planck satellite. These design features allow the entire front-end LNA dissipation to be <0.55 W, which enables the active cooling of the focal assembly. This is achieved with a vibration-less hydrogen sorption cooler, which also provides 18 K pre-cooling to the HFI helium J-T cooler. Two sorption cooler units are included in the flight hardware.<br />
<br />
As shown schematically in Fig. 1 below, the LFI consists of the following subsystems:<br />
* Radiometer Array Assembly (RAA);<br />
* Sorption Cooler Subsystem (SCS);<br />
* Radiometer Electronics Box Assembly (REBA).<br />
<br />
The RAA includes the Front End Unit (FEU) and the Back End Unit (BEU), connected via waveguides. The FEU is located at the focus of the telescope, as one component of the joint LFI/HFI focal assembly (see sections below). The BEU is mounted on the top of the Planck service module (SVM).<br />
The REBA (Radiometer Electronics Box Assembly) and the warm parts of the Sorption Cooler System (SCS) are located on one of the lateral panels of the SVM. The FEU and the Sorption Cooler Compressor (SCC) are connected by concentric stainless steel tubes. The smaller tube carries hydrogen at approximately 60 atmospheres from the cooler compressors to the FEU, while the larger tube returns the hydrogen at about 0.3 atmospheres. These units are described in following sections and in the [[LFIAppendix|Annexes]], while the SCS is described in details in the [[LFI design, qualification, and performance#The Sorption Cooler|Sorption Cooler]] section.<br />
All LFI units are linked together by the LFI harness, which also connects to the spacecraft interface.<br />
<br />
[[File:schema.jpg|thumb|center|500px|'''Figure 1. Block Diagram of LFI.''']]<br />
<br />
=== ''Radiometer Array Assembly (RAA)'' ===<br />
<br />
The Radiometer Array Assembly (RAA) consists of two main units (the front end unit, FPU and the Back End Unit, BEU), connected by a set of waveguides.<br />
The Focal Plane Unit (FPU) is the heart of the LFI instrument; it contains the feed array and associated orthomode transducers (OMTs) and FEMs, all cooled to 20 K by the sorption cooler. The FPU comprises a set of 11 modules, which are mounted on a mechanical support which meets the thermo-mechanical requirements of the instrument and adds thermal inertia.<br />
The BEU comprises the radiometer Back End Modules (BEM) and the Data Acquisition Electronics (DAE), which are connected by an internal harness.<br />
The HFI Unit is located inside the LFI FPU and supported by the LFI structure. The LFI structure gives the mechanical and thermal interface to the HFI unit with the proper stiffness and thermal de-coupling. The LFI structure also guarantees the proper alignment of the HFI detector with the telescope focal plane.<br />
<br />
The timescale of the stability of the receiverS is driven by the 1 rpm rotation speed of the spacecraft, which requires a very low 1/<i>f</i>-noise or gain variation of the low noise amplifiers and other components.<br />
The LFI uses a pseudo-correlation receiver concept (Fig. 2 below). This radiometer concept is chosen to maximize the stability of the instrument by reducing the effect of non-white noise generated in the radiometer itself. In this scheme, the difference between the inputs to each of the chains (the signal from the telescope and that from a reference blackbody, respectively) is continuously being observed. To remove the effect of instability in the back-end amplifiers and detector diodes, it is necessary to switch the signal detected at the diodes at a high rate.<br />
The signals from the sky and from a reference load are combined by a hybrid coupler, amplified in two independent amplifier chains, and separated out by another hybrid. The sky and the reference load power can then be measured and differenced. Since the reference signal has been subject to the same gain variations in the two amplifier chains as the sky signal, the true sky power can be recovered.<br />
The differencing receiver greatly improves the stability if the two input signals are almost equal, at<br />
a cost of a factor of &radic;2 in sensitivity, compared to a perfectly stable total-power radiometer with the same noise temperature and bandwidth. This radiometer concept is also capable of greatly reducing the knee frequency.<br />
A single Radiometer Chain Assembly (RCA; see Fig. 2) consists of each functional unit from the feed horn to the BEM. The RAA therefore includes a set of 11 RCAs and the Data Acquisition Electronics (see also Fig. 1 above), all mounted on a suitable mechanical structure. Although there are differences in the details of the radiometer chains at different frequencies, their overall configuration is similar, and a general description of their design is provided in this section.<br />
Planck LFI has 11 Radiometer Chain Assemblies (RCAs). Each RCA is constituted by a feed horn and FEM in the FEU (at 20 K), BEM (at 300 K) in the BEU, and four waveguides that connect each FEM-BEM couple. The frequency distribution of the RCA is the following:<br />
* 2 RCAs at 30 GHz;<br />
* 3 RCAs at 44 GHz;<br />
* 6 RCAs at 70 GHz.<br />
<br />
[[File:rca_schematic.jpg|thumb|center|640px|'''Figure 2. A complete RCA from feed-horn to analogue voltage output. The insets show the OMT, the details of the 20 K pseudo-correlator and of the back-end radio-frequency amplification, low-pass filtering, detection, and DC amplification.''']]<br />
<br />
==== ''Radiometer Chain Assembly (RCA)''====<br />
<br />
Every RCA consists of two radiometers, each feeding two diode detectors (see Fig. 2 above), for a total of 44 detectors. The 11 RCAs are labelled by a number from 18 to 28, as outlined in Fig. 1 of the [[LFI overview]], right panel.<br />
<br />
Fig. 2 provides a more detailed description of each radiometric receiver. In each RCA, the two perpendicular linear polarization components split by the OMT propagate through two independent pseudo-correlation differential radiometers, labelled as ''M'' or ''S,'' depending on the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2).<br />
<br />
In each radiometer the sky signal coming from the OMT output is continuously compared with a stable 4 K blackbody reference load mounted on the external shield of the HFI 4-K box (Valenziano et al. 2009{{BibCite|valenziano2009}}). After being summed by a first hybrid coupler, the two signals are amplified by approximately 30 dB (see upper-left inset of Fig. 2). The amplifiers were selected for best operation at low drain voltages and for gain and phase match between paired radiometer legs, which is crucial for good balance. Each amplifier is labelled with codes ''1'' or ''2'' so that the four outputs of the LNAs can be named with the sequence: ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). <br />
Tight mass and power constraints called for a simple design of the Data Acquisition Electronics (DAE) box so that power bias lines were divided into five common-grounded power groups with no bias voltage readouts; only the total drain current flowing through the front-end amplifiers is measured and is available to the house-keeping telemetry (this design has important implications for front-end bias tuning, which depends critically on the satellite electrical and thermal configuration and was repeated at all integration stages during on-ground and in-flight satellite tests).<br />
A phase shift (or phase switch) alternating between 0&deg; and 180&deg; at the frequency of 4096 Hz is applied in one of the two amplification chains and then a second hybrid coupler restores the sky and reference load components, which are further amplified and detected in the warm BEU, with a voltage output ranging from -2.5 V to +2.5 V.<br />
<br />
Each radiometer has two output diodes which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence ''M-00'', ''M-01'', ''S-10'', ''S-11''.<br />
<br />
After detection, an analogue circuit in the DAE box removes a programmable offset in order to obtain a nearly null DC output voltage and a programmable gain is applied to increase the signal dynamics and optimally exploit the ADC input range. After the ADC, data are digitally down-sampled, re-quantized and compressed in the REBA according to a scheme described in (Herreros et al. 2009{{BibCite|herreros2009}}, Maris et al. 2009{{BibCite|maris2009}}), before being combined in telemetry packets. On the ground, telemetry packets are converted to time ordered data for both the sky and reference load, after calibrating the ADU (Analog-to-Digital Unit) samples into volts. The calibration takes into account the applied offset and gain factors.<br />
<br />
To first order, the mean differential power output for each of the four receiver diodes can be written as follows (Seiffert et al. 2002{{BibCite|seiffert2002}}, Mennella et al. 2003{{BibCite|mennella2003}}, {{PlanckPapers|bersanelli2010}}):<br />
<br />
<math> \label{eq:power}<br />
P_{\rm out}^{\rm diode} = a\, G_{\rm tot}\,k\,\beta \left[ T_{\rm sky} + T_{\rm noise} - r\left(<br />
T_{\rm ref} + T_{\rm noise}\right) \right]<br />
</math><br />
<br />
where <i>G</i><sub>tot</sub> is the total gain, <i>k</i> is the Boltzmann constant, <i>&beta;</i> the receiver bandwidth, and <i>a</i> is the diode constant. <i>T</i><sub>sky</sub> and <i>T</i><sub>ref</sub> are the average sky and reference load antenna temperatures at the inputs of the first hybrid and <i>T</i><sub>noise</sub> is the receiver noise temperature.<br />
<br />
The gain modulation factor (Mennella et al. 2003{{BibCite|mennella2003}}, {{PlanckPapers|planck2011-1-6 }}), <i>r</i>, is defined by<br />
<br />
<math> \label{eq:erre1} <br />
r = \frac{T_{\rm sky} + T_{\rm noise}}{T_{\rm ref} + T_{\rm noise}} ,<br />
</math><br />
<br />
and is used to balance (in software) the temperature offset between the sky and reference load signals and minimize the residual 1/<i>f</i> noise in the differential data stream. This parameter is calculated from the average uncalibrated total power data using the relationship<br />
<br />
<math> \label{eq:erre2}<br />
r = \langle V_{\rm sky} \rangle/ \langle V_{\rm ref}\rangle,<br />
</math><br />
<br />
where <<i>V</i><sub>sky</sub>> and <<i>V</i><sub>ref</sub>> are the average sky and reference voltages calculated in a defined time range.<br />
The white noise spectral density at the output of each diode is essentially independent of the reference-load absolute temperature and is given by<br />
<br />
<math> \label{eq:dt1}<br />
\Delta T_0^{\rm diode} = \frac{2\,(T_{\rm sky}+T_{\rm noise})}{\sqrt{\beta}}.<br />
</math><br />
<br />
If the front-end components are not perfectly balanced, then the separation of the sky and reference load signals after the second hybrid is not perfect and the outputs are mixed. First-order deviations in white noise sensitivity from the ideal behaviour are caused mainly by noise temperature and phase-switch amplitude mismatches. Following the notation used in (Seiffert et al. 2002 {{BibCite|seiffert2002}}), we define &epsilon;<sub><i>T</i><sub>n</sub></sub>, as the imbalance in front end noise temperature, and &epsilon;<sub><i>A</i><sub>1</sub></sub> and &epsilon;<sub><i>A</i><sub>2</sub></sub>, the imbalance in signal attenuation in the two states of the phase switch. Equation above for the two diodes of a slightly imbalanced radiometer then becomes<br />
<br />
<math> \label{eq:dt2} (\Delta T^{\rm diode} )^2 ≈ (\Delta T_0^{\rm diode})^2 ( 1± \frac{\epsilon_{A1}- \epsilon_{A2}}{2} <br />
+ \alpha \epsilon_{T{\rm n}}),<br />
</math><br />
<br />
which is identical for the two diodes apart from the sign of the term &epsilon;<sub><i>A</i><sub>1</sub></sub> − &epsilon;<sub><i>A</i><sub>2</sub></sub>, representing the phase switch amplitude imbalance. This indicates that the isolation loss caused by this imbalance generates an anti-correlation between the white noise levels of the single-diode data streams.<br />
For this reason, the LFI scientific data streams are obtained by averaging the voltage outputs from the two diodes in each radiometer:<br />
<br />
<math> \label{eq:v1} <br />
V^{\rm rad}_{\rm out} = w_1 V^{\rm diode\,1}_{\rm out} +w_2 V^{\rm diode\,2}_{\rm out} </math>,<br />
<br />
where &omega;<sub>1</sub> and &omega;<sub>2</sub> are inverse-variance weights calculated from the data as discussed in ({{PlanckPapers|planck2011-1-6}}). This way, the diode-diode anti-correlation is cancelled, and the radiometer white noise becomes<br />
<br />
<math> \label{eq:dt3}<br />
\Delta T^{\rm rad} ≈ \frac{ T_0^{\rm diode}}{\sqrt{2}} (1+\alpha \epsilon_{T{\rm n}})^{1/2}.<br />
</math><br />
<br />
In the equations above, &epsilon;&laquo;1, while &alpha; (a term &asymp;1) is given by<br />
<br />
<math> \label{eq:alpha} <br />
\alpha = \frac{ T_{\rm noise} (2 \; T_{\rm noise} + T_{\rm sky} + T_{\rm ref} }<br />
{2 (T_{\rm sky} + T_{\rm noise} )(T_{\rm ref} + T_{\rm noise})}.<br />
</math><br />
<br />
See the [[TOI processing LFI|Diode Combination]] section for the details of the diode combination procedure. <br />
<br />
In Fig. 3 below we show a close-up of the two front end modules of an RCA with the four phase switches, which are labelled with the four letters ''A'' and ''B'' (main arm), and ''C'' and ''D'' (side arm). Each phase switch is characterized by two states: state 0 (no phase shift applied to the incoming wave); and state 1 (180&deg; phase shift applied) and can either stay fixed in a state or switch at 4 kHz between the two states.<br />
<br />
Phase switches are clocked and biased by the DAE and their configuration can be programmed via telecommand. In order to simplify the instrument electronics, phase switches are configured and operated in pairs, by convention they are labelled ''A/C'' (corresponding to the first LNA both of main and side arm) and ''B/D'' (corresponding to the second LNA both of main and side arm). This means that if phase switches ''A'' and ''C'' are switching at 4 kHz then ''B'' and ''D'' are fixed, both in the same state (either 0 or 1); and viceversa. This simplification, required during the design phase to comply with mass and power budgets, comes at the price of losing some setup redundancy.<br />
<br />
[[File:phase_switch_operation.jpg|thumb|center|460px|'''Figure 3. Close-up of the two front-end modules of an RCA. There are four phase switches, labelled A, B, C, and D. Each switch can be fixed in one of its two positions (labelled as 0, 1) or switched at 4 kHz between 0 and 1. Phase switches are clocked and biased by the DAE in pairs: A/C and B/D.''']]<br />
<br />
==== ''Feed Horns (FHs)''====<br />
<br />
Dual profiled corrugated horns have been selected at all LFI frequencies as the best design in terms of the shape of the main lobe, level of the side lobes, control of the phase centre, and compactness. <br />
Details of the design, flight model and tests of Planck-LFI feed horns can be found in (Villa et al. 2009{{BibCite|villa2009}}) and in the corresponding [[LFIAppendix#Feed Horns (FH)|Annex]] section.<br />
<br />
==== ''Ortho-Mode Transducers (OMTs)''====<br />
<br />
The Ortho–Mode Transducer (OMTs) separates the radiation collected by the feedhorn into two orthogonal polarization components. It consists of a circular to square waveguide transition (directly connected to the FH), a square waveguide section and two separate rectangular waveguides (the main and side arms, which separate and pick up the orthogonal polarizations, connected with the FEU). A 90&deg; bend is always present on the side arm, while a twist is also necessary on the main (30 and 44 GHz) and side (70 GHz) arms, in order to match the FEU polarization.<br />
<br />
The details of the flight models and measurements of the Planck LFI ortho-mode transducers can be found in (D'Arcangelo et al. 2009{{BibCite|darcangelo2009b}}) and in the corresponding [[LFIAppendix#OrthoMode Transducers (OMT)|Annex]] section.<br />
<br />
==== ''Front End Modules (FEMs)''====<br />
<br />
Front End Modules are located in the FPU, just behind the Feed Horn and the Ortho Mode Transducers. The 70 GHz FEMs are mounted onto the inner wall of the main frame (the wall facing HFI instrument) from the HFI side. The 44 and 30 GHz FEMs are inserted into the main frame from the waveguide (WG) side and fixed to the bottom plate. Screws to the bottom plate are inserted from the WG side.<br />
The LFI FEMs are the first active stage of amplification of the radiometer chain. Each FEM contains four amplification paths, each of which is composed of several cascaded LNAs followed by a phase switch. Two passive hybrids, at the input and output of the FEM, are used to mix pairs of signals of the same radiometer (see Fig. 3). This cuases the instabilities of each chain to be applied to both the sky and load signals.<br />
<br />
The passive hybrid coupler ("magic-tee") combines the signals from the sky and cold load with a fixed phase offset of either 90&deg; or 180&deg; between them. It has a 20% bandwidth, low loss, and amplitude balance needed at the output to ensure adequate signal isolation.<br />
<br />
The details of the design, development and verification of the 70 GHz front-end modules for the Planck Low Frequency Instrument can be found in (Varis et al. 2009{{BibCite|varis2009}}) and in the corresponding [[LFIAppendix#Front End Modules (FEM)|Annex]] section.<br />
<br />
==== ''Waveguides (WGs)''====<br />
<br />
The LFI Front End Unit (FEU) is connected to the Back End Unit (BEU) by 44 rectangular waveguides approximately 1.5-2.0 m long. Each waveguide exhibits a low voltage standing wave ratio, low thermal conductivity, low insertion loss, and low mass. In addition, the waveguide path permits the LFI/HFI integration and the electrical bonding between the FPU and the BEU. Because of the Focal Plane Unit arrangement, the waveguides are in general twisted and bent in different planes and with different angles, depending on the particular waveguide. From the thermal point of view the waveguides have to connect two systems (the BEM and FEM) that are at very different temperatures. At BEM level the waveguides are at a temperature of 300 K, while at FEM level the temperature is 20 K. The waveguides have to reduce the thermal flow from 300 K to 20 K. In Fig. 1 in the [[LFI overview]] (left panel) a conceptual sketch of the LFI configuration is shown. <br />
<br />
Details of the Planck-LFI flight model of the composite waveguides can be found in (D'Arcangelo et al. 2009{{BibCite|darcangelo2009a}}) and in the corresponding [[LFIAppendix#Waveguides|Annex]] section.<br />
<br />
==== ''Back End Modules (BEMs)''====<br />
<br />
The BEMs are composed of four identical channels each made of Low Noise Amplifiers (LNAs), an RF bandpass Filter, RF to DC diode detector, and DC amplifiers.<br />
The FEM output signals are connected by waveguides from the Focal Plane Unit (FPU) assembly to the Back End Modules (BEMs) housed adjacent to the Data Acquisition Electronics (DAE) assembly. To maintain compatibility with the FEMs, each BEM accommodates four receiver channels from the four waveguide outputs of each FEM. The BEM internal signal routes are not cross-coupled and can be regarded as four identical parallel circuits.<br />
Each BEM is constructed as two mirror halves. The two amplifier/detector assemblies each contain two amplifier/detector circuits. Each is supplied from one of a pair of printed circuit boards, which also house two DC output amplifiers.<br />
<br />
The details of the design, development and verification of the 30 and 44 GHz back-end modules for the Planck Low Frequency Instrument can be found in (Artal et al. 2009{{BibCite|artal2009}}). <br />
Details of the design, development and verification of the 70 GHz back-end modules for the Planck Low Frequency Instrument can be found in (Varis et al. 2009{{BibCite|varis2009}}).<br />
Details are also reported in the corresponding [[LFIAppendix#Back End Modules (BEM)|Annex]] section.<br />
<br />
==== ''4K Load'' ====<br />
<br />
The purpose of the 4K reference load is to provide the radiometer with a stable reference signal. Reducing the input offset (the radiometric temperature difference between the sky and the reference load) reduces the minimum achievable radiometer 1/<i>f</i> noise knee frequency for a given amplifier fluctuation spectrum. A reference load temperature that matches the sky temperature (approximately 2.7 K) would be ideal. <br />
<br />
Details of the design, characteristics, and performance of the LFI 4-K reference load units are given in (Valenziano et al. 2009{{BibCite|valenziano2009}}) and in the corresponding section of the [[LFIAppendix#4K Load|Annexes]].<br />
<br />
=== Naming Convention ===<br />
<br />
The naming of all the LFI elements has been described in the previous sections, but here is summarized again for clarity. <br />
<br />
The 11 RCAs are labelled by numbers from 18 to 28, as outlined in Fig. 1 in the [[LFI overview]] (right panel). In each RCA, the two perpendicular linear polarization components are labelled as ''M'' or ''S'' according to the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2). <br />
<br />
Each front-end amplifier (see upper-left inset of Fig. 2) is labelled with the codes ''1'', ''2'', so that the four outputs of the FEM LNAs can be named with the sequence ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). <br />
<br />
Each radiometer has two output diodes (see upper-right inset of Fig. 2), which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence ''M-00'', ''M-01'', ''S-10'', and ''S-11''.<br />
<br />
=== ''REBA'' ===<br />
<br />
The Radiometer Electronics Box Assembly (REBA) is the electronics unit that processes the digitized scientific data and manages the overall instrument. It is also in charge of communication with the spacecraft.<br />
There are two REBA boxes, one nominal and one redundant. The redundancy concept is cold, which means that both boxes are never ON at the same time; the operation of each unit is managed by the spacecraft switching on the corresponding unit. The REBA ASW (Application SoftWare) is the same in each REBA box.<br />
<br />
A detailed description of the Planck LFI REBA can be found in (Herreros et al. 2009{{BibCite|herreros2009}}) and in the corresponding section of the [[LFIAppendix#REBA|Annexes]].<br />
<br />
=== ''Instrument On-board Software'' ===<br />
<br />
The REBA software is the on-board software of LFI. It is installed in the two computing subunits of REBA: the DPU (Digital Processing Unit), responsible of the control and monitoring of the instrument and the interface with the spacecraft; and the SPU (Signal Processing Unit), responsible for the data reduction and compression.<br />
<br />
Details can be found in the corresponding section of the [[LFIAppendix#Instrument On-board Software|Annexes]]. <br />
<br />
==== ''Reduction and Compression of Science Data'' ====<br />
<br />
To assess stability against 1/<i>f</i> noise, the Low Frequency Instrument (LFI) on board the Planck mission acquired data at a rate much higher than the data rate allowed by the science telemetry bandwidth of 35.5 kbps. The data were processed by an on-board pipeline, followed on the ground by a decoding and reconstruction step, to reduce the volume of data to a level compatible with the bandwidth, while minimizing the loss of information. The on-board processing of the scientific data used by Planck/LFI to fit the allowed data-rate is an intrinsically lossy process which distorts the signal in a manner that depends on a set of five free parameters (<i>N</i><sub>aver</sub>, <i>r</i><sub>1</sub>, <i,>r</i><sub>2</sub>, <i>q</i>, <i>O</i>) for each of the 44 LFI detectors.<br />
A brief description of the characteristics of this algorithm and the level of distortion introduced by the on-board processing as a function of these parameters can be found in the corresponding section of the [[LFIAppendix#Reduction and Compression of Science Data|Annexes]], while a full description of the Planck LFI on-board data handling system and the tuning and optimization method of the on-board processing chain can be found in (Maris et al. 2009{{BibCite|maris2009}}).<br />
<br />
The strategy adopted to fit into the telemetry bandwidth relies on three on-board processing steps: downsampling; pre-processing the data to ensure loss-less compression; and loss-less compression itself. To demonstrate these steps, a model of the input signal was used. Note that while the compression is loss-less, the pre-processing is not, due to the need to rescale the data and convert them to integers (a process named data re-quantization). However, the whole strategy is designed to keep strict control over the way in which lossy operations are done, and to quantify the amount of information loss in order to assess the optimal compression rate with minimal information loss.<br />
<br />
=== ''Instrument Operations'' ===<br />
<br />
==== ''Operational Modes'' ====<br />
<br />
The operations of the LFI are designed to be automatic and require little if any intervention from the ground. A small number of commands are required for operating the instrument and eventually for diagnostic and reconfiguration purposes.<br />
Each sky survey is conducted by the LFI with the instrument in the Normal Operations Mode. No deployable elements, or mechanically moving parts are included in the instrument. The scanning of the sky is achieved by progressive repointing of the satellite spin axis, with the Sun direction always within a cone 10&deg; from the spin axis.<br />
Within the Normal Science Mode the instrument can be configured in order to fit with different science or diagnostic needs without changing the power consumption and thus the temperature in the FPU. <br />
<!-- <br />
Changes in power consumption in the FPU are minimized and should occur only in the case that failures in the radiometers that could create interference problems require an RCA to be switched off. Power adjustments on the first stage of the HEMT amplifiers (which were contemplated), require extremely small power level variations.--><br />
<br />
A brief summary of the LFI Operational Modes and the transitions between them is given in the corresponding section of the [[LFIAppendix#LFI Operational Modes|Annexes]].<br />
<br />
<!--<br />
==== ''In-flight Operations'' ====<br />
<br />
TBW<br />
<br />
<br />
==== ''Anomalies'' ====<br />
<br />
TBW<br />
--><br />
<br />
==<span id="LFITests">Ground Tests</span>==<br />
During its development, the LFI flight model was calibrated and tested at various integration levels from sub-systems (Davis et al. 2009{{BibCite|davis2009}}) to individual integrated receivers ({{PlanckPapers|villa2010}}) and the whole receiver array ({{PlanckPapers|mennella2010}}). In every campaign we performed tests according to the following classification:<br />
<br />
* ''functionality tests'', performed to verify the instrument functionality;<br />
* ''tuning tests'', to tune radiometer parameters (biases, DC electronics gain and offset, digital quantization and compression) for optimal performance in flight-like thermal conditions;<br />
* ''basic calibration and noise performance tests'', to characterize instrument performance (photometric calibration, isolation, linearity, noise and stability) in tuned conditions;<br />
* ''susceptibility tests'', to characterize instrument susceptibility to thermal and electrical variations.<br />
<br />
Where possible, the same tests were repeated in several test campaigns, in order to ensure enough redundancy and confidence in the repeatability of the instrument behaviour. A matrix showing the instrument parameters measured in the various test campaigns is provided in Table 1 of ({{PlanckPapers|mennella2010}}).<br />
<br />
The ground test campaign was developed in three main phases: cryogenic tests on the individual RCAs; cryogenic tests on the integrated receiver array (the so-called radiometer array assembly, RAA); and system-level tests after the integration of the LFI and HFI instruments onto the satellite. The first two phases were carried out at the Thales Alenia Space - Italia laboratories located in Vimodrone (Milano, Italy) (note that receiver tests on 70 GHz RCAs were carried out in Finland, at Yilinen laboratories), while system level tests (SLTs) were conducted in a dedicated cryofacility at the Centre Spatiale de Li&egrave;ge (CSL) located in Liege, Belgium. <br />
<br />
In Table 1 below we list the temperature of the main cold thermal stages during ground tests compared to in-flight nominal values. These values show that system-level tests were conducted in conditions that were as flight-representative as possible, while results obtained during RCA and RAA tests need to be extrapolated to flight conditions to allow comparison. Details of the RCA test campaign are discussed in ({{PlanckPapers|villa2010}}), while the RAA tests and the extrapolation methods are presented in ({{PlanckPapers|mennella2010}}).<br />
<br />
{| border="1" cellspacing="0" cellpadding="2" align="center"<br />
|+ '''<small>Table 1. Temperatures of the main cold stages during the various ground test campaigns compared to in-flight nominal values.</small>'''<br />
|-<br />
!scope="col"| Temperature <br />
!scope="col"| Nominal<br />
!scope="col"| RCA tests<br />
!scope="col"| RAA tests<br />
!scope="col"| System-level<br />
|-<br />
|width="120" | Sky<br />
|width="100" | ~ 3 K<br />
|width="100" | ≳ 8 K<br />
|width="100" | ≳ 18.5 K<br />
|width="100" | ~ 4 K<br />
|-<br />
|width="120" | Ref. load<br />
|width="100" | ~ 4.5 K<br />
|width="100" | ≳ 8 K<br />
|width="100" | ≳ 18.5 K<br />
|width="100" | ~ 4.5 K<br />
|-<br />
|width="120" | Front-end unit<br />
|width="100" | ~ 20 K<br />
|width="100" | ~ 20 K<br />
|width="100" | ~ 26 K<br />
|width="100" | ~ 20 K<br />
|-<br />
|}<br />
<br />
During the various test campaigns the instrument was switched off and moved several times in a time period of about three years. A series of functional tests were always repeated at each location and also in-flight, in order to verify the instrument functionality and the response repeatability. No failures or major problems have been identified due to transport and integration procedures.<br />
<br />
The expected Planck LFI scientific performance, resulting mainly from cryogenic system level tests, are described in ({{PlanckPapers|mennella2010}}).<br />
<br />
== <span id="LFICalibration">In-flight Calibration</span>==<br />
<br />
The LFI Commissioning and Calibration and Performance Verification (CPV) phases started on 4 June 2009 and lasted until 12 August 2009 when Planck started scanning the sky in nominal mode. At the onset of CPV, the active cooling started when the radiating surfaces on the payload module reached their working temperatures (approximately 50 K on the third V-groove, and 40 K on the reflectors) by passive cooling. This was achieved during the transfer phase. Nominal temperatures were achieved on 3 July 2009, when the dilution cooler temperature reached 0.1 K ({{PlanckPapers|planck2011-1-3}}, Meinhold et al. 2009 {{BibCite| meinhold2009}}). The cooldown of the HFI 4-K stage (see Fig. 4 below), was key during CPV for the LFI, because it provided a variable input signal that was exploited during bias tuning.<br />
<br />
The LFI Commissioning and CPV was carried out in four phases: <br />
* LFI switch-on and basic functionality verification (Commissioning);<br />
* tuning of front-end biases and back-end electronics (CPV);<br />
* preliminary calibration tests (CPV);<br />
* thermal tests (CPV). <br />
<br />
[[File:FUNCT_tests_schedule_vs_K-eps-converted-to.jpg|thumb|center|460px|'''Figure 4. Functional tests performed during CPV against timeline. Curves from thermal sensors monitoring the 4-K stage and the FPU temperature are superimposed.''']]<br />
<br />
Details of the LFI Commissioning and CPV test campaign are given in (Gregorio et al. 2013{{BibCite|gregorio2013}}).<br />
<br />
==<span id="LFIPerformance">Performance Summary</span>==<br />
<br />
A summary of the LFI performance parameters is given in Table 1 of the section titled [[Summary LFI|Summary of LFI data characteristics]]. <br />
<br />
=== Instrument scientific performance ===<br />
<br />
==== ''Optical parameters''====<br />
<br />
The most accurate measurements of the LFI main beams were made with Jupiter, the most powerful unresolved (to Planck) celestial source in the LFI frequency range. Since the LFI feedhorns point to different positions on the sky, they detect the signal at different times. <br />
To map the beam, each sample in the selected timelines was projected in the (<i>u</i>, <i>v</i>) plane perpendicular to the nominal line-of-sight (LOS) of the telescope (and at 85&deg; to the satellite spin axis). The <i>u</i> and <i>v</i> coordinates are defined in terms of the usual spherical coordinates (&theta;, &phi;) :<br />
<br />
: <math> u = \sin θ \, \cos φ, </math> <br />
: <math> v = \sin θ \, \sin φ. </math> <br />
<br />
To increase the signal-to-noise ratio, data were binned in an angular region of 2′ for the 70 GHz channels and 4′ for the 30 and 44 GHz channels. We recovered all beams down to −25 dB from the peak. An elliptical Gaussian was fit to each beam for both M and S radiometers. Differences between the M and S beams caused by optics and receiver non-idealities are inevitable at some level, but they appear to be well within the statistical uncertainties, and for the purposes of point-source extraction, the beams may be considered identical. For the details of the typical FWHM and ellipticity averaged over each frequency channel, refer to ({{PlanckPapers|planck2011-1-4 }}) and ({{PlanckPapers|planck2014-a05||Planck-2015-A05}}). Exhaustive details on all LFI beam parameters are presented in the LFI data processing section entitled [[Beams LFI|Beams]].<br />
<br />
==== ''Photometric Calibration''====<br />
<br />
Photometric calibration, i.e., conversion from voltage to antenna temperature, is performed for each radiometer after total power data have been cleaned of 1 Hz frequency spikes (see the LFI data processing section [[TOI processing LFI#Spikes Removal|Spikes Removal]] page and ({{PlanckPapers|planck2011-1-6 }}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}})), and differenced. Here we report a brief overview of the photometric calibration; for details see the LFI data processing section [[TOI processing LFI#Photometric Calibration|Photometric Calibration]].<br />
<br />
Our calibrator is the well-known dipole signal induced by spacecraft motion with respect to the CMB rest frame. The largest calibration uncertainty comes from the presence of the Galaxy and of the CMB anisotropies in the measured signal. We therefore use an iterative calibration procedure in which the dipole is fitted and subtracted, producing a sky map that is then removed from the original data to enhance the dipole signal for the next iteration. Typically, convergence is obtained after a few tens of iterations.<br />
<br />
In our current calibration model we use as a calibration signal the sum of the solar dipole &Delta;T<sub>Sun</sub> and the orbital dipole &Delta;T<sub>orb</sub>, which is the contribution from Planck’s orbital velocity around the Sun,<br />
<br />
<math> \label{eq:cal1} \Delta T= ( \Delta T_{\rm Sun} + \Delta T_{\rm orb} ) \sin \theta_{\rm axis} </math>,<br />
<br />
where &theta;<sub>axis</sub> is the angle between the spacecraft axis and the overall dipole axis (solar + orbital).<br />
In this equation, the absolute calibration uncertainty is dominated by the uncertainty in the solar dipole, which is known to about 0.2%. The modulation of the orbital dipole by Earth's motion around the Sun is known with an uncertainty almost three orders of magnitude smaller; however, at least one complete Planck orbit is needed for its measurement. We employ the orbital dipole as an absolute calibration.<br />
The accuracy of our current calibration can be estimated by taking into account two components: 1) the statistical uncertainty in time periods when the dipole signal is weak; and 2) the systematic uncertainty caused by neglecting gain fluctuations that occur on periods shorter than the smoothing window. In our calibration procedure the gain is estimated for every pointing period; if we call <i>G<sub>i</sub></i> the gain estimate from the <i>i</i>th pointing period, we have that the associated uncertainty is<br />
<br />
<math> \label{eq:cal2} \delta G = \sqrt{\frac{ \Sigma_{i=1}^N (G_i-< G>)^2 }{N-1} } </math>,<br />
<br />
where <i>N</i> is the overall number of pointing and <<i>G</i>> is the average of the <i>N</i> gains.<br />
We then approximate the effect of the smoothing filter as an average over <i>M</i> consecutive pointings, so that the overall uncertainty can be estimated as<br />
<br />
<math> \label{eq:cal3} \delta G |_{\rm stat} = \frac{\delta G}{\sqrt{M}} = \frac{1}{\sqrt{M}} <br />
\sqrt{\frac{ \Sigma_{i=1}^N (G_i-< G>)^2 }{N-1} } </math>.<br />
<br />
==== ''Noise Properties''====<br />
<br />
The noise characteristics of the LFI data streams are closely reproduced by a simple (white + 1/<i>f</i> ) noise model,<br />
<br />
<math> \label{eq:p1} P(f)= \sigma^2 \left[1+ \left(\frac{f}{f_{\rm knee}}\right)^\alpha \right] </math>,<br />
<br />
where <i>P</i>(<i>f</i>) is the power spectrum and &alpha;&asymp;−1.<br />
In this model, noise properties are characterized by three parameters, the white noise limit &sigma;, the knee frequency <i>f</i><sub>knee</sub>, and the exponent of the 1/<i>f</i> component &alpha;, also referred to as the slope. Here we give noise performance estimates based on one year of operations; details of the analysis are given in LFI data processing section ([[TOI processing LFI#Noise|Noise estimation]]) and in <br />
({{PlanckPapers|planck2011-1-6}}, {{PlanckPapers|planck2011-1-4 }}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}).<br />
<br />
Noise properties have been calculated following two different and complementary approaches: 1) fitting the equation above to time-ordered data for each radiometer; and 2) building normalized noise maps by differencing data from the first half of each pointing period with data from the second half of that pointing period to remove the sky signal (“jackknife” data sets).<br />
<br />
Typical uncertainties are 0.5% for the white noise, between 5 and 10% for the slope, and between 10 and 20% for the knee frequency.<br />
<br />
==== ''White Noise Sensitivity''====<br />
<br />
Details of the white noise sensitivity can be found in ({{PlanckPapers|planck2011-1-4}}). <br />
<br />
Table 2 summarizes the sensitivity numbers calculated during the first year of operations using methods and procedures described in detail in ({{PlanckPapers|planck2011-1-6}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}), compared with scientific requirements. The measured sensitivity is in very good agreement with pre-launch expectations. While the white noise moderately exceeds the design specification, this performance is fully in line with the LFI science objectives.<br />
<br />
{| border="1" cellspacing="0" cellpadding="2" align="center"<br />
|+ '''<small>Table 2. White noise sensitivity of the LFI frequency channels compared with requirements.</small>'''<br />
|-<br />
!scope="col"| Channel <br />
!scope="col"| Measurement [&mu;K<sub>CMB</sub> s<sup>1/2</sup>]<br />
!scope="col"| Requirement [&mu;K<sub>CMB</sub> s<sup>1/2</sup>]<br />
|-<br />
|width="120" | 70 GHz<br />
|width="100" | 152.0<br />
|width="100" | 119<br />
|-<br />
|width="120" | 44 GHz<br />
|width="100" | 174.2<br />
|width="100" | 119<br />
|-<br />
|width="120" | 30 GHz<br />
|width="100" | 148.1<br />
|width="100" | 119<br />
|-<br />
|}<br />
<br />
=== Instrument technical performance ===<br />
<br />
<br />
==== ''Spectral response''====<br />
<br />
The in-band receiver response was thoroughly modelled and measured for all the LFI detectors during ground tests. The complete set of bandpass curves was published in (Zonca et al. 2009{{BibCite|zonca2009}}) where all the details of the LFI radiometer's spectral response are given. From each curve we have derived the effective centre frequency according to:<br />
<br />
<math> \label{eq:spectr} <br />
\nu_0 = \frac{ \int_{\nu_{\rm min}}^{\nu_{\rm max}} \nu g(\nu) \; d \nu}<br />
{\int_{\nu_{\rm min}}^{\nu_{\rm max}} g(\nu)\; d\nu }<br />
</math> <br />
<br />
where &Delta;&nu; = &nu;<sub>max</sub> − &nu;<sub>min</sub> is the receiver bandwidth and <i>g</i>(&nu;) is the bandpass response. <br />
Details about colour corrections, <i>C</i>(&alpha;), needed to derive the brightness temperature of a source with a power-law spectral index &alpha;, are provided in <br />
<br />
Some details are also given in the corresponding section of the [[LFIAppendix#Spectral Response|Annexes]].<br />
<br />
<br />
===== ''Bandpass estimation''=====<br />
<br />
As detailed in (Zonca et al. 2009{{BibCite|zonca2009}}), our most accurate method to measure the LFI bandpasses is based on measurements of individual components integrated into the LFI Advanced RF Model (LARFM) to yield a synthesized radiometer bandpass.<br />
The LARFM is a software tool based on the open-source Quasi Universal Circuit Simulator (QUCS). The measured frequency responses of the various subsystems (feed-OMT, FEM, BEM) are considered as lumped S-parameter components. <br />
Measurements of single components are obtained with standard methods and provide highly reliable results, with precision of order 0.1-0.2 dB over the entire band.<br />
Waveguides are simulated with an analytical model, in order to reproduce the effect of their temperature gradient and the effect of standing waves caused by impedance mismatch at the interfaces between the FEM and BEM. This is because the 1.8-m long waveguides were not measured at unit level in cryogenic conditions. The model provides accurate agreement with the measured waveguide response in the conditions of the test measurements (300 K).<br />
The composite bandpasses are estimated to have a precision of about 1.5 to 2 dB.<br />
<br />
Some details are also given in the corresponding section of the [[LFIAppendix#Bandpass Estimation|Annexes]].<br />
<br />
==== ''Stability''====<br />
<br />
Thanks to its differential scheme, the LFI is insensitive to many effects caused by 1/<i>f</i> noise, thermal fluctuations, or electrical instabilities.<br />
As detailed in ({{PlanckPapers|planck2011-1-4}}), one effect detected during the first survey was the daily temperature fluctuation in the back-end unit induced by the downlink transponder, which was powered on each day for downlinks during the first 258 days of the mission. As expected, the effect is highly correlated between the sky and reference load signals. In the difference, the variation is reduced by a factor around (1 − <i>r</i>), where <i>r</i> is the gain modulation factor defined above (see <i>r</i> definition in [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section).<br />
<br />
A particular class of signal fluctuations occasionally observed during operations was due to electrical instabilities that appeared as abrupt increases in the measured drain current of the front-end amplifiers, with a relaxation time variable from few seconds to some hundreds of seconds. Typically, these events caused a simultaneous change in the sky and reference load signals. Because they are essentially common-mode, their residual on the differenced data is negligible, and the data are suitable for science production. In a few cases the residual fluctuation in the differential output was large enough (a few millikelvin in calibrated antenna temperature units) to be flagged, and the data were not used. The total amount of discarded data for all LFI channels until Operational Day 389 was about 2000s per detector, or 0.008%.<br />
<br />
A further peculiar effect appeared in the 44 GHz detectors, where single isolated samples, either on the sky or the reference voltage output, were clear outliers compared with the rest. Over a reference period of four months, 15 occurrences of single-sample spikes (out of 24 total anomaly events) were discarded, an insignificant loss of data.<br />
<br />
==== ''Thermal susceptibility''====<br />
<br />
As mentioned in the section [[LFI design, qualification, and performance#LFI In-flight Calibration|LFI In-flight Calibration]] above, and detailed in (Gregorio et al. 2013{{BibCite|gregorio2013}}), during the CPV campaign, susceptibility tests were performed in order to characterize the LFI instrument susceptibility to thermal and electrical variations.<br />
<br />
The effect of temperature fluctuations on the LFI radiometers originates in the Planck cold end interface of the hydrogen sorption cooler to the instrument focal plane. The temperature is actively controlled through a dedicated stage, the Thermal Stabilization Assembly (TSA), providing a first reduction of the effect. The thermal mass of the focal plane strongly contributes to reduce residual fluctuations.<br />
The physical temperature fluctuations propagated at the front end modules cause a correlated fluctuation in the radiometer signal, degrading the quality of scientific data. The accurate characterization of this effect is crucial for attempts to remove it from raw data by exploiting the housekeeping information on thermal sensors.<br />
<br />
The propagation of the temperature oscillations through the focal plane and the instrument response to thermal changes were characterized through two main tests: <br />
* the thermal dynamic response, aimed at measuring the dynamic thermal behaviour of the LFI Focal Plane;<br />
* the thermal susceptibility of the radiometers.<br />
<br />
Further details are also given in the corresponding section of the [[LFIAppendix#Thermal Susceptibility|Annexes]].<br />
<br />
==== Instrument budgets ====<br />
<br />
LFI power, mass and telemetry budgets are given in the corresponding section of the [[LFIAppendix#Instrument Budgets|Annexes]].<br />
<br />
== <span id="LFISystematics">Systematic Effects </span>==<br />
<br />
The LFI design was driven by the need to suppress systematic effects well below instrument white noise. The differential receiver scheme, with reference loads cooled to 4 K, greatly minimizes the effect of 1/<i>f</i> noise and common-mode fluctuations, such as thermal perturbations in the 20-K LFI focal plane. The use of a gain modulation factor (see <i>r</i> definition in the [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section above) largely compensates for spurious contributions from input offsets. Furthermore, diode averaging (see <i>V</i><sup>rad</sup><sub>out</sub> definition in the [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section above) allows us to cancel second-order correlations, such as those originating from phase switch imbalances.<br />
<br />
We have developed an error budget for systematic effects ({{PlanckPapers|bersanelli2010}}, {{PlanckPapers|planck2011-1-4}}{{PlanckPapers|planck2013-p02a}} and {{PlanckPapers|planck2014-a04||Planck-2015-A04}}) as a reference for both instrument design and data analysis. Our goal is to ensure that each systematic effect is rejected to the specified level, either by design or by robust removal in software. At this stage, the following effects are relevant:<br />
<br />
[[File:Selection_258.png|500px]]<br />
<br />
For each of these effects we used flight data and information from ground tests to build timelines, maps, and angular power spectra that represent our best knowledge of their impact on the scientific analysis.<br />
The details of the systematic effect analysis are given in the section entitled LFI data processing section ([[LFI systematic effect uncertainties|Systematic Effects uncertainties]]).<br />
<br />
== <span id="SCS">The Sorption Cooler</span> ==<br />
The Planck H2 Sorption Cooler is the first stage of the active cryogenic chain. Its task is to maintain the LFI down to the operating temperature while providing a pre-cooling stage for the HFI refrigerators. The system performs a simple thermodynamic cycle based on hydrogen compression, gas pre-cooling by three passive radiators, further cooling due to the heat recovery by the cold low pressure gas stream, expansion through a J-T valve, and evaporation at the cold stage ({{PlanckPapers|planck2011-1-3}}). A schematic of the Planck Sorption Cooler System (SCS) is shown in Fig. 5. The engine of the cryocooler is the compressor. It serves two main functions: to produce the high-pressure hydrogen gas flow; and to maintain a stable gas recovery rate, which keeps the return pressure, hence the liquid temperature, constant. The high pressure gas flowing to the cold end is pre-cooled by exchanging heat with the three passive stages at the V-Grooves and with the evaporated cold gas returning back to the compressor. The gas then expands at the cold end through a J-T valve, producing approximately 1 Watt of cooling power at a temperature of <20K: most of this heat lift is used at the LVHX2 (Liquid Vapour Heat eXchanger 2, see Fig. 5) interface to absorb the LFI heat load at a temperature around 20K. The remaining heat lift is used at the LVHX1 as a pre-cooling stage, at a temperature lower than 19 K, for the two HFI refrigerators. The cooler and its performance are described in detail in (Morgante et al. 2009{{BibCite|morgante2009}}). <br />
<br />
[[File:SCS_CAD_Figure.jpg|thumb|center|480px|'''Figure 5. Planck Sorption Cooler CAD view with labels of the main sub-systems.''']]<br />
<br />
Both LVHXs provide a temperature of around 18 K, with fluctuations driven by the cooler instabilities (compressor element variations, cycling, two-phase flow dynamics, etc.). Stabilization of the HFI interface (LVHX1) temperature is not necessary, since thermal control of the subsequent colder stages is more efficient and very effective. To reduce cold end fluctuations directly transmitted to the LFI radiometers, a copper block, designated as the Temperature Stabilization Assembly (TSA), is inserted, as an intermediate stage, between LVHX2 and the LFI Focal Plane Unit (FPU). The TSA comprises a temperature sensor and a heater, controlled by a PID-type feedback loop, working in combination with the passive thermal inertia. The set-point temperature of the TSA is an adjustable parameter of the sorption cooler system, chosen to provide dynamic range for control during mission: as the compressor elements age, the return gas pressure and thus the temperature of LVHX2 rise slowly. To keep the LFI temperature reference stable during operations the set point must be periodically adjusted to maintain the level of oscillations within the required range (Fig. 6).<br />
<br />
[[File:TSA_LVHX2_mission.jpg|thumb|center|480px|'''Figure 6. LVHX2 (black, HK parameter name SD029540) and TSA (red, HK parameter name SD030540) temperature profile from 125 to 563 days after launch.''']]<br />
<br />
Two sorption cooler units were integrated on-board the Planck spacecraft. Both units were used to cover the mission lifetime, with one cooler operated for the first two sky surveys. At the end of its lifetime a switchover operation, performed on August 11th 2010 (455 days after launch), activated the second unit that ran since then. The LVHX2 temperature change due to the new cooler start, and the subsequent re-adjustment of the LFI temperature stabilization stage, is clear in Fig. 6.<br />
<br />
<!--<br />
== Acronyms ==<br />
<br />
: ADC Analog-to-Digital Converter<br />
: ADU Analog-to-Digital Unit<br />
: BEM Back End Module <br />
: BEU Back End Unit <br />
: CCE Central Check-out Equipment<br />
: CDMS Command and Data Management Subsystem<br />
: CDMU Central Data Management Unit<br />
: CoG Centre of Gravity<br />
: CPV Calibration and Performance Verification<br />
: CSL Centre Spatiale de Liege<br />
: DAE Data Acquisition Electronics <br />
: DC Direct Current<br />
: DPC Data Processing Centre<br />
: DPU Digital Processing Unit<br />
: EMC Electro-Magnetic Compatibility<br />
: EMI Electro-Magnetic Interference<br />
: FEM Front End Module <br />
: FEU Front End Unit<br />
: FH Feed Horn<br />
: FOV Field Of View<br />
: FPU Focal Plane Unit<br />
: HK House Keeping<br />
: ILT Instrument Level Test<br />
: IST Integrated System Test<br />
: JFET Junction Field Effect Transistor<br />
: LEOP Launch and Early Orbit Phase<br />
: MLI Multilayer Insulation<br />
: MoI Moment of Inertia<br />
: MOS Margin Of Safety<br />
: OMT Ortho Module Transducer <br />
: PCS Power Control Subsystem<br />
: PSF Point Spread Function<br />
: RAA Radiometer Array Assembly <br />
: RAM Random Access Memory<br />
: RCA Radiometer Chain Assembly <br />
: REBA Radiometer Electronics Box Assembly <br />
: S/C Spacecraft<br />
: SCC Sorption Cooler Compressor assembly <br />
: SCCE Sorption Cooler Cold End <br />
: SCE Sorption Cooler Electronics <br />
: SCOS Spacecraft Control and Operations System<br />
: SCP Sorption Cooler Piping <br />
: SCS Sorption Cooler Subsystem <br />
: SLT System Level Test<br />
: SPU Signal Processing Unit<br />
: SS Stainless Steel<br />
: SVM Service Module<br />
: TCS Thermal Control System<br />
: TM Telemetry<br />
: TSA Thermal Stabilization Assembly<br />
: TTC Telemetry, Tracking and Command<br />
: VSWR Voltage Standing Wave Ratio <br />
: WG Waveguide<br />
<br />
== Glossary ==<br />
<br />
: Feed Horns xxx <br />
: REBA Radiometer Electronics Box Assembly<br />
--><br />
<br />
== References ==<br />
<br />
<References /><br />
<br />
<br />
[[Category:LFI design, qualification and performance|001]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=LFI_design,_qualification,_and_performance&diff=11316LFI design, qualification, and performance2015-02-04T21:20:23Z<p>Agregori: /* Radiometer Chain Assembly (RCA) */</p>
<hr />
<div>==<span id="LFIDescription">Instrument description</span>==<br />
The Low-Frequency Instrument (see Fig. 1 in the [[LFI overview]]) consists of a 20 K focal plane unit hosting the corrugated feed horns, the orthomode transducers (OMTs) and the receiver front-end modules (FEMs). Forty-four composite waveguides {{BibCite|darcangelo2009a}} are interfaced with three conical thermal shields and connect the front-end modules to the warm (roughly 300 K) back-end unit (BEU) containing a further radio frequency amplification stage, detector diodes, and all the electronics for data acquisition and bias supply. <br />
<br />
Best LFI noise performance is obtained with receivers based on InP High Electron Mobility Transistor (HEMT) low noise amplifiers (LNAs) for minimal power dissipation and best performance. To further minimize power consumption in the focal plane, the radiometers are split into two sub-assemblies connected by waveguides, one located at the telescope focal area, the other on the 300 K portion of the Planck satellite. These design features allow the entire front-end LNA dissipation to be <0.55 W, which enables the active cooling of the focal assembly. This is achieved with a vibration-less hydrogen sorption cooler, which also provides 18 K pre-cooling to the HFI helium J-T cooler. Two sorption cooler units are included in the flight hardware.<br />
<br />
As shown schematically in Fig. 1 below, the LFI consists of the following subsystems:<br />
* Radiometer Array Assembly (RAA);<br />
* Sorption Cooler Subsystem (SCS);<br />
* Radiometer Electronics Box Assembly (REBA).<br />
<br />
The RAA includes the Front End Unit (FEU) and the Back End Unit (BEU), connected via waveguides. The FEU is located at the focus of the telescope, as one component of the joint LFI/HFI focal assembly (see sections below). The BEU is mounted on the top of the Planck service module (SVM).<br />
The REBA (Radiometer Electronics Box Assembly) and the warm parts of the Sorption Cooler System (SCS) are located on one of the lateral panels of the SVM. The FEU and the Sorption Cooler Compressor (SCC) are connected by concentric stainless steel tubes. The smaller tube carries hydrogen at approximately 60 atmospheres from the cooler compressors to the FEU, while the larger tube returns the hydrogen at about 0.3 atmospheres. These units are described in following sections and in the [[LFIAppendix|Annexes]], while the SCS is described in details in the [[LFI design, qualification, and performance#The Sorption Cooler|Sorption Cooler]] section.<br />
All LFI units are linked together by the LFI harness, which also connects to the spacecraft interface.<br />
<br />
[[File:schema.jpg|thumb|center|500px|'''Figure 1. Block Diagram of LFI.''']]<br />
<br />
=== ''Radiometer Array Assembly (RAA)'' ===<br />
<br />
The Radiometer Array Assembly (RAA) consists of two main units (the front end unit, FPU and the Back End Unit, BEU), connected by a set of waveguides.<br />
The Focal Plane Unit (FPU) is the heart of the LFI instrument; it contains the feed array and associated orthomode transducers (OMTs) and FEMs, all cooled to 20 K by the sorption cooler. The FPU comprises a set of 11 modules, which are mounted on a mechanical support which meets the thermo-mechanical requirements of the instrument and adds thermal inertia.<br />
The BEU comprises the radiometer Back End Modules (BEM) and the Data Acquisition Electronics (DAE), which are connected by an internal harness.<br />
The HFI Unit is located inside the LFI FPU and supported by the LFI structure. The LFI structure gives the mechanical and thermal interface to the HFI unit with the proper stiffness and thermal de-coupling. The LFI structure also guarantees the proper alignment of the HFI detector with the telescope focal plane.<br />
<br />
The timescale of the stability of the receiverS is driven by the 1 rpm rotation speed of the spacecraft, which requires a very low 1/<i>f</i>-noise or gain variation of the low noise amplifiers and other components.<br />
The LFI uses a pseudo-correlation receiver concept (Fig. 2 below). This radiometer concept is chosen to maximize the stability of the instrument by reducing the effect of non-white noise generated in the radiometer itself. In this scheme, the difference between the inputs to each of the chains (the signal from the telescope and that from a reference blackbody, respectively) is continuously being observed. To remove the effect of instability in the back-end amplifiers and detector diodes, it is necessary to switch the signal detected at the diodes at a high rate.<br />
The signals from the sky and from a reference load are combined by a hybrid coupler, amplified in two independent amplifier chains, and separated out by another hybrid. The sky and the reference load power can then be measured and differenced. Since the reference signal has been subject to the same gain variations in the two amplifier chains as the sky signal, the true sky power can be recovered.<br />
The differencing receiver greatly improves the stability if the two input signals are almost equal, at<br />
a cost of a factor of &radic;2 in sensitivity, compared to a perfectly stable total-power radiometer with the same noise temperature and bandwidth. This radiometer concept is also capable of greatly reducing the knee frequency.<br />
A single Radiometer Chain Assembly (RCA; see Fig. 2) consists of each functional unit from the feed horn to the BEM. The RAA therefore includes a set of 11 RCAs and the Data Acquisition Electronics (see also Fig. 1 above), all mounted on a suitable mechanical structure. Although there are differences in the details of the radiometer chains at different frequencies, their overall configuration is similar, and a general description of their design is provided in this section.<br />
Planck LFI has 11 Radiometer Chain Assemblies (RCAs). Each RCA is constituted by a feed horn and FEM in the FEU (at 20 K), BEM (at 300 K) in the BEU, and four waveguides that connect each FEM-BEM couple. The frequency distribution of the RCA is the following:<br />
* 2 RCAs at 30 GHz;<br />
* 3 RCAs at 44 GHz;<br />
* 6 RCAs at 70 GHz.<br />
<br />
[[File:rca_schematic.jpg|thumb|center|640px|'''Figure 2. A complete RCA from feed-horn to analogue voltage output. The insets show the OMT, the details of the 20 K pseudo-correlator and of the back-end radio-frequency amplification, low-pass filtering, detection, and DC amplification.''']]<br />
<br />
==== ''Radiometer Chain Assembly (RCA)''====<br />
<br />
Every RCA consists of two radiometers, each feeding two diode detectors (see Fig. 2 above), for a total of 44 detectors. The 11 RCAs are labelled by a number from 18 to 28, as outlined in Fig. 1 of the [[LFI overview]], right panel.<br />
<br />
Fig. 2 provides a more detailed description of each radiometric receiver. In each RCA, the two perpendicular linear polarization components split by the OMT propagate through two independent pseudo-correlation differential radiometers, labelled as ''M'' or ''S,'' depending on the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2).<br />
<br />
In each radiometer the sky signal coming from the OMT output is continuously compared with a stable 4 K blackbody reference load mounted on the external shield of the HFI 4-K box (Valenziano et al. 2009{{BibCite|valenziano2009}}). After being summed by a first hybrid coupler, the two signals are amplified by approximately 30 dB (see upper-left inset of Fig. 2). The amplifiers were selected for best operation at low drain voltages and for gain and phase match between paired radiometer legs, which is crucial for good balance. Each amplifier is labelled with codes ''1'' or ''2'' so that the four outputs of the LNAs can be named with the sequence: ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). <br />
Tight mass and power constraints called for a simple design of the Data Acquisition Electronics (DAE) box so that power bias lines were divided into five common-grounded power groups with no bias voltage readouts; only the total drain current flowing through the front-end amplifiers is measured and is available to the house-keeping telemetry (this design has important implications for front-end bias tuning, which depends critically on the satellite electrical and thermal configuration and was repeated at all integration stages during on-ground and in-flight satellite tests).<br />
A phase shift (or phase switch) alternating between 0&deg; and 180&deg; at the frequency of 4096 Hz is applied in one of the two amplification chains and then a second hybrid coupler restores the sky and reference load components, which are further amplified and detected in the warm BEU, with a voltage output ranging from -2.5 V to +2.5 V.<br />
<br />
Each radiometer has two output diodes which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence ''M-00'', ''M-01'', ''S-10'', ''S-11''.<br />
<br />
After detection, an analogue circuit in the DAE box removes a programmable offset in order to obtain a nearly null DC output voltage and a programmable gain is applied to increase the signal dynamics and optimally exploit the ADC input range. After the ADC, data are digitally down-sampled, re-quantized and compressed in the REBA according to a scheme described in (Herreros et al. 2009{{BibCite|herreros2009}}, Maris et al. 2009{{BibCite|maris2009}}), before being combined in telemetry packets. On the ground, telemetry packets are converted to time ordered data for both the sky and reference load, after calibrating the ADU (Analog-to-Digital Unit) samples into volts. The calibration takes into account the applied offset and gain factors.<br />
<br />
To first order, the mean differential power output for each of the four receiver diodes can be written as follows (Seiffert et al. 2002{{BibCite|seiffert2002}}, Mennella et al. 2003{{BibCite|mennella2003}}, {{PlanckPapers|bersanelli2010}}):<br />
<br />
<math> \label{eq:power}<br />
P_{\rm out}^{\rm diode} = a\, G_{\rm tot}\,k\,\beta \left[ T_{\rm sky} + T_{\rm noise} - r\left(<br />
T_{\rm ref} + T_{\rm noise}\right) \right]<br />
</math><br />
<br />
where <i>G</i><sub>tot</sub> is the total gain, <i>k</i> is the Boltzmann constant, <i>&beta;</i> the receiver bandwidth, and <i>a</i> is the diode constant. <i>T</i><sub>sky</sub> and <i>T</i><sub>ref</sub> are the average sky and reference load antenna temperatures at the inputs of the first hybrid and <i>T</i><sub>noise</sub> is the receiver noise temperature.<br />
<br />
The gain modulation factor (Mennella et al. 2003{{BibCite|mennella2003}}, {{PlanckPapers|planck2011-1-6 }}), <i>r</i>, is defined by<br />
<br />
<math> \label{eq:erre1} <br />
r = \frac{T_{\rm sky} + T_{\rm noise}}{T_{\rm ref} + T_{\rm noise}} ,<br />
</math><br />
<br />
and is used to balance (in software) the temperature offset between the sky and reference load signals and minimize the residual 1/<i>f</i> noise in the differential data stream. This parameter is calculated from the average uncalibrated total power data using the relationship<br />
<br />
<math> \label{eq:erre2}<br />
r = \langle V_{\rm sky} \rangle/ \langle V_{\rm ref}\rangle,<br />
</math><br />
<br />
where <<i>V</i><sub>sky</sub>> and <<i>V</i><sub>ref</sub>> are the average sky and reference voltages calculated in a defined time range.<br />
The white noise spectral density at the output of each diode is essentially independent of the reference-load absolute temperature and is given by<br />
<br />
<math> \label{eq:dt1}<br />
\Delta T_0^{\rm diode} = \frac{2\,(T_{\rm sky}+T_{\rm noise})}{\sqrt{\beta}}.<br />
</math><br />
<br />
If the front-end components are not perfectly balanced, then the separation of the sky and reference load signals after the second hybrid is not perfect and the outputs are mixed. First-order deviations in white noise sensitivity from the ideal behaviour are caused mainly by noise temperature and phase-switch amplitude mismatches. Following the notation used in (Seiffert et al. 2002 {{BibCite|seiffert2002}}), we define &epsilon;<sub><i>T</i><sub>n</sub></sub>, as the imbalance in front end noise temperature, and &epsilon;<sub><i>A</i><sub>1</sub></sub> and &epsilon;<sub><i>A</i><sub>2</sub></sub>, the imbalance in signal attenuation in the two states of the phase switch. Equation above for the two diodes of a slightly imbalanced radiometer then becomes<br />
<br />
<math> \label{eq:dt2} (\Delta T^{\rm diode} )^2 ≈ (\Delta T_0^{\rm diode})^2 ( 1± \frac{\epsilon_{A1}- \epsilon_{A2}}{2} <br />
+ \alpha \epsilon_{T{\rm n}}),<br />
</math><br />
<br />
which is identical for the two diodes apart from the sign of the term &epsilon;<sub><i>A</i><sub>1</sub></sub> − &epsilon;<sub><i>A</i><sub>2</sub></sub>, representing the phase switch amplitude imbalance. This indicates that the isolation loss caused by this imbalance generates an anti-correlation between the white noise levels of the single-diode data streams.<br />
For this reason, the LFI scientific data streams are obtained by averaging the voltage outputs from the two diodes in each radiometer:<br />
<br />
<math> \label{eq:v1} <br />
V^{\rm rad}_{\rm out} = w_1 V^{\rm diode\,1}_{\rm out} +w_2 V^{\rm diode\,2}_{\rm out} </math>,<br />
<br />
where &omega;<sub>1</sub> and &omega;<sub>2</sub> are inverse-variance weights calculated from the data as discussed in ({{PlanckPapers|planck2011-1-6}}). This way, the diode-diode anti-correlation is cancelled, and the radiometer white noise becomes<br />
<br />
<math> \label{eq:dt3}<br />
\Delta T^{\rm rad} ≈ \frac{ T_0^{\rm diode}}{\sqrt{2}} (1+\alpha \epsilon_{T{\rm n}})^{1/2}.<br />
</math><br />
<br />
In the equations above, &epsilon;&laquo;1, while &alpha; (a term &asymp;1) is given by<br />
<br />
<math> \label{eq:alpha} <br />
\alpha = \frac{ T_{\rm noise} (2 \; T_{\rm noise} + T_{\rm sky} + T_{\rm ref} }<br />
{2 (T_{\rm sky} + T_{\rm noise} )(T_{\rm ref} + T_{\rm noise})}.<br />
</math><br />
<br />
See the [[TOI processing LFI|Diode Combination]] section for the details of the diode combination procedure. <br />
<br />
In Fig. 3 below we show a close-up of the two front end modules of an RCA with the four phase switches, which are labelled with the four letters ''A'' and ''B'' (main arm), and ''C'' and ''D'' (side arm). Each phase switch is characterized by two states: state 0 (no phase shift applied to the incoming wave); and state 1 (180&deg; phase shift applied) and can either stay fixed in a state or switch at 4 kHz between the two states.<br />
<br />
Phase switches are clocked and biased by the DAE and their configuration can be programmed via telecommand. In order to simplify the instrument electronics, phase switches are configured and operated in pairs, by convention they are labelled ''A/C'' (corresponding to the first LNA both of main and side arm) and ''B/D'' (corresponding to the second LNA both of main and side arm). This means that if phase switches ''A'' and ''C'' are switching at 4 kHz then ''B'' and ''D'' are fixed, both in the same state (either 0 or 1); and viceversa. This simplification, required during the design phase to comply with mass and power budgets, comes at the price of losing some setup redundancy.<br />
<br />
[[File:phase_switch_operation.jpg|thumb|center|460px|'''Figure 3. Close-up of the two front-end modules of an RCA. There are four phase switches, labelled A, B, C, and D. Each switch can be fixed in one of its two positions (labelled as 0, 1) or switched at 4 kHz between 0 and 1. Phase switches are clocked and biased by the DAE in pairs: A/C and B/D.''']]<br />
<br />
==== ''Feed Horns (FHs)''====<br />
<br />
Dual profiled corrugated horns have been selected at all LFI frequencies as the best design in terms of the shape of the main lobe, level of the side lobes, control of the phase centre, and compactness. <br />
Details of the design, flight model and tests of Planck-LFI feed horns can be found in (Villa et al. 2009{{BibCite|villa2009}}) and in the corresponding [[LFIAppendix#Feed Horns (FH)|Annex]] section.<br />
<br />
==== ''Ortho-Mode Transducers (OMTs)''====<br />
<br />
The Ortho–Mode Transducer (OMTs) separates the radiation collected by the feedhorn into two orthogonal polarization components. It consists of a circular to square waveguide transition (directly connected to the FH), a square waveguide section and two separate rectangular waveguides (the main and side arms, which separate and pick up the orthogonal polarizations, connected with the FEU). A 90&deg; bend is always present on the side arm, while a twist is also necessary on the main (30 and 44 GHz) and side (70 GHz) arms, in order to match the FEU polarization.<br />
<br />
The details of the flight models and measurements of the Planck LFI ortho-mode transducers can be found in (D'Arcangelo et al. 2009{{BibCite|darcangelo2009b}}) and in the corresponding [[LFIAppendix#OrthoMode Transducers (OMT)|Annex]] section.<br />
<br />
==== ''Front End Modules (FEMs)''====<br />
<br />
Front End Modules are located in the FPU, just behind the Feed Horn and the Ortho Mode Transducers. The 70 GHz FEMs are mounted onto the inner wall of the main frame (the wall facing HFI instrument) from the HFI side. The 44 and 30 GHz FEMs are inserted into the main frame from the waveguide (WG) side and fixed to the bottom plate. Screws to the bottom plate are inserted from the WG side.<br />
The LFI FEMs are the first active stage of amplification of the radiometer chain. Each FEM contains four amplification paths, each of which is composed of several cascaded LNAs followed by a phase switch. Two passive hybrids, at the input and output of the FEM, are used to mix pairs of signals of the same radiometer (see Fig. 3). This cuases the instabilities of each chain to be applied to both the sky and load signals.<br />
<br />
The passive hybrid coupler ("magic-tee") combines the signals from the sky and cold load with a fixed phase offset of either 90&deg; or 180&deg; between them. It has a 20% bandwidth, low loss, and amplitude balance needed at the output to ensure adequate signal isolation.<br />
<br />
The details of the design, development and verification of the 70 GHz front-end modules for the Planck Low Frequency Instrument can be found in (Varis et al. 2009{{BibCite|varis2009}}) and in the corresponding [[LFIAppendix#Front End Modules (FEM)|Annex]] section.<br />
<br />
==== ''Waveguides (WGs)''====<br />
<br />
The LFI Front End Unit (FEU) is connected to the Back End Unit (BEU) by 44 rectangular waveguides approximately 1.5-2.0 m long. Each waveguide exhibits a low voltage standing wave ratio, low thermal conductivity, low insertion loss, and low mass. In addition, the waveguide path permits the LFI/HFI integration and the electrical bonding between the FPU and the BEU. Because of the Focal Plane Unit arrangement, the waveguides are in general twisted and bent in different planes and with different angles, depending on the particular waveguide. From the thermal point of view the waveguides have to connect two systems (the BEM and FEM) that are at very different temperatures. At BEM level the waveguides are at a temperature of 300 K, while at FEM level the temperature is 20 K. The waveguides have to reduce the thermal flow from 300 K to 20 K. In Fig. 1 in the [[LFI overview]] (left panel) a conceptual sketch of the LFI configuration is shown. <br />
<br />
Details of the Planck-LFI flight model of the composite waveguides can be found in (D'Arcangelo et al. 2009{{BibCite|darcangelo2009a}}) and in the corresponding [[LFIAppendix#Waveguides|Annex]] section.<br />
<br />
==== ''Back End Modules (BEMs)''====<br />
<br />
The BEMs are composed of four identical channels each made of Low Noise Amplifiers (LNAs), an RF bandpass Filter, RF to DC diode detector, and DC amplifiers.<br />
The FEM output signals are connected by waveguides from the Focal Plane Unit (FPU) assembly to the Back End Modules (BEMs) housed adjacent to the Data Acquisition Electronics (DAE) assembly. To maintain compatibility with the FEMs, each BEM accommodates four receiver channels from the four waveguide outputs of each FEM. The BEM internal signal routes are not cross-coupled and can be regarded as four identical parallel circuits.<br />
Each BEM is constructed as two mirror halves. The two amplifier/detector assemblies each contain two amplifier/detector circuits. Each is supplied from one of a pair of printed circuit boards, which also house two DC output amplifiers.<br />
<br />
The details of the design, development and verification of the 30 and 44 GHz back-end modules for the Planck Low Frequency Instrument can be found in (Artal et al. 2009{{BibCite|artal2009}}). <br />
Details of the design, development and verification of the 70 GHz back-end modules for the Planck Low Frequency Instrument can be found in (Varis et al. 2009{{BibCite|varis2009}}).<br />
Details are also reported in the corresponding [[LFIAppendix#Back End Modules (BEM)|Annex]] section.<br />
<br />
==== ''4K Load'' ====<br />
<br />
The purpose of the 4K reference load is to provide the radiometer with a stable reference signal. Reducing the input offset (the radiometric temperature difference between the sky and the reference load) reduces the minimum achievable radiometer 1/<i>f</i> noise knee frequency for a given amplifier fluctuation spectrum. A reference load temperature that matches the sky temperature (approximately 2.7 K) would be ideal. <br />
<br />
Details of the design, characteristics, and performance of the LFI 4-K reference load units are given in (Valenziano et al. 2009{{BibCite|valenziano2009}}) and in the corresponding section of the [[LFIAppendix#4K Load|Annexes]].<br />
<br />
=== Naming Convention ===<br />
<br />
The naming of all the LFI elements has been described in the previous sections, but here is summarized again for clarity. <br />
<br />
The 11 RCAs are labelled by numbers from 18 to 28, as outlined in Fig. 1 in the [[LFI overview]] (right panel). In each RCA, the two perpendicular linear polarization components are labelled as ''M'' or ''S'' according to the arm of the OMT they are connected to (''Main'' or ''Side'', see lower-left inset of Fig. 2). <br />
<br />
Each front-end amplifier (see upper-left inset of Fig. 2) is labelled with the codes ''1'', ''2'', so that the four outputs of the FEM LNAs can be named with the sequence ''M1'', ''M2'' (radiometer ''M'') and ''S1'', ''S2'' (radiometer ''S''). <br />
<br />
Each radiometer has two output diodes (see upper-right inset of Fig. 2), which are labelled with binary codes ''00'', ''01'' (radiometer ''M'') and ''10'', ''11'' (radiometer ''S''), so that the four outputs of each radiometric chain can be named with the sequence ''M-00'', ''M-01'', ''S-10'', and ''S-11''.<br />
<br />
=== ''REBA'' ===<br />
<br />
The Radiometer Electronics Box Assembly (REBA) is the electronics unit that processes the digitized scientific data and manages the overall instrument. It is also in charge of communication with the spacecraft.<br />
There are two REBA boxes, one nominal and one redundant. The redundancy concept is cold, which means that both boxes are never ON at the same time; the operation of each unit is managed by the spacecraft switching on the corresponding unit. The REBA ASW (Application SoftWare) is the same in each REBA box.<br />
<br />
A detailed description of the Planck LFI REBA can be found in (Herreros et al. 2009{{BibCite|herreros2009}}) and in the corresponding section of the [[LFIAppendix#REBA|Annexes]].<br />
<br />
=== ''Instrument On-board Software'' ===<br />
<br />
The REBA software is the on-board software of LFI. It is installed in the two computing subunits of REBA: the DPU (Digital Processing Unit), responsible of the control and monitoring of the instrument and the interface with the spacecraft; and the SPU (Signal Processing Unit), responsible for the data reduction and compression.<br />
<br />
Details can be found in the corresponding section of the [[LFIAppendix#Instrument On-board Software|Annexes]]. <br />
<br />
==== ''Reduction and Compression of Science Data'' ====<br />
<br />
To assess stability against 1/<i>f</i> noise, the Low Frequency Instrument (LFI) on board the Planck mission acquired data at a rate much higher than the data rate allowed by the science telemetry bandwidth of 35.5 kbps. The data were processed by an on-board pipeline, followed on the ground by a decoding and reconstruction step, to reduce the volume of data to a level compatible with the bandwidth, while minimizing the loss of information. The on-board processing of the scientific data used by Planck/LFI to fit the allowed data-rate is an intrinsically lossy process which distorts the signal in a manner that depends on a set of five free parameters (<i>N</i><sub>aver</sub>, <i>r</i><sub>1</sub>, <i,>r</i><sub>2</sub>, <i>q</i>, <i>O</i>) for each of the 44 LFI detectors.<br />
A brief description of the characteristics of this algorithm and the level of distortion introduced by the on-board processing as a function of these parameters can be found in the corresponding section of the [[LFIAppendix#Reduction and Compression of Science Data|Annexes]], while a full description of the Planck LFI on-board data handling system and the tuning and optimization method of the on-board processing chain can be found in (Maris et al. 2009{{BibCite|maris2009}}).<br />
<br />
The strategy adopted to fit into the telemetry bandwidth relies on three on-board processing steps: downsampling; pre-processing the data to ensure loss-less compression; and loss-less compression itself. To demonstrate these steps, a model of the input signal was used. Note that while the compression is loss-less, the pre-processing is not, due to the need to rescale the data and convert them to integers (a process named data re-quantization). However, the whole strategy is designed to keep strict control over the way in which lossy operations are done, and to quantify the amount of information loss in order to assess the optimal compression rate with minimal information loss.<br />
<br />
=== ''Instrument Operations'' ===<br />
<br />
==== ''Operational Modes'' ====<br />
<br />
The operations of the LFI are designed to be automatic and require little if any intervention from the ground. A small number of commands are required for operating the instrument and eventually for diagnostic and reconfiguration purposes.<br />
Each sky survey is conducted by the LFI with the instrument in the Normal Operations Mode. No deployable elements, or mechanically moving parts are included in the instrument. The scanning of the sky is achieved by progressive repointing of the satellite spin axis, with the Sun direction always within a cone 10&deg; from the spin axis.<br />
Within the Normal Science Mode the instrument can be configured in order to fit with different science or diagnostic needs without changing the power consumption and thus the temperature in the FPU. Changes in power consumption in the FPU are minimized and should occur only in the case that failures in the radiometers that could create interference problems require an RCA to be switched off. Power adjustments on the first stage of the HEMT amplifiers (which were contemplated), require extremely small power level variations.<br />
<br />
A brief summary of the LFI Operational Modes and the transitions between them is given in the corresponding section of the [[LFIAppendix#LFI Operational Modes|Annexes]].<br />
<br />
<!--<br />
==== ''In-flight Operations'' ====<br />
<br />
TBW<br />
<br />
<br />
==== ''Anomalies'' ====<br />
<br />
TBW<br />
--><br />
<br />
==<span id="LFITests">Ground Tests</span>==<br />
During its development, the LFI flight model was calibrated and tested at various integration levels from sub-systems (Davis et al. 2009{{BibCite|davis2009}}) to individual integrated receivers ({{PlanckPapers|villa2010}}) and the whole receiver array ({{PlanckPapers|mennella2010}}). In every campaign we performed tests according to the following classification:<br />
<br />
* ''functionality tests'', performed to verify the instrument functionality;<br />
* ''tuning tests'', to tune radiometer parameters (biases, DC electronics gain and offset, digital quantization and compression) for optimal performance in flight-like thermal conditions;<br />
* ''basic calibration and noise performance tests'', to characterize instrument performance (photometric calibration, isolation, linearity, noise and stability) in tuned conditions;<br />
* ''susceptibility tests'', to characterize instrument susceptibility to thermal and electrical variations.<br />
<br />
Where possible, the same tests were repeated in several test campaigns, in order to ensure enough redundancy and confidence in the repeatability of the instrument behaviour. A matrix showing the instrument parameters measured in the various test campaigns is provided in Table 1 of ({{PlanckPapers|mennella2010}}).<br />
<br />
The ground test campaign was developed in three main phases: cryogenic tests on the individual RCAs; cryogenic tests on the integrated receiver array (the so-called radiometer array assembly, RAA); and system-level tests after the integration of the LFI and HFI instruments onto the satellite. The first two phases were carried out at the Thales Alenia Space - Italia laboratories located in Vimodrone (Milano, Italy) (note that receiver tests on 70 GHz RCAs were carried out in Finland, at Yilinen laboratories), while system level tests (SLTs) were conducted in a dedicated cryofacility at the Centre Spatiale de Li&egrave;ge (CSL) located in Liege, Belgium. <br />
<br />
In Table 1 below we list the temperature of the main cold thermal stages during ground tests compared to in-flight nominal values. These values show that system-level tests were conducted in conditions that were as flight-representative as possible, while results obtained during RCA and RAA tests need to be extrapolated to flight conditions to allow comparison. Details of the RCA test campaign are discussed in ({{PlanckPapers|villa2010}}), while the RAA tests and the extrapolation methods are presented in ({{PlanckPapers|mennella2010}}).<br />
<br />
{| border="1" cellspacing="0" cellpadding="2" align="center"<br />
|+ '''<small>Table 1. Temperatures of the main cold stages during the various ground test campaigns compared to in-flight nominal values.</small>'''<br />
|-<br />
!scope="col"| Temperature <br />
!scope="col"| Nominal<br />
!scope="col"| RCA tests<br />
!scope="col"| RAA tests<br />
!scope="col"| System-level<br />
|-<br />
|width="120" | Sky<br />
|width="100" | ~ 3 K<br />
|width="100" | ≳ 8 K<br />
|width="100" | ≳ 18.5 K<br />
|width="100" | ~ 4 K<br />
|-<br />
|width="120" | Ref. load<br />
|width="100" | ~ 4.5 K<br />
|width="100" | ≳ 8 K<br />
|width="100" | ≳ 18.5 K<br />
|width="100" | ~ 4.5 K<br />
|-<br />
|width="120" | Front-end unit<br />
|width="100" | ~ 20 K<br />
|width="100" | ~ 20 K<br />
|width="100" | ~ 26 K<br />
|width="100" | ~ 20 K<br />
|-<br />
|}<br />
<br />
During the various test campaigns the instrument was switched off and moved several times in a time period of about three years. A series of functional tests were always repeated at each location and also in-flight, in order to verify the instrument functionality and the response repeatability. No failures or major problems have been identified due to transport and integration procedures.<br />
<br />
The expected Planck LFI scientific performance, resulting mainly from cryogenic system level tests, are described in ({{PlanckPapers|mennella2010}}).<br />
<br />
== <span id="LFICalibration">In-flight Calibration</span>==<br />
<br />
The LFI Commissioning and Calibration and Performance Verification (CPV) phases started on 4 June 2009 and lasted until 12 August 2009 when Planck started scanning the sky in nominal mode. At the onset of CPV, the active cooling started when the radiating surfaces on the payload module reached their working temperatures (approximately 50 K on the third V-groove, and 40 K on the reflectors) by passive cooling. This was achieved during the transfer phase. Nominal temperatures were achieved on 3 July 2009, when the dilution cooler temperature reached 0.1 K ({{PlanckPapers|planck2011-1-3}}, Meinhold et al. 2009 {{BibCite| meinhold2009}}). The cooldown of the HFI 4-K stage (see Fig. 4 below), was key during CPV for the LFI, because it provided a variable input signal that was exploited during bias tuning.<br />
<br />
The LFI Commissioning and CPV was carried out in four phases: <br />
* LFI switch-on and basic functionality verification (Commissioning);<br />
* tuning of front-end biases and back-end electronics (CPV);<br />
* preliminary calibration tests (CPV);<br />
* thermal tests (CPV). <br />
<br />
[[File:FUNCT_tests_schedule_vs_K-eps-converted-to.jpg|thumb|center|460px|'''Figure 4. Functional tests performed during CPV against timeline. Curves from thermal sensors monitoring the 4-K stage and the FPU temperature are superimposed.''']]<br />
<br />
Details of the LFI Commissioning and CPV test campaign are given in (Gregorio et al. 2013{{BibCite|gregorio2013}}).<br />
<br />
==<span id="LFIPerformance">Performance Summary</span>==<br />
<br />
A summary of the LFI performance parameters is given in Table 1 of the section titled [[Summary LFI|Summary of LFI data characteristics]]. <br />
<br />
=== Instrument scientific performance ===<br />
<br />
==== ''Optical parameters''====<br />
<br />
The most accurate measurements of the LFI main beams were made with Jupiter, the most powerful unresolved (to Planck) celestial source in the LFI frequency range. Since the LFI feedhorns point to different positions on the sky, they detect the signal at different times. <br />
To map the beam, each sample in the selected timelines was projected in the (<i>u</i>, <i>v</i>) plane perpendicular to the nominal line-of-sight (LOS) of the telescope (and at 85&deg; to the satellite spin axis). The <i>u</i> and <i>v</i> coordinates are defined in terms of the usual spherical coordinates (&theta;, &phi;) :<br />
<br />
: <math> u = \sin θ \, \cos φ, </math> <br />
: <math> v = \sin θ \, \sin φ. </math> <br />
<br />
To increase the signal-to-noise ratio, data were binned in an angular region of 2′ for the 70 GHz channels and 4′ for the 30 and 44 GHz channels. We recovered all beams down to −25 dB from the peak. An elliptical Gaussian was fit to each beam for both M and S radiometers. Differences between the M and S beams caused by optics and receiver non-idealities are inevitable at some level, but they appear to be well within the statistical uncertainties, and for the purposes of point-source extraction, the beams may be considered identical. For the details of the typical FWHM and ellipticity averaged over each frequency channel, refer to ({{PlanckPapers|planck2011-1-4 }}) and ({{PlanckPapers|planck2014-a05||Planck-2015-A05}}). Exhaustive details on all LFI beam parameters are presented in the LFI data processing section entitled [[Beams LFI|Beams]].<br />
<br />
==== ''Photometric Calibration''====<br />
<br />
Photometric calibration, i.e., conversion from voltage to antenna temperature, is performed for each radiometer after total power data have been cleaned of 1 Hz frequency spikes (see the LFI data processing section [[TOI processing LFI#Spikes Removal|Spikes Removal]] page and ({{PlanckPapers|planck2011-1-6 }}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}})), and differenced. Here we report a brief overview of the photometric calibration; for details see the LFI data processing section [[TOI processing LFI#Photometric Calibration|Photometric Calibration]].<br />
<br />
Our calibrator is the well-known dipole signal induced by spacecraft motion with respect to the CMB rest frame. The largest calibration uncertainty comes from the presence of the Galaxy and of the CMB anisotropies in the measured signal. We therefore use an iterative calibration procedure in which the dipole is fitted and subtracted, producing a sky map that is then removed from the original data to enhance the dipole signal for the next iteration. Typically, convergence is obtained after a few tens of iterations.<br />
<br />
In our current calibration model we use as a calibration signal the sum of the solar dipole &Delta;T<sub>Sun</sub> and the orbital dipole &Delta;T<sub>orb</sub>, which is the contribution from Planck’s orbital velocity around the Sun,<br />
<br />
<math> \label{eq:cal1} \Delta T= ( \Delta T_{\rm Sun} + \Delta T_{\rm orb} ) \sin \theta_{\rm axis} </math>,<br />
<br />
where &theta;<sub>axis</sub> is the angle between the spacecraft axis and the overall dipole axis (solar + orbital).<br />
In this equation, the absolute calibration uncertainty is dominated by the uncertainty in the solar dipole, which is known to about 0.2%. The modulation of the orbital dipole by Earth's motion around the Sun is known with an uncertainty almost three orders of magnitude smaller; however, at least one complete Planck orbit is needed for its measurement. We employ the orbital dipole as an absolute calibration.<br />
The accuracy of our current calibration can be estimated by taking into account two components: 1) the statistical uncertainty in time periods when the dipole signal is weak; and 2) the systematic uncertainty caused by neglecting gain fluctuations that occur on periods shorter than the smoothing window. In our calibration procedure the gain is estimated for every pointing period; if we call <i>G<sub>i</sub></i> the gain estimate from the <i>i</i>th pointing period, we have that the associated uncertainty is<br />
<br />
<math> \label{eq:cal2} \delta G = \sqrt{\frac{ \Sigma_{i=1}^N (G_i-< G>)^2 }{N-1} } </math>,<br />
<br />
where <i>N</i> is the overall number of pointing and <<i>G</i>> is the average of the <i>N</i> gains.<br />
We then approximate the effect of the smoothing filter as an average over <i>M</i> consecutive pointings, so that the overall uncertainty can be estimated as<br />
<br />
<math> \label{eq:cal3} \delta G |_{\rm stat} = \frac{\delta G}{\sqrt{M}} = \frac{1}{\sqrt{M}} <br />
\sqrt{\frac{ \Sigma_{i=1}^N (G_i-< G>)^2 }{N-1} } </math>.<br />
<br />
==== ''Noise Properties''====<br />
<br />
The noise characteristics of the LFI data streams are closely reproduced by a simple (white + 1/<i>f</i> ) noise model,<br />
<br />
<math> \label{eq:p1} P(f)= \sigma^2 \left[1+ \left(\frac{f}{f_{\rm knee}}\right)^\alpha \right] </math>,<br />
<br />
where <i>P</i>(<i>f</i>) is the power spectrum and &alpha;&asymp;−1.<br />
In this model, noise properties are characterized by three parameters, the white noise limit &sigma;, the knee frequency <i>f</i><sub>knee</sub>, and the exponent of the 1/<i>f</i> component &alpha;, also referred to as the slope. Here we give noise performance estimates based on one year of operations; details of the analysis are given in LFI data processing section ([[TOI processing LFI#Noise|Noise estimation]]) and in <br />
({{PlanckPapers|planck2011-1-6}}, {{PlanckPapers|planck2011-1-4 }}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}).<br />
<br />
Noise properties have been calculated following two different and complementary approaches: 1) fitting the equation above to time-ordered data for each radiometer; and 2) building normalized noise maps by differencing data from the first half of each pointing period with data from the second half of that pointing period to remove the sky signal (“jackknife” data sets).<br />
<br />
Typical uncertainties are 0.5% for the white noise, between 5 and 10% for the slope, and between 10 and 20% for the knee frequency.<br />
<br />
==== ''White Noise Sensitivity''====<br />
<br />
Details of the white noise sensitivity can be found in ({{PlanckPapers|planck2011-1-4}}). <br />
<br />
Table 2 summarizes the sensitivity numbers calculated during the first year of operations using methods and procedures described in detail in ({{PlanckPapers|planck2011-1-6}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}), compared with scientific requirements. The measured sensitivity is in very good agreement with pre-launch expectations. While the white noise moderately exceeds the design specification, this performance is fully in line with the LFI science objectives.<br />
<br />
{| border="1" cellspacing="0" cellpadding="2" align="center"<br />
|+ '''<small>Table 2. White noise sensitivity of the LFI frequency channels compared with requirements.</small>'''<br />
|-<br />
!scope="col"| Channel <br />
!scope="col"| Measurement [&mu;K<sub>CMB</sub> s<sup>1/2</sup>]<br />
!scope="col"| Requirement [&mu;K<sub>CMB</sub> s<sup>1/2</sup>]<br />
|-<br />
|width="120" | 70 GHz<br />
|width="100" | 152.0<br />
|width="100" | 119<br />
|-<br />
|width="120" | 44 GHz<br />
|width="100" | 174.2<br />
|width="100" | 119<br />
|-<br />
|width="120" | 30 GHz<br />
|width="100" | 148.1<br />
|width="100" | 119<br />
|-<br />
|}<br />
<br />
=== Instrument technical performance ===<br />
<br />
<br />
==== ''Spectral response''====<br />
<br />
The in-band receiver response was thoroughly modelled and measured for all the LFI detectors during ground tests. The complete set of bandpass curves was published in (Zonca et al. 2009{{BibCite|zonca2009}}) where all the details of the LFI radiometer's spectral response are given. From each curve we have derived the effective centre frequency according to:<br />
<br />
<math> \label{eq:spectr} <br />
\nu_0 = \frac{ \int_{\nu_{\rm min}}^{\nu_{\rm max}} \nu g(\nu) \; d \nu}<br />
{\int_{\nu_{\rm min}}^{\nu_{\rm max}} g(\nu)\; d\nu }<br />
</math> <br />
<br />
where &Delta;&nu; = &nu;<sub>max</sub> − &nu;<sub>min</sub> is the receiver bandwidth and <i>g</i>(&nu;) is the bandpass response. <br />
Details about colour corrections, <i>C</i>(&alpha;), needed to derive the brightness temperature of a source with a power-law spectral index &alpha;, are provided in <br />
<br />
Some details are also given in the corresponding section of the [[LFIAppendix#Spectral Response|Annexes]].<br />
<br />
<br />
===== ''Bandpass estimation''=====<br />
<br />
As detailed in (Zonca et al. 2009{{BibCite|zonca2009}}), our most accurate method to measure the LFI bandpasses is based on measurements of individual components integrated into the LFI Advanced RF Model (LARFM) to yield a synthesized radiometer bandpass.<br />
The LARFM is a software tool based on the open-source Quasi Universal Circuit Simulator (QUCS). The measured frequency responses of the various subsystems (feed-OMT, FEM, BEM) are considered as lumped S-parameter components. <br />
Measurements of single components are obtained with standard methods and provide highly reliable results, with precision of order 0.1-0.2 dB over the entire band.<br />
Waveguides are simulated with an analytical model, in order to reproduce the effect of their temperature gradient and the effect of standing waves caused by impedance mismatch at the interfaces between the FEM and BEM. This is because the 1.8-m long waveguides were not measured at unit level in cryogenic conditions. The model provides accurate agreement with the measured waveguide response in the conditions of the test measurements (300 K).<br />
The composite bandpasses are estimated to have a precision of about 1.5 to 2 dB.<br />
<br />
Some details are also given in the corresponding section of the [[LFIAppendix#Bandpass Estimation|Annexes]].<br />
<br />
==== ''Stability''====<br />
<br />
Thanks to its differential scheme, the LFI is insensitive to many effects caused by 1/<i>f</i> noise, thermal fluctuations, or electrical instabilities.<br />
As detailed in ({{PlanckPapers|planck2011-1-4}}), one effect detected during the first survey was the daily temperature fluctuation in the back-end unit induced by the downlink transponder, which was powered on each day for downlinks during the first 258 days of the mission. As expected, the effect is highly correlated between the sky and reference load signals. In the difference, the variation is reduced by a factor around (1 − <i>r</i>), where <i>r</i> is the gain modulation factor defined above (see <i>r</i> definition in [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section).<br />
<br />
A particular class of signal fluctuations occasionally observed during operations was due to electrical instabilities that appeared as abrupt increases in the measured drain current of the front-end amplifiers, with a relaxation time variable from few seconds to some hundreds of seconds. Typically, these events caused a simultaneous change in the sky and reference load signals. Because they are essentially common-mode, their residual on the differenced data is negligible, and the data are suitable for science production. In a few cases the residual fluctuation in the differential output was large enough (a few millikelvin in calibrated antenna temperature units) to be flagged, and the data were not used. The total amount of discarded data for all LFI channels until Operational Day 389 was about 2000s per detector, or 0.008%.<br />
<br />
A further peculiar effect appeared in the 44 GHz detectors, where single isolated samples, either on the sky or the reference voltage output, were clear outliers compared with the rest. Over a reference period of four months, 15 occurrences of single-sample spikes (out of 24 total anomaly events) were discarded, an insignificant loss of data.<br />
<br />
==== ''Thermal susceptibility''====<br />
<br />
As mentioned in the section [[LFI design, qualification, and performance#LFI In-flight Calibration|LFI In-flight Calibration]] above, and detailed in (Gregorio et al. 2013{{BibCite|gregorio2013}}), during the CPV campaign, susceptibility tests were performed in order to characterize the LFI instrument susceptibility to thermal and electrical variations.<br />
<br />
The effect of temperature fluctuations on the LFI radiometers originates in the Planck cold end interface of the hydrogen sorption cooler to the instrument focal plane. The temperature is actively controlled through a dedicated stage, the Thermal Stabilization Assembly (TSA), providing a first reduction of the effect. The thermal mass of the focal plane strongly contributes to reduce residual fluctuations.<br />
The physical temperature fluctuations propagated at the front end modules cause a correlated fluctuation in the radiometer signal, degrading the quality of scientific data. The accurate characterization of this effect is crucial for attempts to remove it from raw data by exploiting the housekeeping information on thermal sensors.<br />
<br />
The propagation of the temperature oscillations through the focal plane and the instrument response to thermal changes were characterized through two main tests: <br />
* the thermal dynamic response, aimed at measuring the dynamic thermal behaviour of the LFI Focal Plane;<br />
* the thermal susceptibility of the radiometers.<br />
<br />
Further details are also given in the corresponding section of the [[LFIAppendix#Thermal Susceptibility|Annexes]].<br />
<br />
==== Instrument budgets ====<br />
<br />
LFI power, mass and telemetry budgets are given in the corresponding section of the [[LFIAppendix#Instrument Budgets|Annexes]].<br />
<br />
== <span id="LFISystematics">Systematic Effects </span>==<br />
<br />
The LFI design was driven by the need to suppress systematic effects well below instrument white noise. The differential receiver scheme, with reference loads cooled to 4 K, greatly minimizes the effect of 1/<i>f</i> noise and common-mode fluctuations, such as thermal perturbations in the 20-K LFI focal plane. The use of a gain modulation factor (see <i>r</i> definition in the [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section above) largely compensates for spurious contributions from input offsets. Furthermore, diode averaging (see <i>V</i><sup>rad</sup><sub>out</sub> definition in the [[LFI design, qualification, and performance#Radiometer Chain Assembly (RCA)|RCA]] section above) allows us to cancel second-order correlations, such as those originating from phase switch imbalances.<br />
<br />
We have developed an error budget for systematic effects ({{PlanckPapers|bersanelli2010}}, {{PlanckPapers|planck2011-1-4}}{{PlanckPapers|planck2013-p02a}} and {{PlanckPapers|planck2014-a04||Planck-2015-A04}}) as a reference for both instrument design and data analysis. Our goal is to ensure that each systematic effect is rejected to the specified level, either by design or by robust removal in software. At this stage, the following effects are relevant:<br />
<br />
[[File:Selection_258.png|500px]]<br />
<br />
For each of these effects we used flight data and information from ground tests to build timelines, maps, and angular power spectra that represent our best knowledge of their impact on the scientific analysis.<br />
The details of the systematic effect analysis are given in the section entitled LFI data processing section ([[LFI systematic effect uncertainties|Systematic Effects uncertainties]]).<br />
<br />
== <span id="SCS">The Sorption Cooler</span> ==<br />
The Planck H2 Sorption Cooler is the first stage of the active cryogenic chain. Its task is to maintain the LFI down to the operating temperature while providing a pre-cooling stage for the HFI refrigerators. The system performs a simple thermodynamic cycle based on hydrogen compression, gas pre-cooling by three passive radiators, further cooling due to the heat recovery by the cold low pressure gas stream, expansion through a J-T valve, and evaporation at the cold stage ({{PlanckPapers|planck2011-1-3}}). A schematic of the Planck Sorption Cooler System (SCS) is shown in Fig. 5. The engine of the cryocooler is the compressor. It serves two main functions: to produce the high-pressure hydrogen gas flow; and to maintain a stable gas recovery rate, which keeps the return pressure, hence the liquid temperature, constant. The high pressure gas flowing to the cold end is pre-cooled by exchanging heat with the three passive stages at the V-Grooves and with the evaporated cold gas returning back to the compressor. The gas then expands at the cold end through a J-T valve, producing approximately 1 Watt of cooling power at a temperature of <20K: most of this heat lift is used at the LVHX2 (Liquid Vapour Heat eXchanger 2, see Fig. 5) interface to absorb the LFI heat load at a temperature around 20K. The remaining heat lift is used at the LVHX1 as a pre-cooling stage, at a temperature lower than 19 K, for the two HFI refrigerators. The cooler and its performance are described in detail in (Morgante et al. 2009{{BibCite|morgante2009}}). <br />
<br />
[[File:SCS_CAD_Figure.jpg|thumb|center|480px|'''Figure 5. Planck Sorption Cooler CAD view with labels of the main sub-systems.''']]<br />
<br />
Both LVHXs provide a temperature of around 18 K, with fluctuations driven by the cooler instabilities (compressor element variations, cycling, two-phase flow dynamics, etc.). Stabilization of the HFI interface (LVHX1) temperature is not necessary, since thermal control of the subsequent colder stages is more efficient and very effective. To reduce cold end fluctuations directly transmitted to the LFI radiometers, a copper block, designated as the Temperature Stabilization Assembly (TSA), is inserted, as an intermediate stage, between LVHX2 and the LFI Focal Plane Unit (FPU). The TSA comprises a temperature sensor and a heater, controlled by a PID-type feedback loop, working in combination with the passive thermal inertia. The set-point temperature of the TSA is an adjustable parameter of the sorption cooler system, chosen to provide dynamic range for control during mission: as the compressor elements age, the return gas pressure and thus the temperature of LVHX2 rise slowly. To keep the LFI temperature reference stable during operations the set point must be periodically adjusted to maintain the level of oscillations within the required range (Fig. 6).<br />
<br />
[[File:TSA_LVHX2_mission.jpg|thumb|center|480px|'''Figure 6. LVHX2 (black, HK parameter name SD029540) and TSA (red, HK parameter name SD030540) temperature profile from 125 to 563 days after launch.''']]<br />
<br />
Two sorption cooler units were integrated on-board the Planck spacecraft. Both units were used to cover the mission lifetime, with one cooler operated for the first two sky surveys. At the end of its lifetime a switchover operation, performed on August 11th 2010 (455 days after launch), activated the second unit that ran since then. The LVHX2 temperature change due to the new cooler start, and the subsequent re-adjustment of the LFI temperature stabilization stage, is clear in Fig. 6.<br />
<br />
<!--<br />
== Acronyms ==<br />
<br />
: ADC Analog-to-Digital Converter<br />
: ADU Analog-to-Digital Unit<br />
: BEM Back End Module <br />
: BEU Back End Unit <br />
: CCE Central Check-out Equipment<br />
: CDMS Command and Data Management Subsystem<br />
: CDMU Central Data Management Unit<br />
: CoG Centre of Gravity<br />
: CPV Calibration and Performance Verification<br />
: CSL Centre Spatiale de Liege<br />
: DAE Data Acquisition Electronics <br />
: DC Direct Current<br />
: DPC Data Processing Centre<br />
: DPU Digital Processing Unit<br />
: EMC Electro-Magnetic Compatibility<br />
: EMI Electro-Magnetic Interference<br />
: FEM Front End Module <br />
: FEU Front End Unit<br />
: FH Feed Horn<br />
: FOV Field Of View<br />
: FPU Focal Plane Unit<br />
: HK House Keeping<br />
: ILT Instrument Level Test<br />
: IST Integrated System Test<br />
: JFET Junction Field Effect Transistor<br />
: LEOP Launch and Early Orbit Phase<br />
: MLI Multilayer Insulation<br />
: MoI Moment of Inertia<br />
: MOS Margin Of Safety<br />
: OMT Ortho Module Transducer <br />
: PCS Power Control Subsystem<br />
: PSF Point Spread Function<br />
: RAA Radiometer Array Assembly <br />
: RAM Random Access Memory<br />
: RCA Radiometer Chain Assembly <br />
: REBA Radiometer Electronics Box Assembly <br />
: S/C Spacecraft<br />
: SCC Sorption Cooler Compressor assembly <br />
: SCCE Sorption Cooler Cold End <br />
: SCE Sorption Cooler Electronics <br />
: SCOS Spacecraft Control and Operations System<br />
: SCP Sorption Cooler Piping <br />
: SCS Sorption Cooler Subsystem <br />
: SLT System Level Test<br />
: SPU Signal Processing Unit<br />
: SS Stainless Steel<br />
: SVM Service Module<br />
: TCS Thermal Control System<br />
: TM Telemetry<br />
: TSA Thermal Stabilization Assembly<br />
: TTC Telemetry, Tracking and Command<br />
: VSWR Voltage Standing Wave Ratio <br />
: WG Waveguide<br />
<br />
== Glossary ==<br />
<br />
: Feed Horns xxx <br />
: REBA Radiometer Electronics Box Assembly<br />
--><br />
<br />
== References ==<br />
<br />
<References /><br />
<br />
<br />
[[Category:LFI design, qualification and performance|001]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Cosmological_Parameters&diff=11295Cosmological Parameters2015-02-04T19:04:16Z<p>Agregori: </p>
<hr />
<div>{{DISPLAYTITLE:Cosmological parameters and MC chains}}<br />
== Description ==<br />
<br />
The cosmological parameter results explore a variety of cosmological models with combinations of Planck and other data. We provide results from MCMC exploration chains, as well as best fits, and sets of parameter tables. Definitions, conventions and reference are contained in {{PlanckPapers|planck2013-p11}} {{PlanckPapers|planck2014-a15||Planck-2015-A15}}.<br />
<br />
==Production process==<br />
<br />
Parameter chains are produced using CosmoMC, a sampling package available [http://cosmologist.info/cosmomc here]. This includes the sample analysis package (and GUI) GetDist, and the scripts for managing, analysing, and plotting results from the full grid or runs. Chain products provided here have had burn in removed. Some results with additional data are produced by importance sampling.<br />
<br />
Note that the baseline model includes one massive neutrino (0.06eV). Grid outputs include WMAP 9 results for consistent assumptions.<br />
<br />
== Caveats and known issues ==<br />
<br />
# Confidence intervals are derived from the MCMC samples, and assume the input likelihoods are exactly correct, so there is no quantification for systematic errors other than via the covariance, foreground and beam error models assumed in the likelihood codes. <br />
# Non-linear lensing modelling uses Halofit; for some extended models and CMB lensing only analyses, tails of the chains may be away from the domain of validity.<br />
# The CAMB version used for most results is Dec 2014; the Jan 2015 version is used for lensing-only models with neutrinos, and only differs in the neutrino corrections to the Halofit model.<br />
# There is evidence of temperature-polarization leakage that may affect results including high-L polarization, use caution in the interpretation of results including polarization<br />
# Alternative CamSpec likelihood results in the tables are generated using a slightly older CosmoMC version, with fewer derived parameters and a slightly different BBN predictions for the helium abundance.<br />
<br />
== Related products ==<br />
<br />
Results of the parameter exploration runs should be reproducible using CosmoMC with the Planck likelihood code.<br />
<br />
== Parameter Tables ==<br />
<br />
These list parameter constraints for each considered model and data combination separately. For the baseline likelihood see<br />
<br />
* PDF tables with 68% limits [[File:baseline_params_table_2015_limit68.pdf]]<br />
* PDF tables with 95% limits [[File:baseline_params_table_2015_limit95.pdf]]<br />
<br />
There are also larger files including alternative CamSpec and DetSet likelihood results, along with shifts in parameters compared to baseline in units of the baseline error:<br />
<br />
* PDF tables with 68% limits [[File:params_table_2015_limit68.pdf]]<br />
* PDF tables with 95% limits [[File:params_table_2015_limit95.pdf]]<br />
<br />
<br />
Data combination tags used to label results are as follows (see {{PlanckPapers|planck2013-p11}} for full description and references):<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Tag|| Data<br />
|-<br />
| '''plikHM''' || baseline high-L Planck power spectra (plik cross half-mission, 30 <= l <= 2508)<br />
|-<br />
| '''plikDS''' || high-L Planck power spectra (plik cross detsets, 30 <= l <= 2508)<br />
|-<br />
| '''CamSpecHM''' || high-L Planck power spectra (CamSpec cross half-mission, 30 <= l <= 2500)<br />
|-<br />
| '''CamSpecDS''' || high-L Planck power spectra (CamSpec cross detsets, 30 <= l <= 2500)<br />
|-<br />
| '''lowl''' || low-L: Planck temperature only (2 <= l <= 29)<br />
|-<br />
| '''lowTEB''' || low-L temperature and LFI polarization (2 <= l <= 29)<br />
|-<br />
| '''lowEB''' || low-L LFI polarization only (2 <= l <= 29)<br />
|-<br />
| '''WMAPTEB''' || low-L temperature, and LFI+WMAP polarization (2 <= l <= 29)<br />
|-<br />
| '''lensing''' || Planck lensing power spectrum reconstruction<br />
|-<br />
| '''lensingonly''' || Planck lensing power spectrum reconstruction only; T,E fixed to best-fit spectrum + priors<br />
|-<br />
| '''BKP''' || The Bicep-Keck-Planck fiducial B mode likelihood<br />
|-<br />
| '''zre6p5''' || A hard prior z_re > 6.5<br />
|-<br />
| '''tau07''' || A Gaussian prior on the optical depth, tau = 0.07 +- 0.02<br />
|-<br />
| '''reion''' || A hard prior z_re > 6.5, combined with Gaussian prior z_re = 7 +- 1<br />
|-<br />
| '''BAO''' || Baryon oscillation data from DR11LOWZ, DR11CMASS, MGS and 6DF<br />
|-<br />
| '''JLA''' || Supernova data from the SDSS-II/SNLS3 Joint Light-curve Analysis<br />
|-<br />
| '''H070p6''' || Hubble parameter constraint, H_0 = 70.6 +- 3.3<br />
|-<br />
| '''theta''' || theta_MC fixed to 1.0408<br />
|-<br />
| '''WLonlyHeymans''' || Conservative cut of the CFHTLenS weak lensing data + priors<br />
|-<br />
| '''WMAP''' || The full WMAP (temperature and polarization) 9 year data <br />
|}<br />
<br />
The high-L Planck likelihoods have TT, TE, EE variants from each spectrum alone, plus the TTTEEE joint constraint.<br />
<br />
<br />
Tags used to identify the model parameters that are varied are described in [[File:parameter_tag_definitions_2015.pdf]]. <br />
<br />
== Parameter Chains ==<br />
<br />
We provide the full chains and getdist outputs for our parameter results. The entire grid of results is available from as a 3.7GB compressed file:<br />
<!--- * {{PLASingleFile|fileType=cosmo|name= COM_CosmoParams_R2.00.tar.gz|link=Full Grid Download}} ----><br />
* ''COM_CosmoParams_R2.nn.tar.gz''<br />
Where ''nn'' is the most recent update. You can also download the Bicep2/Keck/Planck (BKP) joint constraints for +r models, and smaller files containing key results in the base model only: <br />
<!---* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_plikHM_TT_lowTEB_R2.00.tar.gz|link=Baseline LCDM chains with plikHM_TT_lowTEB}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_plikHM_TT_lowTEB_R2.00.tar.gz|link=Baseline LCDM chains with all plikHM combinations}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_lensonly_R2.00.tar.gz|link=CMB lensing only in LCDM}} ---><br />
* ''COM_CosmoParams_base_plikHM_TT_lowTEB_R2.nn.tar.gz''<br />
* ''COM_CosmoParams_base_plikHM_R2.nn.tar.gz''<br />
* ''COM_CosmoParams_base_lensonly_R2.nn.tar.gz''<br />
* ''COM_CosmoParams_base_r_plikHM_BKP_R2.nn.tar.gz''<br />
<br />
The download contains a hierarchy of directories, with each separate chain in a separate directory. The structure for the directories is<br />
<br />
: '' base_AAA_BBB/XXX_YYY_.../''<br />
<br />
where AAA and BBB are any additional parameters that are varied in addition to the six parameters of the baseline model. XXX, YYY, etc encode the data combinations used. These follow the naming conventions described above under Parameter Tables. Each directory contains the main chains, 4-8 text files with one chain in each, and various other files all with names of the form<br />
<br />
: ''base_AAA_BBB_XXX_YYY.ext''<br />
<br />
where ''ext'' describes the type of file, and the possible values or ''ext'' are<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Extension || Data<br />
|-<br />
| '''.txt''' || parameter chain file with burn in removed<br />
|-<br />
| '''.paramnames''' || File that describes the parameters included in the chains<br />
|-<br />
| '''.inputparams''' || Input parameters used when generating the chain<br />
|-<br />
| '''.minimum''' || Best-fit parameter values, -log likelihoods and chi-square<br />
|-<br />
| '''.minimum.theory_cl''' || The best-fit temperature and polarization power spectra and lensing potential (see below)<br />
|-<br />
| '''.minimum.plik_foregrounds''' || The best-fit foreground model (additive component) for each data power spectrum used<br />
|-<br />
| '''.minimum.inputparams''' || Input parameters used when generating the best fit<br />
|-<br />
| '''.ranges''' || prior ranges assumed for each parameter<br />
|}<br />
<br />
<br />
In addition each directory contains any importance sampled outputs with additional data. These have names of the form<br />
<br />
: ''base_AAA_BBB_XXX_YYY_post_ZZZ.ext''<br />
<br />
where ZZZ is the data likelihood that is added by importance sampling. Finally, each directory contains a ''dist'' subdirectory, containing results of chain analysis. File names follow the above conventions, with the following extensions<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Extension || Data<br />
|-<br />
| '''.margestats''' || mean, variance and 68, 95 and 99% limits for each parameter (see below)<br />
|-<br />
| '''.likestats''' || parameters of best-fitting sample in the chain (generally different from the .minmum global best-fit)<br />
|-<br />
| '''.covmat''' || Covariance matrix for the MCMC parameters<br />
|-<br />
| '''.corr''' || Correlation matrix for the parameters<br />
|-<br />
| '''.converge''' || A summary of various convergence diagnostics<br />
|}<br />
<br />
<br />
Python scripts for reading in chains and calculating new derived parameter constraints are available as part of CosmoMC, see the readme for details [http://cosmologist.info/cosmomc/readme_planck.html]. The config directory in the download includes information about the grid configuration used by the plotting and grid scripts.<br />
<br />
== File formats ==<br />
<br />
The file formats are standard Jan 2015 CosmoMC outputs. CosmoMC includes python scripts for generating tables, 1D, 2D and 3D plots using the provided data, as well as a GUI for conveniently making plots from grid downloads. The formats are summarised here:<br />
<br />
; Chain files<br />
: Each chain file is ASCII and contains one sample on each line. Each line is of the format<br />
<br />
: '' weight like param1 param2 param3 …''<br />
<br />
: Here ''weight'' is the importance weight or multiplicity count, and ''like'' is the total -log Likelihood. ''param1'',''param2'', etc are the parameter values for the sample, where the numbering is defined by the position in the accompanying .paramnames files.<br />
<br />
: Note that burn in has been removed from the cosmomc outputs, so full chains provided can be used for analysis. Importance sampled results (with ''_post'') in the name have been thinned by a factor of 10 compared to the original chains, so the files are smaller, but this does not significantly affect the effective number of samples. Note that due to the way MCMC works, the samples in the chain outputs are not independent, but it is safe to use all the samples for estimating posterior averages.<br />
<br />
;.margestats files<br />
: Each row contains the marginalized constraint on individual parameters. The format is fairly self explanatory given the text description in the file, with each line of the form<br />
<br />
: '' parameter mean sddev lower1 upper1 limit1 lower2 upper2 limit2 lower3 upper3 limit3''<br />
<br />
: where sddev is the standard deviation, and the limits are 1: 68%, 2: 95%, 3: 99%. The limit tags specify whether a given limit is one tail, two tail or none (if no constraint within the assumed prior boundary). <br />
<br />
;.minimum.theory_cl files<br />
: They contain the best-fit theoretical power spectra (without foregrounds) for each model. The columns are: <math>l</math>, <math>D^{TT}_l</math>, <math>D^{TE}_l</math>, <math>D^{EE}_l</math>, <math>D^{BB}_l</math>, and <math>D^{dd}_l</math>, were <math>D_l \equiv l(l+1) C_l / (2\pi)</math> in <math>\mu{\rm K}^2</math>. Also <math>D^{dd}_l= [l(l+1)]^2 C^{\phi\phi}_l/(2\pi)</math> is the power spectrum of the lensing deflection angle, where <math>C^{\phi\phi}_l</math> is the lensing potential power spectrum. Note that the lensing spectrum may not be accurate at L > 400 due to the maximum wavenumber and non-linear correction accuracy settings.<br />
<br />
<br />
== References ==<br />
<br />
<br />
<References /><br />
<br />
<br />
<br />
<br />
<br />
[[Category:Mission products|009]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_and_astrophysical_component_maps&diff=11293CMB and astrophysical component maps2015-02-04T18:58:44Z<p>Agregori: /* SMICA */</p>
<hr />
<div>== Overview ==<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the product and how it is obtained, followed by a description of the FITS file containing the data and associated information.<br />
All the details can be found in {{PlanckPapers|planck2014-a11}} and {{PlanckPapers|planck2014-a12}}.<br />
<br />
==CMB maps==<br />
CMB maps have been produced by the COMMANDER, NILC, SEVEM, and SMICA pipelines, which are described in the [[Astrophysical_component_separation#CMB_and_foreground_separation | CMB and foreground separation]] section and also in Appendices A-D of {{PlanckPapers|planck2014-a11}} and references therein.. For each pipeline we provide:<br />
* Full-mission CMB intensity map, confidence mask and beam transfer function.<br />
* Full-mission high-pass filtered CMB polarisation map, <br />
* A confidence mask.<br />
* A beam transfer function.<br />
In addition, and for characterisation purposes, there are six other sets of maps from three data splits: first/second half-ring, odd/even years and first/second half-mission. And for each of these data splits we provide half-sum and half-difference maps. The half-difference maps can be used to provide an approximate noise estimate for the full mission, but they should be used with caution. Each split has caveats in this regard: there are noise correlations between the half-ring maps, and missing pixels in the other splits. The Intensity maps are provided at Nside = 2048, at 5 arcmin resolution, while the Polarisation ones are provided at Nside = 1024 at 10 arcmin resolution. All maps are in units of K<sub>cmb</sub>.<br />
<br />
These maps can be found in the files <br />
* ''COM_CMB_IQU-{pipeline}-field-{Int/Pol}_Nside_R2.00.fits''. <br />
The ''Int'' files have two extensions, for the Intensity maps and the beam transfer function, the ''Pol'' files have three extensions, for Q and U maps, and for the beam transfer function.<br />
For a complete description of the data structure, see the [[#File names and structure | below]]; the content of the first extensions is illustrated and commented in the table below.<br />
<br />
The gallery below shows the Intensity, noise from half-mission, half-difference, and confidence mask for the four pipelines, in the order SMICA, SEVEM, NILC and COMMANDER, from top to bottom. The Intensity maps scale is [–500.+500] μK, and the noise are between [–25,+25] μK. We do not show the Q and U maps since they have no significant visible structure to contemplate.<br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=300px heights=180> <br />
File:CMB_commander_tsig.png | '''commander temperature'''<br />
File:CMB_commander_tnoi.png | '''commander noise'''<br />
File:CMB_commander_tmask.png | '''commander mask'''<br />
File:CMB_nilc_tsig.png | '''nilc temperature'''<br />
File:CMB_nilc_tnoi.png | '''nilc noise'''<br />
File:CMB_nilc_tmask.png | '''nilc mask'''<br />
File:CMB_sevem_tsig.png | '''sevem temperature'''<br />
File:CMB_sevem_tnoi.png | '''sevem noise'''<br />
File:CMB_sevem_tmask.png | '''sevem mask'''<br />
File:CMB_smica_tsig.png | '''smica temperature'''<br />
File:CMB_smica_tnoi.png | '''smica noise'''<br />
File:CMB_smica_tmask.png | '''smica mask'''</gallery><br />
</center><br />
<br />
===Product description ===<br />
<br />
====COMMANDER====<br />
<br />
;Principle<br />
<br />
: COMMANDER is a Planck software code implementing pixel based Bayesian parametric component separation. Each astrophysical signal component is modelled in terms of a small number of free parameters per pixel, typically in terms of an amplitude at a given reference frequency and a small set of spectral parameters, and these are fitted to the data with an MCMC Gibbs sampling algorithm. Instrumental parameters, including calibration, bandpass corrections, monopole and dipoles, are fitted jointly with the astrophysical components. A new feature in the Planck 2015 analysis is that the astrophysical model is derived from a combination of Planck, WMAP and a 408 MHz (Haslam et al. 1982) survey, providing sufficient frequency support to resolve the low-frequency components into synchrotron, free-free and spinning dust. For full details, see {{PlanckPapers|planck2014-a12}}.<br />
<br />
; Resolution (effective beam)<br />
<br />
: The Commander sky maps have different angular resolutions depending on data products:<br />
* The components of the full astrophysical sky model derived from the complete data combination (Planck, WMAP, 408 MHz) have a 1 degree FWHM resolution, and are pixelized at N<sub>side</sub>=256. The corresponding CMB map defines the input map for the low-l Planck 2015 temperature likelihood. <br />
* The Commander CMB temperature map derived from Planck-only observations have an angular resolution of ~5 arcmin and is pixelized at N<sub>side</sub>=2048. This map is produced by harmonic space hybridiziation, in which independent solutions derived at 40 arcmin (using 30-857 GHz data), 7.5 arcmin (using 143-857 GHz data), and 5 arcmin (using 217-857 GHz data) are coadded into a single map.<br />
* The Commander CMB polarization map has an angular resolution of 10 arcmin and is pixelized at N<sub>side</sub>=1024. As for the temperature case, this map is produced by harmonic space hybridiziation, in which independent solutions derived at 40 arcmin (using 30-353 GHz data) and 10 arcmin (using 100-353 GHz data) are coadded into a single map.<br />
<br />
; Confidence mask<br />
<br />
: The Commander confidence masks are produced by thresholding the chi-square map characterizing the global fits, combined with direct CO amplitude thresholding to eliminate known leakage effects. In addition, we exclude the 9-year WMAP point source mask in the temperature mask. For full details, see Sections 5 and 6 in {{PlanckPapers|planck2014-a12}}. A total of 81% of the sky is admitted for high-resolution temperature analysis, and 83% for polarization analysis. For low-resolution temperature analysis, for which the additional WMAP and 408 MHz observations improve foreground constraints, a total of 93% of the sky is admitted. <br />
<br />
====NILC====<br />
<br />
;Principle<br />
<br />
: The Needlet-ILC (hereafter NILC) CMB map is constructed both in total intensity as well as polarization, Q and U Stokes parameters. For total intensity, all Planck frequency channels are included. For polarization, all polarization sensitive frequency channels are included, from 30 to 353 GHz. The solution, for T, Q and U is obtained by applying the Internal Linear Combination (ILC) technique in needlet space, that is, with combination weights which are allowed to vary over the sky and over the whole multipole range. <br />
<br />
; Resolution (effective beam)<br />
<br />
: The spectral analysis, and estimation of the NILC coefficients, is performed up to a maximum <math>\ell=4000</math>. The effective beam is equivalent of a Gaussian circular beam with FWHM=5 arcminutes. <br />
<br />
; Confidence mask<br />
<br />
: The same procedure is followed by SMICA and NILC for producing confidence masks, though with different parametrizations. A low resolution smoothed version of the NILC map, noise subtracted, is thresholded to 73.5 squared micro-K for T, and 6,75 squared micro-K for Q and U.<br />
<br />
<br />
====SEVEM====<br />
;Principle<br />
<br />
:SEVEM produces clean CMB maps at several frequencies by using a procedure based on template fitting in real space. The templates are typically constructed from the lowest and highest Planck frequencies and then subtracted from the CMB-dominated channels, with coefficients that are chosen to minimize the variance of the clean map outside a considered mask. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. Two single frequency clean maps are then combined to obtain the final CMB map.<br />
<br />
;Resolution<br />
<br />
:For intensity the clean CMB map is constructed up to a maximum <math>\ell=4000</math> at Nside=2048 and at the standard resolution of 5 arcminutes (Gaussian beam).<br />
:For polarization the clean CMB map is produced at Nside=1024 with a resolution of 10 arcminutes (Gaussian beam) and a maximum <math>\ell=3071</math>.<br />
<br />
;Confidence masks<br />
<br />
:The confidence masks cover the most contaminated regions of the sky, leaving approximately 85 per cent of useful sky for intensity and 80 per cent for polarization.<br />
<br />
<br />
<br />
====SMICA====<br />
; Principle<br />
: SMICA produces CMBs map by linearly combining all Planck input channels with multipole-dependent weights. It includes multipoles up to <math>\ell = 4000</math>. Temperature and polarization maps are produced independently.<br />
; Resolution (effective beam)<br />
: The SMICA intensity map has an effective beam window function of 5 arc-minutes which is truncated at <math>\ell=4000</math> and is '''not''' deconvolved from the pixel window function. Thus the delivered beam window function is the product of a Gaussian beam at 5 arcminutes and the pixel window function for <math>N_{side}</math>=2048.<br />
: The SMICA Q and U maps are obtained similarly but are produced at <math>N_{side}</math>=1024 with an effective beam of 10 arc-minutes (to be multiplied by the pixel window function, as for the intensity map).<br />
; Confidence mask<br />
: A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and the masked point sources. This mask provides a qualitative (and subjective) indication of the cleanliness of a pixel. See section below detailing the production process.<br />
<br />
===Production process===<br />
<br />
====COMMANDER====<br />
<br />
; Pre-processing<br />
<br />
: All sky maps are first convolved to a common resolution that is larger than the largest beam of any frequency channel. For the combined Planck, WMAP and 408 MHz temperature analysis, the common resolution is 1 degree FWHM; for the Planck-only all-frequency analysis it is 40 arcmin FWHM; and for the intermediate-resolution analysis it is 7.5 arcmin; while for the full-resolution analysis, we assume all frequencies between 217 and 857 GHz have a common resolution, and no additional convolution is performed. For polarization, only two smoothing scales are employed, 40 and 10 arcmin, respectively. The instrumental noise rms maps are convolved correspondingly, properly accouting for their matrix-like nature. <br />
<br />
; Priors<br />
<br />
: The following priors are enforced in the Commander analysis:<br />
* All foreground amplitudes are enforced to be positive definite in the low-resolution analysis, while no amplitude priors are enforced in the high-resolution analyses<br />
* Monopoles and dipoles are fixed to nominal values for a small set of reference frequencies<br />
* Gaussian priors are enforced on spectral parameters, with values informed by the values derived in the high signal-to-noise areas of the sky<br />
* The Jeffreys ignorance prior is enforced on spectral parameters in addition to the informative Gaussian priors<br />
<br />
; Fitting procedure<br />
<br />
: Given data and priors, Commander either maximizes, or samples from, the Bayesian posterior, P(theta|data). Because this is a highly non-Gaussian and correlated distribution, involving millions of parameters, these operations are performed by means of the Gibbs sampling algorithm, in which joint samples from the full distributions are generated by iteratively sampling from the corresponding conditional posterior distributions, P(theta_i| data, theta_{j/=i}). For the low-resolution analysis, all parameters are optimized jointly, while in the high-resolution analyses, which employs fewer frequency channels, low signal-to-noise parameters are fixed to those derived at low resolution. Examples of such parameters include monopoles and dipoles, calibration and bandpass parameters, thermal dust temperature etc.<br />
<br />
====NILC====<br />
<br />
; Pre-processing<br />
<br />
: All sky frequency maps are deconvolved using the DPC beam transfer function provided, and re-convolved with a 5 arcminutes FWHM circular Gaussian beam. In polarization, prior to the smoothing process, all sky E and B maps are derived from Q and U using standard HEALPix tools from each individual frequency channels <br />
<br />
; Linear combination<br />
<br />
: Pre-processed input frequency maps are decomposed in needlet coefficients, specified in the Appendix B of the Planck A11 paper, with shape given by Table B.1. Minimum variance coefficients are then obtained, using all channels for T, from 30 to 353 for E and B. <br />
<br />
; Post-processing<br />
<br />
: E and B maps are re-combined into Q and U products using standard HEALPix tools. <br />
<br />
====SEVEM====<br />
<br />
The templates used in the SEVEM pipeline are typically constructed by subtracting two close Planck frequency channel maps, after first smoothing them to a common resolution to ensure that the CMB signal is properly removed. A linear combination of the templates <math>t_j</math> is then subtracted from (hitherto unused) map d to produce a clean CMB map at that frequency. This is done in real space at each position on the sky: <math> T_c(\mathbf{x}, ν) = d(\mathbf{x}, ν) − \sum_{j=1}^{n_t} α_j t(\mathbf{x}) </math><br />
where <math>n_t</math> is the number of templates. The <math>α_j</math> coefficients are obtained by minimising the variance of the clean map <math>T_c</math> outside a given mask. Note that the same expression applies for I, Q and U. Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although we expect that foreground residuals are present in the excluded areas).<br />
<br />
There are several possible configurations of SEVEM with regard to the number of frequency maps which are cleaned or the number of templates that are used in the fitting. Note that the production of clean maps at different frequencies is of great interest in order to test the robustness of the results. Therefore, to define the best strategy, one needs to find a compromise between the number of maps that can be cleaned independently and the number of templates that can be constructed.<br />
<br />
;Intensity<br />
<br />
For the CMB intensity map, we have cleaned the 100 GHz, 143 GHz and 217 GHz maps using a total of four templates. Three of them are constructed as the difference of two consecutive Planck channels smoothed to a common resolution (30-44, 44-70 and 545-353) while the 857 GHz channel is chosen as the fourth template. First of all, the six frequency channels which are going to be part of the templates are inpainted at the point source positions detected using the Mexican Hat Wavelet algorithm. The size of the holes to be inpainted is determined taking into account the beam size of the channel as well as the flux of each source. The inpainting algorithm is based on simple diffuse inpainting, which fills one pixel with the mean value of the neighbouring pixels in an iterative way. To avoid inconsistencies when subtracting two channels, each frequency map is inpainted on the sources detected in that map and on the second map (if any) used to construct the template. Then the maps are smoothed to a common resolution (the first channel in the subtraction is smoothed with the beam of the second map and viceversa). For the 857 GHz template, we simply filter the inpainted map with the 545 GHz beam.<br />
<br />
The coefficients are obtained by minimising the variance outside the analysis mask, that covers the 1 per cent brightest emission of the sky as well as point sources detected at all frequency channels. Once the maps are cleaned, each of them is inpainted on the point sources positions detected at that (raw) channel. Then, the MHW algorithm is run again, now on the clean maps. A relatively small number of new sources are found and are also inpainted at each channel. The resolution of the clean map is the same as that of the original data. Our final CMB map is then constructed by combining the 143 and 217 GHz maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of fwhm=5 arcminutes.<br />
<br />
The confidence mask is produced by studying the differences between several SEVEM CMB reconstructions, which correspond to maps cleaned at different frequencies or using different analysis masks. The obtained mask leaves a useful sky fraction of approximately 85 per cent.<br />
<br />
;Polarization<br />
<br />
To clean the polarization maps, a procedure similar to the one used for intensity data is applied to the Q and U maps independently. However, given that a narrower frequency coverage is available for polarization, the selected templates and maps to be cleaned are different. In particular, we clean the 70, 100 and 143 GHz using three templates for each channel. The first step of the pipeline is to inpaint the positions of the point sources using the MHW, in those channels which are going to be used in the construction of templates, following the same procedure as for the intensity case. The inpainting is performed in the frequency maps at their native resolution. These inpainted maps are then used to construct a total of four templates. To trace the synchrotron emission, we construct a template as the subtraction of the 30 GHz minus the 44 GHz <br />
map, after being convolved with the beam of each other. For the dust emission, the following templates are considered: 353-217 GHz (smoothed at 10' resolution), 217-143 GHz (used <br />
to clean 70 and 100 GHz) and 217-100 GHz (to clean 143 GHz). These two last templates are constructed at 1 degree resolution since an additional smoothing becomes necessary in<br />
order to increase the signal-to-noise ratio of the template. Conversely to the <br />
intensity case and due to the lower availability of frequency channels, it becomes necessary to use the maps to be cleaned as part of one of the templates. In this way, the 100 GHz <br />
map is used to clean the 143 GHz frequency channel and viceversa, making the clean maps less independent between them than in the intensity case.<br />
<br />
These templates are then used to clean the non-inpainted 70 (at its native resolution), 100 (at 10' resolution) and 143 GHz maps (also at 10'). The corresponding linear coefficients are estimated independently for Q and U by minimising the variance of the clean maps outside a mask, that covers point sources and the 3 per cent brightest Galactic emission. Once the maps have been cleaned, inpainting of the point sources detected at the corresponding raw maps is carried out. The size of the holes to be inpainted takes<br />
into account the additional smoothing of the 100 and 143 GHz maps. The 100 and 143 GHz clean maps are then combined in harmonic space, using E and B decomposition, to produce the final CMB maps for the Q and U components at a resolution of 10' (Gaussian beam) for a HEALPix parameter Nside=1024. Each map is weighted taking into account its <br />
corresponding noise level at each multipole. Finally, before applying the post-processing HPF to the clean polarization data, the region with the brightest Galactic residuals is inpainted (5 per cent of the sky) to avoid the introduction of ringing around the Galactic centre in the filtering process.<br />
<br />
The confidence mask includes all the pixels above a given threshold in a smoothed version of the clean CMB map, the regions more contaminated by the CO emission and those pixels more affected by the high-pass filtering, leaving a useful sky fraction of approximately 80 per cent.<br />
<br />
<br />
<br />
====SMICA====<br />
<br />
A) Production of the intensity map.<br />
<br />
; 1) Pre-processing<br />
: Before computing spherical harmonic coefficients, all input maps undergo a pre-processing step to deal with regions of very strong emission (such as the Galactic center) and point sources. The point sources with SNR > 5 in the PCCS catalogue are fitted in each input map. If the fit is successful, the fitted point source is removed from the map; otherwise it is masked and the hole is filled in by a simple diffusive process to ensure a smooth transition and mitigate spectral leakage. The diffusive inpainting process is also applied to some regions of very strong emissions. This is done at all frequencies but 545 and 857 GHz, here all point sources with SNR > 7.5 are masked and filled-in similarly.<br />
; 2) Linear combination<br />
: The nine pre-processed Planck frequency channels from 30 to 857 GHz are harmonically transformed up to <math>\ell = 4000</math> and co-added with multipole-dependent weights as shown in the figure.<br />
; 3) Post-processing<br />
: A confidence mask is determined (see the Planck paper) and all regions which have been masked in the pre-processing step are added to it.<br />
<br />
<!--[[File:Smica_filter_dx11.png|thumb|center|600px|'''Weights given by SMICA to the input intensity maps (after they are re-beamed to 5 arc-minutes and expressed in K<math>_\rm{RJ}</math>), as a function of multipole.''']]--><br />
<br />
B) Production of the Q and U polarisation maps.<br />
<br />
The SMICA pipeline for polarization uses all the 7 polarized Planck channels. The production of the Q and U maps is similar to the production of the intensity map. However, there is no input point source pre-processing of the input maps. The regions of very strong emission are masked out using an apodized mask before computing the E and B modes of the input maps and combining them to produce the E and B modes of the CMB map. Those modes are then used to synthesize the U and Q CMB maps. The E and B parts of the input frequency maps being processed jointly, there are, at each multipole, 2*7=14 coefficients (weights) defined to produce the E modes of the CMB map and as many to produce the B part. The weights are displayed in the figure below. The Q and U maps were originally produced at Nside=2048 with a 5-arc-minute resolution, but were downgraded to Nside=1024 with a 10 arc-minute resolution for this release.<br />
<br />
<!--[[File:Smica_filterEB_dx11.png|thumb|center|600px|'''Weights given by SMICA to the input E and B modes (after they are re-beamed to 5 arcmin and expressed in K<math>_\rm{RJ}</math>), in order to produce the E and B modes of the CMB map. A given frequency channel is encoded in a given color. Solid lines are for E modes and dashed lines are for B modes. The thick lines are for the EE or BB weights; the thin lines are for the EB or BE weights. See the paper for more details.''']]--><br />
<br />
===Inputs===<br />
The input maps are the sky temperature maps described in the [[Frequency Maps | Sky temperature maps]] section. SMICA and SEVEM use all the maps between 30 and 857 GHz; NILC uses the ones between 44 and 857 GHz. Commander-Ruler uses frequency channel maps from 30 to 353 GHz. <br />
<br />
===File names and structure===<br />
The FITS files corresponding to the three CMB products are the following:<br />
<br />
''COM_CMB_IQU-{method}-field-{Int,Pol}_Nside_R2.nn.fits''<br />
<br />
where ''method'' is mica, nilc, sevem, or commander, and Int and Pol indicate whether the file contains the temperature (Int) or the polarisation (Pol) maps. For this release the temperature maps are provided at Nside = 2048, and the polarisation maps at Nside = 1024. <br />
<br />
The files contain <br />
* a minimal primary extension with no data;<br />
* one or two ''BINTABLE'' data extensions with a table of Npix lines by 14 columns in which the first 13 columns is a CMB maps produced from the full or a subset of the data, as described in the table below, and the last column in a confidence mask. There is a single extension for ''Int'' files, and two, for Q and U, for ''Pol'' files. <br />
* a ''BINTABLE'' extension containing the beam window function.<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. or 2. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I or Q or U || Real*4 || uK_cmb || I or Q or U map <br />
|- <br />
|HM1 || Real*4 || uK_cmb || Half-miss 1 <br />
|-<br />
|HM2 || Real*4 || uK_cmb || Half-miss 2 <br />
|-<br />
|YR1 || Real*4 || uK_cmb || Year 1 <br />
|-<br />
|YR2 || Real*4 || uK_cmb || Year 2 <br />
|-<br />
|HR1 || Real*4 || uK_cmb || Half-ring 1 <br />
|-<br />
|HR2 || Real*4 || uK_cmb || Half-ring 2 <br />
|-<br />
|HMHS || Real*4 || uK_cmb || Half-miss, half sum <br />
|-<br />
|HMHD || Real*4 || uK_cmb || Half-miss, half diff <br />
|-<br />
|YRHS || Real*4 || uK_cmb || Year, half sum <br />
|-<br />
|YRHD || Real*4 || uK_cmb || Year, half diff <br />
|-<br />
|HRHS || Real*4 || uK_cmb || Half-ring half sum <br />
|-<br />
|HRHD || Real*4 || uK_cmb || Half-ring half diff <br />
|-<br />
|MASK || BYTE || || Confidence mask <br />
|-<br />
<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CMB || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (smica/nilc/sevem/commander)<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 2. or 3. EXTNAME = ''BEAM_WF'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BEAM_WF || Real*4 || none || The effective beam window function, including the pixel window function. See Note 1.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX || Int || value || Lsst multipole of beam WF<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|}<br />
<br />
Notes:<br />
# The beam window function <math>B_\ell</math> given here includes the pixel window function <math>p_\ell</math> for the Nside=2048 pixelization. It means that, ideally, <math>C_\ell(map) = C_\ell(sky) \, B_\ell^2 \, p_\ell^2</math>.<br />
<br />
<!--- mi sembra che questa non serva più <br />
The low resolution COMMANDER-Ruler CMB product is organized in the following way:<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB low resolution COMMANDER-Ruler map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK_cmb || CMB temperature map obtained as average over 1000 samples<br />
|-<br />
|I_stdev || Real*4 || uK_cmb || Corresponding Standard deviation amongst the 1000 samples<br />
|-<br />
|VALMASK|| Byte || none || Confidence mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 2. EXTNAME = ''CMB-Sample'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_SIM01 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM02 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM03 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM04 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM05 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM06 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM07 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM08 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM09 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM10 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 4. EXTNAME = ''BEAM_WF'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BEAM_WF || Real*4 || none || The effective beam window function, including the pixel window function.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX || Int || value || Lsst multipole of beam WF<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|}<br />
<br />
---><br />
<br />
<!---- anche queste non servono più <br />
<br />
The FITS files containing the ''union'' (or common) maks is:<br />
* {{PLASingleFile|fileType=map|name=COM_Mask_CMB-union_2048_R1.10.fits|link=COM_Mask_CMB-common}}<br />
which contains a single ''BINTABLE'' extension with a single column (named ''U73'') for the mask, which is boolean (FITS ''TFORM = B''), in GALACTIC coordinates, NESTED ordering, and Nside=2048.<br />
<br />
For the benefit of users who are only looking for a small file containing the SMICA cmb map with no additional information (noise or masks) we provide such a file here<br />
*{{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica-field-I_2048_R1.20.fits|link=COM_CompMap_CMB-smica-field-I_2048_R1.20.fits}}<br />
This file contains a single extension with a single column containing the SMICA cmb temperature map.<br />
<br />
---><br />
<br />
== Astrophysical foregrounds from parametric component separation ==<br />
We describe diffuse foreground products for the Planck 2015 release. See the Planck Foregrounds Component Separation paper {{PlanckPapers|planck2014-a12}} for a detailed description of these products. Further scientific discussion and interpretation may be found in {{PlanckPapers|planck2014-a31}}.<br />
<br />
===Low-resolution temperature products===<br />
<br />
: The Planck 2015 astrophysical component separation analysis combines Planck observations with the 9-year WMAP temperature sky maps (Bennett et al. 2013) and the 408 MHz survey by Haslam et al. (1982). This allows a direct decomposition of the low-frequency foregrounds into separate synchrotron, free-free and spinning dust components without strong spatial priors. <br />
<br />
====Inputs====<br />
<br />
The following data products are used for the low-resolution analysis:<br />
* Full-mission 30 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=30|period=Full|link=LFI 30 GHz frequency maps}}<br />
* Full-mission 44 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=44|period=Full|link=LFI 44 GHz frequency maps}}<br />
* Full-mission 70 GHz ds1 (18+23), ds2 (19+22), and ds3 (20+21) detector-set maps<br />
* Full-mission 100 GHz ds1 and ds2 detector set maps<br />
* Full-mission 143 GHz ds1 and ds2 detector set maps and detectors 5, 6, and 7 maps<br />
* Full-mission 217 GHz detector 1, 2, 3 and 4 maps<br />
* Full-mission 353 GHz detector set ds2 and detector 1 maps<br />
* Full-mission 545 GHz detector 2 and 4 maps<br />
* Full-mission 857 GHz detector 2 map<br />
* Beam-symmetrized 9-year WMAP K-band map [http://lambda.gsfc.nasa.gov/product/map/dr5/skymap_info.cfm (Lambda)]<br />
* Beam-symmetrized 9-year WMAP Ka-band map [http://lambda.gsfc.nasa.gov/product/map/dr5/skymap_info.cfm (Lambda)]<br />
* Default 9-year WMAP Q1 and Q2 differencing assembly maps [http://lambda.gsfc.nasa.gov/product/map/dr5/skymap_info.cfm (Lambda)]<br />
* Default 9-year WMAP V1 and V2 differencing assembly maps [http://lambda.gsfc.nasa.gov/product/map/dr5/skymap_info.cfm (Lambda)]<br />
* Default 9-year WMAP W1, W2, W3, and W4 differencing assembly maps [http://lambda.gsfc.nasa.gov/product/map/dr5/skymap_info.cfm (Lambda)]<br />
* Re-processed 408 MHz survey map, Remazeilles et al. (2014) [http://lambda.gsfc.nasa.gov/product/foreground/2014_haslam_408_info.cfm (Lambda)]<br />
All maps are smoothed to a common resolution of 1 degree FWHM by deconvolving their original instrumental beam and pixel window, and convolving with the new common Gaussian beam, and repixelizing at Nside=256.<br />
<br />
====Outputs====<br />
<br />
=====Synchrotron emission=====<br />
<br />
<!--<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=800px heights=500px> <br />
File:commander_synch_amp.png | '''Commander low-resolution synchrotron amplitude'''<br />
</gallery><br />
</center>--><br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_Synchrotron-commander_0256_R2.00.fits|link=COM_CompMap_Synchrotron-commander_0256_R2.00.fits}}<br />
: Reference frequency: 408 MHz<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-Synchrotron<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || uK_RJ || Amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || uK_RJ || Amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || uK_RJ || Amplitude posterior rms<br />
|}<br />
<br />
<br />
=====Free-free emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_freefree-commander_0256_R2.00.fits|link=COM_CompMap_freefree-commander_0256_R2.00.fits}}<br />
: Reference frequency: NA<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-freefree<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|EM_ML || Real*4 || cm^-6 pc || Emission measure posterior maximum <br />
|-<br />
|EM_MEAN || Real*4 || cm^-6 pc || Emission measure posterior mean <br />
|-<br />
|EM_RMS || Real*4 || cm^-6 pc || Emission measure posterior rms<br />
|-<br />
|TEMP_ML || Real*4 || K || Electron temperature posterior maximum <br />
|-<br />
|TEMP_MEAN || Real*4 || K || Electron temperature posterior mean <br />
|-<br />
|TEMP_RMS || Real*4 || K || Electron temperature posterior rms<br />
|}<br />
<br />
<br />
=====Spinning dust emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_AME-commander_0256_R2.00.fits|link=COM_CompMap_AME-commander_0256_R2.00.fits}}<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
Note: The spinning dust component has two independent constituents, each corresponding to one spdust2 component, but with different peak frequencies. The two components are stored in the two first FITS extensions, and the template frequency spectrum is stored in the third extension. <br />
<br />
: Reference frequency: 22.8 GHz<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-AME1<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || uK_RJ || Primary amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || uK_RJ || Primary amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || uK_RJ || Primary amplitude posterior rms<br />
|-<br />
|FREQ_ML || Real*4 || GHz || Primary peak frequency posterior maximum <br />
|-<br />
|FREQ_MEAN || Real*4 || GHz || Primary peak frequency posterior mean <br />
|-<br />
|FREQ_RMS || Real*4 || GHz || Primary peak frequency posterior rms<br />
|}<br />
<br />
: Reference frequency: 41.0 GHz<br />
: Peak frequency: 33.35 GHz<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Extension 1 -- COMP-MAP-AME2<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || uK_RJ || Secondary amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || uK_RJ || Secondary amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || uK_RJ || Secondary amplitude posterior rms<br />
|}<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Extension 2 -- SPINNING-DUST-TEMP<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|nu || Real*4 || GHz || Frequency <br />
|-<br />
|j_nu/nH || Real*4 || Jy sr-1 cm2/H || spdust2 spectrum <br />
|}<br />
<br />
=====CO line emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_CO-commander_0256_R2.00.fits|link=COM_CompMap_CO-commander_0256_R2.00.fits}}<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
Note: The CO line emission component has three independent objects, corresponding to the J1->0, 2->1 and 3->2 lines, stored in separate extensions. <br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-co10<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || K_RJ km/s || CO(1-0) amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || K_RJ km/s || CO(1-0) amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || K_RJ km/s || CO(1-0) amplitude posterior rms<br />
|}<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Extension 1 -- COMP-MAP-co21<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || K_RJ km/s || CO(2-1) amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || K_RJ km/s || CO(2-1) amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || K_RJ km/s || CO(2-1) amplitude posterior rms<br />
|}<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Extension 2 -- COMP-MAP-co32<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || K_RJ km/s || CO(3-2) amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || K_RJ km/s || CO(3-2) amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || K_RJ km/s || CO(3-2) amplitude posterior rms<br />
|}<br />
<br />
=====94/100 GHz line emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_xline-commander_0256_R2.00.fits|link=COM_CompMap_xline-commander_0256_R2.00.fits}}<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-xline<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || uK_cmb || Amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || uK_cmb || Amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || uK_cmb || Amplitude posterior rms<br />
|}<br />
<br />
Note: The amplitude of this component is normalized according to the 100-ds1 detector set map, ie., it is the amplitude as measured by this detector combination.<br />
<br />
=====Thermal dust emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commander_0256_R2.00.fits|link=COM_CompMap_dust-commander_0256_R2.00.fits}}<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
: Reference frequency: 545 GHz<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-dust<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML || Real*4 || uK_RJ || Amplitude posterior maximum <br />
|-<br />
|I_MEAN || Real*4 || uK_RJ || Amplitude posterior mean <br />
|-<br />
|I_RMS || Real*4 || uK_RJ || Amplitude posterior rms<br />
|-<br />
|TEMP_ML || Real*4 || K || Dust temperature posterior maximum <br />
|-<br />
|TEMP_MEAN || Real*4 || K || Dust temperature posterior mean <br />
|-<br />
|TEMP_RMS || Real*4 || K || Dust temperature posterior rms<br />
|-<br />
|BETA_ML || Real*4 || NA || Emissivity index posterior maximum <br />
|-<br />
|BETA_MEAN || Real*4 || NA || Emissivity index posterior mean <br />
|-<br />
|BETA_RMS || Real*4 || NA || Emissivity index posterior rms<br />
|}<br />
<br />
=====Thermal Sunyaev-Zeldovich emission around the Coma and Virgo clusters=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_SZ-commander_0256_R2.00.fits|link=COM_CompMap_SZ-commander_0256_R2.00.fits}}<br />
: Nside = 256<br />
: Angular resolution = 60 arcmin<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-SZ<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Y_ML || Real*4 || y_SZ || Y parameter posterior maximum <br />
|-<br />
|Y_MEAN || Real*4 || y_SZ || Y parameter posterior mean <br />
|-<br />
|Y_RMS || Real*4 || y_SZ || Y parameter posterior rms<br />
|}<br />
<br />
===High-resolution temperature products===<br />
<br />
High-resolution foreground products at 7.5 arcmin FWHM are derived with the same algorithm as for the low-resolution analyses, but including frequency channels above (and including) 143 GHz. <br />
<br />
====Inputs====<br />
<br />
The following data products are used for the low-resolution analysis:<br />
* Full-mission 143 GHz ds1 and ds2 detector set maps and detectors 5, 6, and 7 maps<br />
* Full-mission 217 GHz detector 1, 2, 3 and 4 maps<br />
* Full-mission 353 GHz detector set ds2 and detector 1 maps<br />
* Full-mission 545 GHz detector 2 and 4 maps<br />
* Full-mission 857 GHz detector 2 map<br />
All maps are smoothed to a common resolution of 7.5 arcmin FWHM by deconvolving their original instrumental beam and pixel window, and convolving with the new common Gaussian beam, and repixelizing at Nside=2048.<br />
<br />
====Outputs====<br />
<br />
=====CO J2->1 emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_CO21-commander_2048_R2.00.fits|link=COM_CompMap_CO21-commander_2048_R2.00.fits}}<br />
: Nside = 2048<br />
: Angular resolution = 7.5 arcmin<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-CO21<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML_FULL || Real*4 || K_RJ km/s || Full-mission amplitude posterior maximum <br />
|-<br />
|I_ML_HM1 || Real*4 || K_RJ km/s || First half-mission amplitude posterior maximum <br />
|-<br />
|I_ML_HM2 || Real*4 || K_RJ km/s || Second half-mission amplitude posterior maximum <br />
|-<br />
|I_ML_HR1 || Real*4 || K_RJ km/s || First half-ring amplitude posterior maximum <br />
|-<br />
|I_ML_HR2 || Real*4 || K_RJ km/s || Second half-ring amplitude posterior maximum <br />
|-<br />
|I_ML_YR1 || Real*4 || K_RJ km/s || "First year" amplitude posterior maximum <br />
|-<br />
|I_ML_YR2 || Real*4 || K_RJ km/s || "Second year" amplitude posterior maximum <br />
|}<br />
<br />
<br />
=====Thermal dust emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_ThermalDust-commander_2048_R2.00.fits|link=COM_CompMap_ThermalDust-commander_2048_R2.00.fits}}<br />
: Nside = 2048<br />
: Angular resolution = 7.5 arcmin<br />
<br />
: Reference frequency: 545 GHz<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-dust<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_ML_FULL || Real*4 || uK_RJ || Full-mission amplitude posterior maximum <br />
|-<br />
|I_ML_HM1 || Real*4 || uK_RJ || First half-mission amplitude posterior maximum <br />
|-<br />
|I_ML_HM2 || Real*4 || uK_RJ || Second half-mission amplitude posterior maximum <br />
|-<br />
|I_ML_HR1 || Real*4 || uK_RJ || First half-ring amplitude posterior maximum <br />
|-<br />
|I_ML_HR2 || Real*4 || uK_RJ || Second half-ring amplitude posterior maximum <br />
|-<br />
|I_ML_YR1 || Real*4 || uK_RJ || "First year" amplitude posterior maximum <br />
|-<br />
|I_ML_YR2 || Real*4 || uK_RJ || "Second year" amplitude posterior maximum <br />
|-<br />
|BETA_ML_FULL || Real*4 || NA || Full-mission emissivity index posterior maximum <br />
|-<br />
|BETA_ML_HM1 || Real*4 || NA || First half-mission emissivity index posterior maximum <br />
|-<br />
|BETA_ML_HM2 || Real*4 || NA || Second half-mission emissivity index posterior maximum <br />
|-<br />
|BETA_ML_HR1 || Real*4 || NA || First half-ring emissivity index posterior maximum <br />
|-<br />
|BETA_ML_HR2 || Real*4 || NA || Second half-ring emissivity index posterior maximum <br />
|-<br />
|BETA_ML_YR1 || Real*4 || NA || "First year" emissivity index posterior maximum <br />
|-<br />
|BETA_ML_YR2 || Real*4 || NA || "Second year" emissivity index posterior maximum <br />
|-<br />
|}<br />
<br />
===Polarization products===<br />
<br />
Two polarization foreground products are provided, namely synchrotron and thermal dust emission. The spectral models are assumed identical to the corresponding temperature spectral models.<br />
<br />
====Inputs====<br />
<br />
The following data products are used for the polarization analysis:<br />
* (Only low-resolution analysis) Full-mission 30 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=30|period=Full|link=LFI 30 GHz frequency maps}}<br />
* (Only low-resolution analysis) Full-mission 44 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=44|period=Full|link=LFI 44 GHz frequency maps}}<br />
* (Only low-resolution analysis) Full-mission 70 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=70|period=Full|link=LFI 70 GHz frequency maps}}<br />
* Full-mission 100 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=100|period=Full|link=HFI 100 GHz frequency maps}}<br />
* Full-mission 143 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=143|period=Full|link=HFI 143 GHz frequency maps}}<br />
* Full-mission 217 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=217|period=Full|link=HFI 217 GHz frequency maps}}<br />
* Full-mission 353 GHz frequency map, {{PLAFreqMaps|inst=LFI|freq=353|period=Full|link=HFI 353 GHz frequency maps}}<br />
In the low-resolution analysis, all maps are smoothed to a common resolution of 40 arcmin FWHM by deconvolving their original instrumental beam and pixel window, and convolving with the new common Gaussian beam, and repixelizing at Nside=256. In the high-resolution analysis (including only CMB and thermal dust emission), the corresponding resolution is 10 arcmin FWHM and Nside=1024.<br />
<br />
====Outputs====<br />
=====Synchrotron emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_SynchrotronPol-commander_0256_R2.00.fits|link=COM_CompMap_SynchrotronPol-commander_0256_R2.00.fits}}<br />
: Nside = 256<br />
: Angular resolution = 40 arcmin<br />
<br />
: Reference frequency: 30 GHz<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-SynchrotronPol<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Q_ML_FULL || Real*4 || K_RJ km/s || Full-mission Stokes Q posterior maximum <br />
|-<br />
|U_ML_FULL || Real*4 || K_RJ km/s || Full-mission Stokes U posterior maximum <br />
|-<br />
|Q_ML_HM1 || Real*4 || K_RJ km/s || First half-mission Stokes Q posterior maximum <br />
|-<br />
|U_ML_HM1 || Real*4 || K_RJ km/s || First half-mission Stokes U posterior maximum <br />
|-<br />
|Q_ML_HM2 || Real*4 || K_RJ km/s || Second half-mission Stokes Q posterior maximum <br />
|-<br />
|U_ML_HM2 || Real*4 || K_RJ km/s || Second half-mission Stokes U posterior maximum <br />
|-<br />
|Q_ML_HR1 || Real*4 || K_RJ km/s || First half-ring Stokes Q posterior maximum <br />
|-<br />
|U_ML_HR1 || Real*4 || K_RJ km/s || First half-ring Stokes U posterior maximum <br />
|-<br />
|Q_ML_HR2 || Real*4 || K_RJ km/s || Second half-ring Stokes Q posterior maximum <br />
|-<br />
|U_ML_HR2 || Real*4 || K_RJ km/s || Second half-ring Stokes U posterior maximum <br />
|-<br />
|Q_ML_YR1 || Real*4 || K_RJ km/s || "First year" Stokes Q posterior maximum <br />
|-<br />
|U_ML_YR1 || Real*4 || K_RJ km/s || "First year" Stokes U posterior maximum <br />
|-<br />
|Q_ML_YR2 || Real*4 || K_RJ km/s || "Second year" Stokes Q posterior maximum <br />
|-<br />
|U_ML_YR2 || Real*4 || K_RJ km/s || "Second year" Stokes U posterior maximum <br />
|}<br />
<br />
<br />
=====Thermal dust emission=====<br />
<br />
: File name: {{PLASingleFile|fileType=map|name=COM_CompMap_DustPol-commander_1024_R2.00.fits|link=COM_CompMap_DustPol-commander_1024_R2.00.fits}}<br />
: Nside = 1024<br />
: Angular resolution = 10 arcmin<br />
<br />
: Reference frequency: 353 GHz<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ HDU -- COMP-MAP-DustPol<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Q_ML_FULL || Real*4 || uK_RJ || Full-mission Stokes Q posterior maximum <br />
|-<br />
|U_ML_FULL || Real*4 || uK_RJ || Full-mission Stokes U posterior maximum <br />
|-<br />
|Q_ML_HM1 || Real*4 || uK_RJ || First half-mission Stokes Q posterior maximum <br />
|-<br />
|U_ML_HM1 || Real*4 || uK_RJ || First half-mission Stokes U posterior maximum <br />
|-<br />
|Q_ML_HM2 || Real*4 || uK_RJ || Second half-mission Stokes Q posterior maximum <br />
|-<br />
|U_ML_HM2 || Real*4 || uK_RJ || Second half-mission Stokes U posterior maximum <br />
|-<br />
|Q_ML_HR1 || Real*4 || uK_RJ || First half-ring Stokes Q posterior maximum <br />
|-<br />
|U_ML_HR1 || Real*4 || uK_RJ || First half-ring Stokes U posterior maximum <br />
|-<br />
|Q_ML_HR2 || Real*4 || uK_RJ || Second half-ring Stokes Q posterior maximum <br />
|-<br />
|U_ML_HR2 || Real*4 || uK_RJ || Second half-ring Stokes U posterior maximum <br />
|-<br />
|Q_ML_YR1 || Real*4 || uK_RJ || "First year" Stokes Q posterior maximum <br />
|-<br />
|U_ML_YR1 || Real*4 || uK_RJ || "First year" Stokes U posterior maximum <br />
|-<br />
|Q_ML_YR2 || Real*4 || uK_RJ || "Second year" Stokes Q posterior maximum <br />
|-<br />
|U_ML_YR2 || Real*4 || uK_RJ || "Second year" Stokes U posterior maximum <br />
|}<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Effective_Beams&diff=11284Effective Beams2015-02-04T18:43:24Z<p>Agregori: /* Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian */</p>
<hr />
<div><span style="color:red"></span><br />
<br />
==Product description==<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
Details of the beam processing are given in the respective pages for [[Beams|HFI]] and [[Beams_LFI|LFI]].<br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}, and a discussion of its application to Planck data is given in the appropriate LFI {{PlanckPapers|planck2013-p02d}}, {{PlanckPapers|planck2014-a05||Planck-2015-A05}} and HFI {{PlanckPapers|planck2013-p03c}} papers. Relevant details of the processing steps are given in the [[Beams|Effective Beams]] section of this document.<br />
<br />
<!-- Everything from here down to the "Production Process" section should eventually be moved to a new section the Joint Processing pages --><br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions, PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for all LFI and HFI frequency channels, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<center><br />
<br />
<gallery widths=400px heights=400px perrow=2 caption="Comparison images of compact sources and effective beams, PSFs"><br />
File:30.png| '''30GHz'''<br />
File:44.png| '''44GHz'''<br />
File:70.png| '''70GHz'''<br />
File:100.png| '''100GHz'''<br />
File:143.png| '''143GHz'''<br />
File:217.png| '''217GHz'''<br />
File:353.png| '''353GHz'''<br />
File:545.png| '''545GHz'''<br />
File:857.png| '''857GHz'''<br />
</gallery><br />
</center><br />
<br />
===Histograms of the effective beam parameters===<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 3072 directions which were chosen as HEALpix nside=16 pixel centers for HFI and at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''<math> 4 \pi \sum</math>(effbeam)/max(effbeam)'''<br />
i.e., <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 800px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
[[File:ist_BS_Mars12.png | 800px| thumb | center| '''Histograms for HFI effective beam parameters''' ]]<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:e_044_GB.png| '''ellipticity - 44GHz'''<br />
File:e_070_GB.png| '''ellipticity - 70GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:e_143_BS_Mars12.png| '''ellipticity - 143GHz'''<br />
File:e_217_BS_Mars12.png| '''ellipticity - 217GHz'''<br />
File:e_353_BS_Mars12.png| '''ellipticity - 353GHz'''<br />
File:e_545_BS_Mars12.png| '''ellipticity - 545GHz'''<br />
File:e_857_BS_Mars12.png| '''ellipticity - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams solid angle of the best-fit Gaussian"><br />
File:solidarc_030_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 30GHz'''<br />
File:solidarc_044_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 44GHz'''<br />
File:solidarc_070_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 70GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 100GHz'''<br />
File:solidarc_143_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 143GHz'''<br />
File:solidarc_217_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 217GHz'''<br />
File:solidarc_353_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 353GHz'''<br />
File:solidarc_545_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 545GHz'''<br />
File:solidarc_857_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams fwhm of the best-fit Gaussian"><br />
File:fwhm_030_GB.png| '''fwhm (relative) variations wrt scanning beam - 30GHz'''<br />
File:fwhm_044_GB.png| '''fwhm (relative) variations wrt scanning beam - 44GHz'''<br />
File:fwhm_070_GB.png| '''fwhm (relative) variations wrt scanning beam - 70GHz'''<br />
File:fwhm_100_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 100GHz'''<br />
File:fwhm_143_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 143GHz'''<br />
File:fwhm_217_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 217GHz'''<br />
File:fwhm_353_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 353GHz'''<br />
File:fwhm_545_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 545GHz'''<br />
File:fwhm_857_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams <math>\psi</math> angle of the best-fit Gaussian"><br />
File:psi_030_GB.png| '''<math>\psi</math> - 30GHz'''<br />
File:psi_044_GB.png| '''<math>\psi</math> - 44GHz'''<br />
File:psi_070_GB.png| '''<math>\psi</math> - 70GHz'''<br />
File:psi_100_BS_Mars12.png| '''<math>\psi</math> - 100GHz'''<br />
File:psi_143_BS_Mars12.png| '''<math>\psi</math> - 143GHz'''<br />
File:psi_217_BS_Mars12.png| '''<math>\psi</math> - 217GHz'''<br />
File:psi_353_BS_Mars12.png| '''<math>\psi</math> - 353GHz'''<br />
File:psi_545_BS_Mars12.png| '''<math>\psi</math> - 545GHz'''<br />
File:psi_857_BS_Mars12.png| '''<math>\psi</math> - 857GHz'''<br />
</gallery><br />
<br />
<!--<br />
<gallery widths=500px heights=500px perrow=2 caption="Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:solidarc_030_GB.png| '''beam solid angle (relative variations wrt scanning beam - 30GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative variations wrt scanning beam - 100GHz'''<br />
</gallery><br />
--><br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 3072 and 768 directions on the sky for HFI and LFI data respectively. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 and 2048 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|-<br />
| 100 || 9.651 || 0.014 || 1.186 || 0.023 || -0.024 || 55.400 || 105.778 || 0.311 || 9.66 <br />
|-<br />
| 143 || 7.248 || 0.015 || 1.036 || 0.009 || 0.383 || 54.130 || 59.954 || 0.246 || 7.27 <br />
|-<br />
| 217 || 4.990 || 0.025 || 1.177 || 0.030 || 0.836 || 54.999 || 28.447 || 0.271 || 5.01<br />
|-<br />
| 353 || 4.818 || 0.024 || 1.147 || 0.028 || 0.655 || 54.745 || 26.714 || 0.250 || 4.86<br />
|- <br />
| 545 || 4.682 || 0.044 || 1.161 || 0.036 || 0.544 || 54.876 || 26.535 || 0.339 || 4.84 <br />
|-<br />
| 857 || 4.325 || 0.055 || 1.393 || 0.076 || 0.876 || 54.779 || 24.244 || 0.193 || 4.63 <br />
|}<br />
<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: '''<math>4 \pi \sum </math>(effbeam)/max(effbeam)''', i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|-<br />
| 100 || 105.778 || 0.311 || 100.830 || 0.410 || 105.777 || 0.311 <br />
|-<br />
| 143 || 59.954 || 0.246 || 56.811 || 0.419 || 59.952 || 0.246 <br />
|-<br />
| 217 || 28.447 || 0.271 || 26.442 || 0.537 || 28.426 || 0.271 <br />
|-<br />
| 353 || 26.714 || 0.250 || 24.827 || 0.435 || 26.653 || 0.250 <br />
|-<br />
| 545 || 26.535 || 0.339 || 24.287 || 0.455 || 26.302 || 0.337 <br />
|-<br />
| 857 || 24.244 || 0.193 || 22.646 || 0.263 || 23.985 || 0.191 <br />
|}<br />
<br />
==Production process==<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space{{BibCite|mitra2010}}, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
===Pixel Ordered Detector Angles (PODA)===<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels - the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
===effBeam===<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
===Computational Cost===<br />
The computation of the effective beams has been performed at the NERSC Supercomputing Center. The table below shows the computation cost for FEBeCoP processing of the nominal mission.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Computational cost for PODA, Effective Beam and single map convolution. Wall-clock time is given as a guide, as found on the NERSC supercomputers.'''<br />
|-<br />
|Channel ||030 || 044 || 070 || 100 || 143 || 217 || 353 || 545 || 857<br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 || 500 || 500 || 500 || 500 || 500 || 500 <br />
|-<br />
|PODA/Detector Computation time (wall clock hrs) || 7 || 10 || 20 || 20 || 20 || 20 || 20 || 20 || 20<br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 || 2800 || 3800 || 3200 || 3000 || 900 || 1100<br />
|-<br />
|Beam/Channel Computation time (wall clock hrs) || 0.5 || 0.8 || 1 || 1.5 || 2 || 1.2 || 1 || 0.5 || 0.5<br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 || 3.6 || 4.8 || 4.0 || 4.1 || 4.1 || 3.7 <br />
|-<br />
|Convolution Computation time (wall clock sec) || 1 || 1 || 1 || 4 || 4 || 4 || 4 || 4 || 4 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 || 187 || 182 || 146 || 132 || 139 || 124<br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
==Inputs==<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 500px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
===The Focal Plane DataBase (FPDB)===<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
*HFI - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
<br />
<!--<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
{{PLADoc|fileType=rimo|link=The Plank RIMOS}}<br />
--><br />
<br />
===The scanning strategy===<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
===The scanbeam===<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
* HFI: [[Beams#Scanning beams|B-Spline, BS]] based on 2 observations of Mars.<br />
<br />
(see the instrument [[The RIMO|RIMOs]]).<br />
<br />
<!--<br />
<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
[[Beams LFI#Effective beams|LFI effective beams]]<br />
--><br />
<br />
===Beam cutoff radii===<br />
N times geometric mean of FWHM of all detectors in a channel, where N<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' || '''fwhm of full beam extent''' <br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|-<br />
|100 || 2.25 || 23.703699<br />
|-<br />
|143 || 3 || 21.057402<br />
|-<br />
|217-353 || 4 || 18.782754<br />
|-<br />
|sub-mm || 4 || 18.327635(545GHz) ; 17.093706(857GHz) <br />
|}<br />
<br />
===Map resolution for the derived beam data object===<br />
* <math>N_{side} = 1024 </math> for LFI frequency channels<br />
* <math>N_{side} = 2048 </math> for HFI frequency channels<br />
<br />
==Related products==<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for dDX9 data and Nominal Mission<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, and 1 <math>\sigma</math> errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations, FFP#.<br />
For example [[HL-sims#FFP6 data set|FFP6]] <br />
<br />
===Beam Window Functions===<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> W_l </math> relates the true angular power spectra <math>C_l </math> with the observed angular power spectra <math>\widetilde{C}_l </math>:<br />
<br />
<math><br />
W_l= \widetilde{C}_l / C_l <br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_l </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_l </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_l </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
W^{est}_l = < C^{conv}_l / C^{in}_l ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing C^{conv}_l with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, Wl, for Planck mission====<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, Wl, for LFI channels''']] <br />
[[File:plot_dx9_HFI_BS_M12_CMB.png | 600px | thumb | |center |'''Beam Window functions, Wl, for HFI channels''']]<br />
<br />
== Retrieval of effective beam information from the PLA interface ==<br />
In order to retrieve the effective beam information, the user should:<br />
#Launch the Java interface from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive]; [[File:PLALink.png| 1000px | thumb | |center |'''Link to PLA Java interface.''']]<br />
#Once the PLA interface is loaded go to '''Sky maps'''; [[File:PLAinterface.png| 600px | thumb | |center |'''PLA java interface.''']]<br />
#On the '''Sky maps''' interface click on the icon on the left of the Effective beams area;<br />
[[File:Skymapsinterface.png| 600px | thumb | |center |'''Sky maps interface on the PLA''']]<br />
#The search interface for effective beams allows the user to retrieve the beam nearest to the input source (name or coordinates), or to retrieve a set of beams in a grid defined by the <math>N_{\rm side}</math> and the size of the region around a source (name or coordinates). The resolution of this grid is defined by the <math>N_{\rm side}</math> parametera and the size of the region is defined by the "Radius of <span class="noglossary">ROI</span>" parameter.[[File:EffectiveBeamsInterface.png| 600px | thumb | |center |'''Link to PLA Java interface.''']]<br />
Once the user proceeds with querying the beams, the PLA software retrieves the appropriate set of effective beams from the database and delivers it in a FITS file containin a HEALPix map of the beam which can be directly downloaded.<br />
<br />
==File Names==<br />
The effective beams are provided by the PLA as FITS files containg HEALPix maps of the beams. For the file names the following convention is used:<br />
*Single beam query: '''beams_FFF_''PixelNumber''.fits''' <br />
**FFF is the channel frequency (one of '''30''', '''44''', '''70''', '''100''', '''143''', '''217''', '''353''', '''545''', '''857'''); <br />
** ''PixelNumber'' is the number of the pixel to which the beam corresponds (<math>0</math> - <math>12 \times N_{\rm side}^2 - 1</math>). For the LFI <math>N_{\rm side}=1024</math>, for the HFI <math>N_{\rm side}=2048</math>;<br />
*Multiple beam query: '''beams_FFF_''FirstPixelNumber''-''LastPixelNumber''.zip''' <br /> The compressed files contains a set of files with the beams for the pixels covereing the selected region. FFF as for sinle beam query. The naming convention for the beam files contained in the ''.zip'' file is the same as for single beam queries.<br />
** ''FirstPixelNumber'' is the lowest pixel number for the area covered by the request;<br />
** ''LastPixelNumber'' is the highest pixel number for the area covered by the request;<br />
<br />
==File format==<br />
The FITS files provided by the PLA contain HEALPix maps of the beams.<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
<br />
[[Category:Mission products|004]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Effective_Beams&diff=11282Effective Beams2015-02-04T18:41:35Z<p>Agregori: /* Product description */</p>
<hr />
<div><span style="color:red"></span><br />
<br />
==Product description==<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
Details of the beam processing are given in the respective pages for [[Beams|HFI]] and [[Beams_LFI|LFI]].<br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}, and a discussion of its application to Planck data is given in the appropriate LFI {{PlanckPapers|planck2013-p02d}}, {{PlanckPapers|planck2014-a05||Planck-2015-A05}} and HFI {{PlanckPapers|planck2013-p03c}} papers. Relevant details of the processing steps are given in the [[Beams|Effective Beams]] section of this document.<br />
<br />
<!-- Everything from here down to the "Production Process" section should eventually be moved to a new section the Joint Processing pages --><br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions, PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for all LFI and HFI frequency channels, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<center><br />
<br />
<gallery widths=400px heights=400px perrow=2 caption="Comparison images of compact sources and effective beams, PSFs"><br />
File:30.png| '''30GHz'''<br />
File:44.png| '''44GHz'''<br />
File:70.png| '''70GHz'''<br />
File:100.png| '''100GHz'''<br />
File:143.png| '''143GHz'''<br />
File:217.png| '''217GHz'''<br />
File:353.png| '''353GHz'''<br />
File:545.png| '''545GHz'''<br />
File:857.png| '''857GHz'''<br />
</gallery><br />
</center><br />
<br />
===Histograms of the effective beam parameters===<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 3072 directions which were chosen as HEALpix nside=16 pixel centers for HFI and at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''<math> 4 \pi \sum</math>(effbeam)/max(effbeam)'''<br />
i.e., <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 800px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
[[File:ist_BS_Mars12.png | 800px| thumb | center| '''Histograms for HFI effective beam parameters''' ]]<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:e_044_GB.png| '''ellipticity - 44GHz'''<br />
File:e_070_GB.png| '''ellipticity - 70GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:e_143_BS_Mars12.png| '''ellipticity - 143GHz'''<br />
File:e_217_BS_Mars12.png| '''ellipticity - 217GHz'''<br />
File:e_353_BS_Mars12.png| '''ellipticity - 353GHz'''<br />
File:e_545_BS_Mars12.png| '''ellipticity - 545GHz'''<br />
File:e_857_BS_Mars12.png| '''ellipticity - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams solid angle of the best-fit Gaussian"><br />
File:solidarc_030_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 30GHz'''<br />
File:solidarc_044_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 44GHz'''<br />
File:solidarc_070_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 70GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 100GHz'''<br />
File:solidarc_143_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 143GHz'''<br />
File:solidarc_217_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 217GHz'''<br />
File:solidarc_353_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 353GHz'''<br />
File:solidarc_545_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 545GHz'''<br />
File:solidarc_857_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams fwhm of the best-fit Gaussian"><br />
File:fwhm_030_GB.png| '''fwhm (relative) variations wrt scanning beam - 30GHz'''<br />
File:fwhm_044_GB.png| '''fwhm (relative) variations wrt scanning beam - 44GHz'''<br />
File:fwhm_070_GB.png| '''fwhm (relative) variations wrt scanning beam - 70GHz'''<br />
File:fwhm_100_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 100GHz'''<br />
File:fwhm_143_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 143GHz'''<br />
File:fwhm_217_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 217GHz'''<br />
File:fwhm_353_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 353GHz'''<br />
File:fwhm_545_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 545GHz'''<br />
File:fwhm_857_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams $\psi$ angle of the best-fit Gaussian"><br />
File:psi_030_GB.png| '''$\psi$ - 30GHz'''<br />
File:psi_044_GB.png| '''$\psi$ - 44GHz'''<br />
File:psi_070_GB.png| '''$\psi$ - 70GHz'''<br />
File:psi_100_BS_Mars12.png| '''$\psi$ - 100GHz'''<br />
File:psi_143_BS_Mars12.png| '''$\psi$ - 143GHz'''<br />
File:psi_217_BS_Mars12.png| '''$\psi$ - 217GHz'''<br />
File:psi_353_BS_Mars12.png| '''$\psi$ - 353GHz'''<br />
File:psi_545_BS_Mars12.png| '''$\psi$ - 545GHz'''<br />
File:psi_857_BS_Mars12.png| '''$\psi$ - 857GHz'''<br />
</gallery><br />
<br />
<!--<br />
<gallery widths=500px heights=500px perrow=2 caption="Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:solidarc_030_GB.png| '''beam solid angle (relative variations wrt scanning beam - 30GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative variations wrt scanning beam - 100GHz'''<br />
</gallery><br />
--><br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 3072 and 768 directions on the sky for HFI and LFI data respectively. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 and 2048 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|-<br />
| 100 || 9.651 || 0.014 || 1.186 || 0.023 || -0.024 || 55.400 || 105.778 || 0.311 || 9.66 <br />
|-<br />
| 143 || 7.248 || 0.015 || 1.036 || 0.009 || 0.383 || 54.130 || 59.954 || 0.246 || 7.27 <br />
|-<br />
| 217 || 4.990 || 0.025 || 1.177 || 0.030 || 0.836 || 54.999 || 28.447 || 0.271 || 5.01<br />
|-<br />
| 353 || 4.818 || 0.024 || 1.147 || 0.028 || 0.655 || 54.745 || 26.714 || 0.250 || 4.86<br />
|- <br />
| 545 || 4.682 || 0.044 || 1.161 || 0.036 || 0.544 || 54.876 || 26.535 || 0.339 || 4.84 <br />
|-<br />
| 857 || 4.325 || 0.055 || 1.393 || 0.076 || 0.876 || 54.779 || 24.244 || 0.193 || 4.63 <br />
|}<br />
<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: '''<math>4 \pi \sum </math>(effbeam)/max(effbeam)''', i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|-<br />
| 100 || 105.778 || 0.311 || 100.830 || 0.410 || 105.777 || 0.311 <br />
|-<br />
| 143 || 59.954 || 0.246 || 56.811 || 0.419 || 59.952 || 0.246 <br />
|-<br />
| 217 || 28.447 || 0.271 || 26.442 || 0.537 || 28.426 || 0.271 <br />
|-<br />
| 353 || 26.714 || 0.250 || 24.827 || 0.435 || 26.653 || 0.250 <br />
|-<br />
| 545 || 26.535 || 0.339 || 24.287 || 0.455 || 26.302 || 0.337 <br />
|-<br />
| 857 || 24.244 || 0.193 || 22.646 || 0.263 || 23.985 || 0.191 <br />
|}<br />
<br />
==Production process==<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space{{BibCite|mitra2010}}, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
===Pixel Ordered Detector Angles (PODA)===<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels - the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
===effBeam===<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
===Computational Cost===<br />
The computation of the effective beams has been performed at the NERSC Supercomputing Center. The table below shows the computation cost for FEBeCoP processing of the nominal mission.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Computational cost for PODA, Effective Beam and single map convolution. Wall-clock time is given as a guide, as found on the NERSC supercomputers.'''<br />
|-<br />
|Channel ||030 || 044 || 070 || 100 || 143 || 217 || 353 || 545 || 857<br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 || 500 || 500 || 500 || 500 || 500 || 500 <br />
|-<br />
|PODA/Detector Computation time (wall clock hrs) || 7 || 10 || 20 || 20 || 20 || 20 || 20 || 20 || 20<br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 || 2800 || 3800 || 3200 || 3000 || 900 || 1100<br />
|-<br />
|Beam/Channel Computation time (wall clock hrs) || 0.5 || 0.8 || 1 || 1.5 || 2 || 1.2 || 1 || 0.5 || 0.5<br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 || 3.6 || 4.8 || 4.0 || 4.1 || 4.1 || 3.7 <br />
|-<br />
|Convolution Computation time (wall clock sec) || 1 || 1 || 1 || 4 || 4 || 4 || 4 || 4 || 4 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 || 187 || 182 || 146 || 132 || 139 || 124<br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
==Inputs==<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 500px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
===The Focal Plane DataBase (FPDB)===<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
*HFI - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
<br />
<!--<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
{{PLADoc|fileType=rimo|link=The Plank RIMOS}}<br />
--><br />
<br />
===The scanning strategy===<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
===The scanbeam===<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
* HFI: [[Beams#Scanning beams|B-Spline, BS]] based on 2 observations of Mars.<br />
<br />
(see the instrument [[The RIMO|RIMOs]]).<br />
<br />
<!--<br />
<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
[[Beams LFI#Effective beams|LFI effective beams]]<br />
--><br />
<br />
===Beam cutoff radii===<br />
N times geometric mean of FWHM of all detectors in a channel, where N<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' || '''fwhm of full beam extent''' <br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|-<br />
|100 || 2.25 || 23.703699<br />
|-<br />
|143 || 3 || 21.057402<br />
|-<br />
|217-353 || 4 || 18.782754<br />
|-<br />
|sub-mm || 4 || 18.327635(545GHz) ; 17.093706(857GHz) <br />
|}<br />
<br />
===Map resolution for the derived beam data object===<br />
* <math>N_{side} = 1024 </math> for LFI frequency channels<br />
* <math>N_{side} = 2048 </math> for HFI frequency channels<br />
<br />
==Related products==<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for dDX9 data and Nominal Mission<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, and 1 <math>\sigma</math> errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations, FFP#.<br />
For example [[HL-sims#FFP6 data set|FFP6]] <br />
<br />
===Beam Window Functions===<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> W_l </math> relates the true angular power spectra <math>C_l </math> with the observed angular power spectra <math>\widetilde{C}_l </math>:<br />
<br />
<math><br />
W_l= \widetilde{C}_l / C_l <br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_l </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_l </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_l </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
W^{est}_l = < C^{conv}_l / C^{in}_l ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing C^{conv}_l with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, Wl, for Planck mission====<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, Wl, for LFI channels''']] <br />
[[File:plot_dx9_HFI_BS_M12_CMB.png | 600px | thumb | |center |'''Beam Window functions, Wl, for HFI channels''']]<br />
<br />
== Retrieval of effective beam information from the PLA interface ==<br />
In order to retrieve the effective beam information, the user should:<br />
#Launch the Java interface from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive]; [[File:PLALink.png| 1000px | thumb | |center |'''Link to PLA Java interface.''']]<br />
#Once the PLA interface is loaded go to '''Sky maps'''; [[File:PLAinterface.png| 600px | thumb | |center |'''PLA java interface.''']]<br />
#On the '''Sky maps''' interface click on the icon on the left of the Effective beams area;<br />
[[File:Skymapsinterface.png| 600px | thumb | |center |'''Sky maps interface on the PLA''']]<br />
#The search interface for effective beams allows the user to retrieve the beam nearest to the input source (name or coordinates), or to retrieve a set of beams in a grid defined by the <math>N_{\rm side}</math> and the size of the region around a source (name or coordinates). The resolution of this grid is defined by the <math>N_{\rm side}</math> parametera and the size of the region is defined by the "Radius of <span class="noglossary">ROI</span>" parameter.[[File:EffectiveBeamsInterface.png| 600px | thumb | |center |'''Link to PLA Java interface.''']]<br />
Once the user proceeds with querying the beams, the PLA software retrieves the appropriate set of effective beams from the database and delivers it in a FITS file containin a HEALPix map of the beam which can be directly downloaded.<br />
<br />
==File Names==<br />
The effective beams are provided by the PLA as FITS files containg HEALPix maps of the beams. For the file names the following convention is used:<br />
*Single beam query: '''beams_FFF_''PixelNumber''.fits''' <br />
**FFF is the channel frequency (one of '''30''', '''44''', '''70''', '''100''', '''143''', '''217''', '''353''', '''545''', '''857'''); <br />
** ''PixelNumber'' is the number of the pixel to which the beam corresponds (<math>0</math> - <math>12 \times N_{\rm side}^2 - 1</math>). For the LFI <math>N_{\rm side}=1024</math>, for the HFI <math>N_{\rm side}=2048</math>;<br />
*Multiple beam query: '''beams_FFF_''FirstPixelNumber''-''LastPixelNumber''.zip''' <br /> The compressed files contains a set of files with the beams for the pixels covereing the selected region. FFF as for sinle beam query. The naming convention for the beam files contained in the ''.zip'' file is the same as for single beam queries.<br />
** ''FirstPixelNumber'' is the lowest pixel number for the area covered by the request;<br />
** ''LastPixelNumber'' is the highest pixel number for the area covered by the request;<br />
<br />
==File format==<br />
The FITS files provided by the PLA contain HEALPix maps of the beams.<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
<br />
[[Category:Mission products|004]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Scanning_Beams&diff=11281Scanning Beams2015-02-04T18:39:03Z<p>Agregori: /* File Names */</p>
<hr />
<div><br />
We released maps of the Stokes parameters of the band-averaged [[Beams LFI#Polarized_Scanning_Beams_and_Focal_Plane_calibration|scanning beams]]. The averages are performed using the [[The_RIMO#LFI_2|RIMO]] bandpass, assuming a flat spectrum of the incoming radiation. The Stokes parameters maps contain the complete information about the field intensity and polarization properties. Main Beam, Intermediate Beam, and Sidelobes are released separately.<br />
<br />
==File Names==<br />
<br />
The file names are of the form:<br />
<br />
''LFI_ScanBeam-{mb,ib,sl}_{fff}-{rrr}_R2.{nn}.stokes''<br />
<br />
where<br />
* ''fff'' denotes the frequency<br />
* ''mb'' denotes the Main Beams<br />
* ''ib'' denotes the Intermediate Beam <br />
* ''sl'' denotes the Sidelobes<br />
* ''rrr'' denotes the radiometer<br />
* ''R2.nn'' is the version.<br />
<br />
<br />
At the present time, HFI is not releasing the Scanning Beams.<br />
<br />
==FITS file structure==<br />
The FITS files contain a primary extension with no data and a minimal header, and one BINTABLE extension with data and with a description of the data in the header keywords. <br />
The BINTABLE extension consist in four columns, each containing the array of one Stokes parameter. <br />
The columns are called:<br />
* ''Beamdata'' , containing <math>I</math><br />
* ''BeamdataQ'', containing <math>Q</math><br />
* ''BeamdataU'', containing <math>U</math><br />
* ''BeamdataV'', containing <math>V</math>.<br />
<br />
Main Beam, Intermediate Beams and Sidelobes are saved with a different data format: <br />
<br />
* Main Beams are projected on the tangent plane to the sphere, and sampled on a grid. The grid include an angular region expressed by the keyword ''angularCut'', and its dimensions are given by the keywords ''Nx'' and ''Ny'', representing the number of columns and rows. Each column of the BINDATA extension contain the sequence of the <math>Nx \times Ny</math> samples of the map in row major order. The keywords ''Xcentre'' and ''Ycentre'' express the coordinates of the beam maximum (i.e. where the sphere intersect the tangent plane).<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Main Beam file structure''' <br />
<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description || Comment<br />
|-<br />
|BEAMDATA || Real*4 || none || Stokes parameter I || <br />
|-<br />
|BEAMDATAQ || Real*4 || none || Stokes parameter Q ||<br />
|-<br />
|BEAMDATAU || Real*4 || none || Stokes parameter U ||<br />
|-<br />
|BEAMDATAV || Real*4 || none || Stokes parameter V ||<br />
<br />
|- bgcolor="ffdead" <br />
<br />
! Keyword || Data Type || Value || Description || Comment<br />
|-<br />
|Nx || Int || 601 || X axis samples number || X axis aligned with the direction of the S arm<br />
|-<br />
|Ny || Int || 601 || Y axis samples number || Y axis aligned with the direction of the M arm<br />
|-<br />
|Xcentre || Int || 301 || X coordinate of the beam centre ||<br />
|-<br />
|Ycentre || Int || 301 || Y coordinate of the beam centre || <br />
|-<br />
|Xdelta || Float || || X step in radians || <br />
|-<br />
|Ydelta || Float || || Y step in radians || <br />
|}<br />
<br />
<br />
<br />
<br />
* Intermediate Beams and Sidelobes are sampled on the sphere. The resolution in <math>\theta</math> and <math>\phi</math> is given by the keywords "Ntheta" and "Nphi". The columns of the BINDATA extension contain the sequence of Nphi Stokes parameters for each <math>\theta</math>.<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Intermediate Beam and Sidelobes file structure''' <br />
<br />
|- bgcolor="ffdead"<br />
! Column Name || Data Type || Units || Description ||Comment<br />
|-<br />
|BEAMDATA || Real*4 || none || Stokes parameter I || <br />
|-<br />
|BEAMDATAQ || Real*4 || none || Stokes parameter Q ||<br />
|-<br />
|BEAMDATAU || Real*4 || none || Stokes parameter U ||<br />
|-<br />
|BEAMDATAV || Real*4 || none || Stokes parameter V ||<br />
<br />
|- bgcolor="ffdead" <br />
<br />
! Keyword || Data Type || Value || Description || Comment<br />
|-<br />
|Ntheta || Int || || <math>\theta</math> samples number || colatitude<br />
|-<br />
|Nphi || Int || || <math>\phi</math> samples number || longitude<br />
|-<br />
|Mintheta || Float || || Minimum value of <math>\theta</math> ||<br />
|-<br />
|Maxtheta || Float || || Maximum value of <math>\theta</math> ||<br />
|-<br />
|angularCut || Float || || Angular cut [deg] ||<br />
<br />
|}</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Sky_temperature_maps&diff=11278Sky temperature maps2015-02-04T18:24:28Z<p>Agregori: /* LFI processing */</p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature and polarization maps}}<br />
==General description==<br />
<br />
Sky maps give the best estimate of the intensity and polarization (Stokes Q and U components), if available, of the signal from the sky after removal, as far as possible, of known systematic effects (mostly instrumental, but including also the solar and earth-motion dipole, Galactic strylight and the Zodiacal light). Sky maps are provided for the full Planck mission using all valid detectors in each frequency channel, and also for various subsets by splitting the mission in various time ranges or in subsets of the detectors in a given channel. These products are useful for the study of source variability, but they are especially interesting for characterisation purposes (see also the [[HFI-Validation | data validation]] section). The details of the start and end of the time ranges are given in the table below.<br />
<br />
To help in further processing, there are also masks of the Galactic Plane and of point sources, each provided for several different depths.<br />
<br />
All sky maps are in Healpix format, with Nside of 1024 (LFI 30, 44 and 70) and 2048 (LFI 70 and HFI), in Galactic coordinates, and Nested ordering. The signal is given in units of K<sub>cmb</sub> for 30-353 GHz, and of MJy/sr (for a constant <math>\nu F_\nu</math> energy distribution ) for 545 and 857 GHz. For each frequency channel, the intensity and polarization maps are packaged into a ''BINTABLE'' extension of a FITS file together with a hit-count map (or hit map, for short, giving the number of observation samples that are cumulated in a pixel, all detectors combined) and with the variance and covariance maps. Additional information is given in the FITS file header. The structure of the FITS file is given in the [[#Format | FITS file structure]] section below. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Ranges for mission and surveys'''<br />
|- bgcolor="ffdead" <br />
! Range || ODs || HFI rings || pointing-IDs || Comment<br />
|-<br />
|nominal mission || 91 - 563 || 240 - 14723 || 00004200 - 03180200 ||<br />
|-<br />
|full mission || 91 - 974 || 240 - 27005 || 00004200 - 05322620 || for HFI<br />
|-<br />
|full mission || 91 - 1543 || n/a || 00004200 - 06511160 || for LFI<br />
|-<br />
|Survey 1 || 91 - 270 || 240 - 5720 || 00004200 - 01059820 ||<br />
|-<br />
|Survey 2 || 270 - 456 || 5721 - 11194 || 01059830 - 02114520 ||<br />
|-<br />
|Survey 3 || 456 - 636 || 11195 - 16691 || 02114530 - 03193660 ||<br />
|-<br />
|Survey 4 || 636 - 807 || 16692 - 21720 || 03193670 - 04243900 ||<br />
|-<br />
|Survey 5 || 807 - 974 || 21721 - 27005 || 05267180 - 05322590 || end of mission for HFI<br />
|-<br />
|Survey 5 || 807 - 993 || n/a || 05267180 - 06344800 || end of survey for LFI<br />
|-<br />
|Survey 6 || 993 - 1177 || n/a || 06344810 - 06398120 || LFI only <br />
|-<br />
|Survey 7 || 1177 - 1358 || n/a || 06398130 - 06456410 || LFI only <br />
|-<br />
|Survey 8 || 1358 - 1543 || n/a || 06456420 - 06511160 || LFI only <br />
|-<br />
|Survey 9 || 1543 - 1604 || n/a || 06511170 - 06533320 || LFI only Not in this delivery<br />
|-<br />
|HFI mission-half-1 || 91 - 531 || 240 - 13471 || 00004200 - 03155580 ||<br />
|-<br />
|HFI mission-half-2 || 531 - 974 || 13472 - 27005 || 03155590 - 05322590 ||<br />
|-<br />
|LFI Year 1 || 91 - 456 || n/a || 00004200 - 02114520 ||<br />
|-<br />
|LFI Year 2 || 456 - 807 || n/a || 02114530 - 04243900 ||<br />
|-<br />
|LFI Year 3 || 807 - 1177 || n/a || 05267180 - 06398120 ||<br />
|-<br />
|LFI Year 4 || 1177 - 1543 || n/a || 06398130 - 06511160 ||<br />
|-<br />
|}<br />
<br />
==Production process==<br />
<br />
Sky maps are produced by combining appropriately the data of all working detectors in a frequency channel over some period of the mission. They give the best estimate of the signal from the sky (unpolarised) after removal, as far as possible, of known systematic effects and of the dipole signals induced by the motion of the solar system in the CMB and of the Planck satellite in the solar system. In particular, they include the Zodiacal light emission (Zodi for short) and also the scattering from the far-side lobes of the beams (FSL). More on this below.<br />
<br />
=== HFI processing ===<br />
<br />
The mapmaking and calibration process is described in detail in the [[Map-making_LFI | Map-making]] section and in the [[A08 paper| mapmaking]] paper, where detailed references are found. In brief it consists of:<br />
<br />
; binning the TOI data onto ''rings'' : Healpix rings (HPRs) are used here, each ring containing the combined data of one pointing period. <br />
; flux calibration : at 100-353 GHz, the flux calibration factors are determined by correlating the signal with the orbital dipole, which is determined very accurately from the Planck satellite orbital parameters provided by Flight Dynamics. This provides a single gain factor per bolometer. At 545 and 857 GHz the gain is determined from the observation of Uranus and Neptune (but not Jupiter which is too bright) and comparison to recent models made explicitly for this mission. A single gain is applied to all rings at these frequencies.<br />
; destriping : in order to remove low-frequency noise, an offset per ring is determined by minimizing the differences between HPRs at their crossings, and removed.<br />
; Zodiacal light correction : a Zodiacal light model is used to build HPRs of the the Zodi emission, which is subtracted from the calibrated HPRs.<br />
; projection onto the map : the offset-corrected, flux-calibrated, and Zodi-cleaned HPRs are projected onto Healpix maps, with the data of each bolometer weighted by a factor of 1/NET of that bolometer.<br />
<br />
These steps are followed by some post-processing which is designed to prepare the maps for the component separation work. This post processing consists of: <br />
<br />
; Dust bandpass leakage correction : the Q and U maps are corrected for the dust leakage due to the different bandpasses that is determined using the ''ground'' method as described [[MISSING REF| here]]<br />
; Far Side Lobe calibration correction : the 100-217 maps are multiplied by factors of 1.00087, 1.00046, and 1.00043, respectively, to compensate for the non-removal of the far-side lobes, and similarly the corresponding covariance maps have also been corrected by multiplication by the square of the factor.<br />
; Fill missing pixels : missing pixels are filled in with a value that is the mean of valid pixels within a given radius. A radius of 1 deg is used for the full channel maps, and 1.5 deg is used for the detset maps. This step is not applied to the single survey maps since they have large swaths of the sky that are not covered.<br />
<br />
These maps provide the main mission products. Together with signal maps, hit count, variance, and variance maps are also produced. The hit maps give the (integer) number of valid TOI-level samples that contribute to the signal of each pixel. All valid samples are counted in the same way, i.e., there is no weighting factor applied. The variance maps project the white noise estimate, provided by the NETs, in the sky domain.<br />
<br />
Note that the nominal mission maps have not had the post-processing applied, which makes them more easily comparable to the PR1 products.<br />
<br />
=== LFI processing ===<br />
Input timelines are cleaned by 4pi convolved dipole and Galactic Straylight obtained as convolution of the 4pi in band far sidelobes and Galactic Simulation<br />
<br />
LFI maps were constructed with the Madam map-making code, version 3.7.4. The code is based on generalized destriping technique, where the correlated noise component is modeled as a sequence of constant offset, called baselines. A noise filter was used to constrain the baseline solution allowing the use of 1 second baselines.<br />
<br />
Radiometers were combined according to the horn-uniform weighting scheme to minimize systematics. The used weights are listed in [[Map-making LFI#Map-making|Map-making]]. The flagged samples were excluded from the analysis by setting their weights to <math>C_{w}^{-1}</math> = 0. The galaxy region was masked out in the destriping phase, to reduce error arising from strong signal gradients. The polarization component was included in the analysis... <br />
<br />
A detailed description of the map-making procedure is given in {{PlanckPapers|planck2013-p02}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}}, {{PlanckPapers|planck2014-a07||Planck-2015-A07}} and in section [[Map-making LFI#Map-making|Map-making]].<br />
<br />
==Types of maps ==<br />
<br />
=== Full mission, full channel maps (6 HFI, 4 LFI)===<br />
<br />
Full channel maps are built using all the valid detectors of a frequency channel and cover the either the full or the nominal mission. For HFI, the 143-8 and 545-3 bolometers are rejected entirely as they are seriously affected by RTS noise. For this release, HFI provides the Q and U components for the 353 GHz channel only. LFI provides the I, Q and U maps for all the channels. The I maps are displayed in the figures below. The color range is set using a histogram equalisation scheme (from HEALPIX) that is useful for these non-Gaussian data fields. The Q and U maps are not shown as they look like noise to the naked eye.<br />
The 70 GHz full map is available also at <math>N_{side}</math> 2048.<br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=260px heights=160px> <br />
File: SkyMap30e.png| '''Full mission, 30 GHz'''<br />
File: SkyMap44e.png | '''Full mission, 44 GHz'''<br />
File: SkyMap70e.png | '''Full mission, 70 GHz'''<br />
File: SkyMap100e.png | '''Full mission, 100 GHz'''<br />
File: SkyMap143e.png | '''Full mission, 143 GHz'''<br />
File: SkyMap217e.png | '''Full mission, 217 GHz'''<br />
File: SkyMap353e.png | '''Full mission, 353 GHz'''<br />
File: SkyMap545e.png | '''Full mission, 545 GHz'''<br />
File: SkyMap857e.png | '''Full mission, 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
=== Nominal mission, full channel maps (6 HFI)===<br />
<br />
These maps are similar to the ones above, but cover the nominal mission only. They are meant primarily to be compared to the PR1 products in order to see the level of improvements in the processing. Because of this, they are produced in Temperature only, and have not had the post-processing applied.<br />
<br />
=== Single survey, full channel maps (30 HFI, 35 LFI)===<br />
<br />
Single survey maps are built using all valid detectors of a frequency channel; they cover separately the different sky surveys. The surveys are defined as the times over which the satellite spin axis rotates but 180 degrees, which, due to the position of the detectors in the focal plane does not cover the full sky, but a fraction between ~80 and 90% depending on detector position. During adjacent surveys the sky is scanned in opposite directions. More precisely it is the ecliptic equator that is scanned in opposite directions. While these are useful to investigate variable sources, they are also used to study the systematics of the time-response of the detectors as they scan bright sources, like the Galactic Plane, in different directions during different survey. Note that the HFI and LFI missions cover 5 and 8 surveys, respectively, and in case of HFI the last survey in incomplete.<br />
The 70 GHz surveys maps are available also at <math>N_{side}</math> 2048.<br />
Note LFI provide a special surveys maps combination used in the low l analysis. This maps, available at the three LFI frequency 30, 44 and 70 GHz, was built using the combination of survey 1, 3, 5, 6, 7 and 8. <br />
<br />
=== Year maps, full channel maps (12 HFI, 16 LFI)===<br />
<br />
These maps are built using the data of surveys 1+2, surveys 3+4, and so forth. They are used to study long-term systematic effects.<br />
The 70 GHz years maps are available also at <math>N_{side}</math> 2048.<br />
<br />
===Half-mission maps, full channel maps (12 HFI, 12 LFI)===<br />
<br />
For HFI, the half mission is defined after eliminating those rings discarded for all bolometers. There are 347 such rings, may of which are during the 5th survey when the ''End-of-Life'' tests were performed. The remaining 26419 rings are divided in half (up to the odd ring) to define the two halves of the mission. This exercise is done for the full mission only.<br />
<br />
For LFI instead of the half-mission the following year combination has been created: Year 1+2, Year 1+3, Year 2+4, Year 3+4, <br />
<br />
===Full mission, single detector maps (18 HFI, 22 LFI)===<br />
<br />
IN case of HFI these maps are built only for the SWBs (non polarized) and contain only temperature data, of course. They are not built for the polarisation sensitive detectors because they are not fixed on the sky as the polarisation component depends on the position angle at the time of observation. Instead, we provide maps built by ''quads'' of polarisation-sensitive detectors (see next section), which have different polarisation angles and that can be used to built I, Q, and U maps<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''HFI Temperature sensitive bolometers'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Detector names<br />
|-<br />
|143 GHz || 143-5, 6, 7<br />
|-<br />
|217 GHz || 217-1, 2, 3, 4<br />
|-<br />
|353 GHz || 353-1, 2, 7, 8<br />
|-<br />
|545 GHz || 545-1, 2, 4<br />
|-<br />
|857 GHz || 857-1, 2 , 3, 4<br />
|}<br />
<br />
The 143-8 and 353-3 bolometer data are affected by strong RTS (random telegraphic signal) noise. They have not been used in the data processing, and are not delivered. For a figure showing the focal plane layout, see [[Detector_pointing#Introduction_and_Summary | this Introduction]] of the Detector Pointing chapter.<br />
<br />
In case of LFI, all the 22 Radiometers maps are available, those, obviously, are only in temperature.<br />
<br />
===Full mission, detector set or detector pairs maps (8 HFI, 8 LFI)===<br />
<br />
The objective here is to build independent temperature (I) and polarisation (Q and U) maps with the two pairs of polarisation sensitive detectors of each channel where they are available, i.e. in the 44-353 GHz channels. The table below indicates which detectors were used to built each detector set (detset).<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of HFI Detector Sets'''<br />
|- bgcolor="ffdead" <br />
!Frequency || DetSet1 || DetSet2 <br />
|-<br />
|100 GHz || 100-1a/b & 100-4a/b || 100-2a/b & 100-3a/b<br />
|-<br />
|143 GHz || 143-1a/b 1 & 43-3a/b || 143-2a/b & 143-4a/b<br />
|-<br />
|217 GHz || 217-5a/b & 217-7a/b || 217-6a/b & 217-8a/b<br />
|-<br />
|353 GHz || 353-3a/b & 353-5a/b || 353-4a/b & 353-6a/b<br />
|}<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of LFI Detector Pairs'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Horn Pair || Comment <br />
|-<br />
|44 GHz || 24 || This maps is only in temperature<br />
|-<br />
|44 GHz || 25 & 26 || <br />
|-<br />
|70 GHz || 18 & 23 || Available also at <math>N_{side}</math> = 2048<br />
|-<br />
|70 GHz || 19 & 22 || Available also at <math>N_{side}</math> = 2048<br />
|-<br />
|70 GHz || 20 & 21 || Available also at <math>N_{side}</math> = 2048<br />
|}<br />
<br />
<br />
===Half-ring maps (64 HFI, 62 LFI)===<br />
<br />
These maps are similar to the ones above, but are built using only the first or the second half of each ring (or pointing period). The HFI provides half-ring maps for the full mission only, and for the full channel, the detsets, and the single bolometers. The LFI provides half-rings maps for the channel full mission (70 GHz also at <math>N_{side}</math> 2048), for the radiometer full mission and the horn pairs full mission.<br />
<!----<br />
===Masks===<br />
<br />
Masks are provided of the Galactic Plane and of the point sources. For the Galactic Plane, eight masks are given covering different fractions of the sky, and for the points sources two masks are given, at the 5 and 10 sigma level, for each Planck HFI and LFI frequency channel. These are generic masks, specific masks applicable to other products are delivered with the products themselves.<br />
---><br />
<br />
=== The Zodiacal light correction maps ===<br />
<br />
The Zodiacal light signal depends on the location of the observer relative to the Zodiacal light bands, and thus it is not a fixed pattern on the sky but depends on the period of observation. The maps presented here are the difference between the uncorrected (and not delivered) and the corrected maps. <br />
<br />
<br />
<!---center><br />
<gallery perrow=3 widths=260px heights=170px><br />
File: ZodiRes100.png | '''zodi/FSL rediduals - 100 GHz'''<br />
File: ZodiRes143.png | '''zodi/FSL rediduals - 143 GHz''' <br />
File: ZodiRes217.png | '''zodi/FSL rediduals - 217 GHz'''<br />
File: ZodiRes353.png | '''zodi/FSL rediduals - 353 GHz'''<br />
File: ZodiRes545.png | '''zodi/FSL rediduals - 545 GHz'''<br />
File: ZodiRes857.png | '''zodi/FSL rediduals - 857 GHz'''<br />
</gallery><br />
</center ---><br />
<br />
=== Caveats and known issues ===<br />
<br />
TBW<br />
<br />
==== Map zero-level ====<br />
<br />
For the 100 to 857 GHz maps, the zero levels are set to their optimal levels for Galactic and CIB studies. A procedure for adjusting them to astrophysical values is given in the HFI Mapmaking and Calibration paper {{PlanckPapers|????}}.<br />
<br />
For the 30, 44 and 70 GHz, maps are corrected for zero level monopole by applying an offset correction, see LFI Calibration paper {{PlanckPapers|planck2013-p02b}} section 3.4 "Setting the zero levels in the maps" and {{PlanckPapers|planck2014-a06||Planck-2015-A06}}. Note that the offset applied is indicated in the header as a comment keyword.<br />
<br />
==Inputs==<br />
=== HFI inputs ===<br />
<br />
* The cleaned TOIs of signal of each detector, together with their flags, produced by the [[TOI processing|TOI processing]] pipeline<br />
* The TOIs of pointing (quaternions), described in [[Detector_pointing|Detector pointing]]<br />
* Bolometer-level characterization data, from the DPC's internal IMO (not distributed)<br />
* Planck orbit data used to compute and remove the earth dipole<br />
* Planck solar dipole information used to calibrate the CMB channels<br />
* Planet models used to calibrate the Galactic channels.<br />
<br />
=== LFI inputs ===<br />
<br />
The Madam map-maker takes as an input:<br />
<br />
* The calibrated timelines (for details see [[TOI processing LFI|TOI Processing]])<br />
* The detector pointings (for details see [[Detector_pointing|Detector pointing]])<br />
* The noise information in the form of three-parameter (white noise level (<math>\sigma</math>), slope, and knee frequency ($f_\mathrm{knee}$)) noise model (for details see [[The RIMO|RIMO]])<br />
<br />
==Related products==<br />
=== Masks ===<br />
<br />
This section presents the masks of the point sources and of the Galactic plane. These are ''general purpose'' masks. Other masks specific to certain products are packaged with the products.<br />
<br />
====Point source masks====<br />
<br />
For HFI and LFI two sets of masks are provided: <br />
* Intensity masks, which removes sources detected with SNR > 5. <br />
* Polarisation masks, which remove sources which have polarisation detection significance of 99.97 % or greater at the position of a source detected in intensity. They were derived from the polarisation maps with dust ground bandpass mismatch leakage correction applied. The cut around each source has a radius of 3σ (width) of the beam ~ 1.27 FWHM (for LFI the cut around each source has a radius of 32 arcmin at 30GHz, 27 arcmin at 44 GHz and 13 arcmin at 70 GHz).<br />
<br />
Both sets are found in the file ''HFI_Mask_PointSrc_2048_R2.00.fits'' in which the first extension contains the Intensity masks, and the second contains the Polarisation masks.<br />
<br />
====Galactic Plane masks====<br />
<br />
Eight masks are provided giving 20, 40, 60, 70, 80, 90, 97, and 99% sky coverage derived from the 353 GHz map, after CMB subtraction. They are independent of frequency channel. Three versions of these are given: not apodized, and apodized by 2 and 5 deg. The filenames are ''HFI_Mask_GalPlane-apoN_2048_R2.00.fits'', where N = 0, 2, 5.<br />
<br />
The masks are shows below. The 8 GalPlane masks are combined (added together) and shown in a single figure for each of the three apodization. While the result is quite clear for the case of no apodization, it is less so for the apodized case. The point source masks are shown separately for the Intensity case.<br />
<br />
<center><br />
<gallery perrow=3 widths=260px heights=160px ><br />
File: GalPlaneMask_apo0.png | '''Galactic Plane masks, no apod'''<br />
File: GalPlaneMask_apo2.png | '''Galactic Plane masks, apod 2 deg'''<br />
File: GalPlaneMask_apo5.png | '''Galactic Plane masks, apod 5 deg'''<br />
File: PointSrcMask_100.png | '''PointSource mask 100 GHz'''<br />
File: PointSrcMask_143.png | '''PointSource mask 143 GHz'''<br />
File: PointSrcMask_217.png | '''PointSource mask 217 GHz'''<br />
File: PointSrcMask_353.png | '''PointSource mask 343 GHz'''<br />
File: PointSrcMask_545.png | '''PointSource mask 545 GHz'''<br />
File: PointSrcMask_857.png | '''PointSource mask 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
== File names ==<br />
The FITS filenames are of the form ''{H|L}FI_SkyMap_fff{-tag}_Nside_R2.nn_{coverage}-{type}.fits'', where ''fff'' are three digits to indicate the Planck frequency band, ''tag'' indicates the single detector or the detset, ''Nside'' is the Healpix Nside of the map, ''coverage'' indicates which part of the mission is covered (full, half mission, survey, year, ...) , and the optional ''type'' indicates the subset of input data used. The table below lists the products by type, with the appropriate unix wildcards that form the full filename.<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=880px<br />
|+ '''HFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename <br />
|-<br />
| Full chan, full mission ||HFI_SkyMap_???_2048_R2.??_full.fits ||HFI_SkyMap_???_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
| Full channel, nominal mission ||HFI_SkyMap_???_2048_R2.??_nominal.fits || n/a<br />
|-<br />
| Full channel, single survey || HFI_SkyMap_???_2048_R2.??_survey-?.fits || n/a<br />
|-<br />
| Full channel, single year || HFI_SkyMap_???_2048_R2.??_year-?.fits || n/a<br />
|-<br />
| Full channel, half mission || HFI_SkyMap_???_2048_R2.??_halfmission*-?.fits || n/a<br />
|-<br />
| Det-set, full mission || HFI_SkyMap_???-ds?_2048_R2.??_full.fits || HFI_SkyMap_???-ds?_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
|Single SWB, full mission || HFI_SkyMap_???-?_2048_R2.??_full.fits || HFI_SkyMap_???-?_2048_R2.??_full-ringhalf-?.fits<br />
|}<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=1000px<br />
|+ '''LFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename || Comment<br />
|-<br />
| Full channel, full mission ||LFI_SkyMap_???_1024_R2.??_full.fits ||LFI_SkyMap_???_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Full channel, single survey || LFI_SkyMap_???_1024_R2.??_survey-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, survey combination || LFI_SkyMap_???_1024_R2.??_survey-1-3-5-6-7-8.fits || n/a || n/a<br />
|-<br />
| Full channel, single year || LFI_SkyMap_???_1024_R2.??_year-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, year combination || LFI_SkyMap_???_1024_R2.??_year?-?.fits || n/a || n/a<br />
|-<br />
| Horn pair, full mission || LFI_SkyMap_???-??-??_1024_R2.??_full.fits || LFI_SkyMap_???_??-??_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Single radiometer, full mission || LFI_SkyMap_???-???_1024_R2.??_full.fits || LFI_SkyMap_???-???_1024_R2.??_full-ringhalf-?.fits || n/a<br />
|}<br />
<br />
<br />
<br />
For the benefit of users who are only looking for the frequency maps with no additional information, we also provide a file combining the 9 frequency maps as separate columns in a single extension. The 9 columns in this file contain the intensity maps ONLY and no other information (hit maps and variance maps) is provided.<br />
<br />
<!---<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=500px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal.fits|link=LFI_SkyMap_030_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal.fits|link=LFI_SkyMap_044_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal.fits|link=LFI_SkyMap_070_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal.fits|link=LFI_SkyMap_070_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal.fits|link=HFI_SkyMap_100_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal.fits|link=HFI_SkyMap_143_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal.fits|link=HFI_SkyMap_217_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal.fits|link=HFI_SkyMap_353_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal.fits|link=HFI_SkyMap_545_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal.fits|link=HFI_SkyMap_857_2048_R1.10_nominal.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel, Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits}} <br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Combined frequency maps<br />
|-<br />
| '''All''' || {{PLASingleFile|fileType=file|name=COM_MapSet_I-allFreqs_R1.10_nominal.fits|link=COM_MapSet_I-allFreqs_R1.10_nominal.fits}} <br />
|}<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=850px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 maps || Survey 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_1.fits|link=LFI_SkyMap_030_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_2.fits|link=LFI_SkyMap_030_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_1.fits|link=LFI_SkyMap_044_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_2.fits|link=LFI_SkyMap_044_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_1.fits|link=LFI_SkyMap_070_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_2.fits|link=LFI_SkyMap_070_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_1.fits|link=LFI_SkyMap_070_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_2.fits|link=LFI_SkyMap_070_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 Zodi-corrected maps || Survey 2 Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Half-ring 1 maps ||Half-ring 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|}<br />
---><br />
<br />
== FITS file structure ==<br />
<br />
The FITS files for the sky maps contain a minimal primary header with no data, and a ''BINTABLE'' extension (EXTENSION 1, EXTNAME = ''FREQ-MAP'') containing the data. The structure is shows schematically in the figure below. The ''FREQ-MAP'' extension contains a 3- or a 10-column table that contain the signal, hit-count and variance maps, all in Healpix format. The 3-column case is for intensity only maps, the 10-column case is for polarisation. The number of rows is the number of map pixels, which is Npix = 12 <math>N_{side}</math><sup>2</sup> for Healpix maps, where <math>N_{side}</math> = 1024 or 2048 for most the maps presented in this chapter.<br />
<br />
[[File:FITS_FreqMap.png | 550px | center | thumb | '''FITS file structure''']]<br />
<br />
Note that file sizes are ~0.6 GB for I-only maps and ~1.9 GB for I,Q,U maps at <math>N_{side}</math> 2048 and ~0.14 GB for I-only maps and ~0.45 GB for I,Q,U maps at <math>N_{side}</math> 1024 .<br />
<br />
Keywords indicate the coordinate system (GALACTIC), the Healpix ordering scheme (NESTED), the units (K_cmb or MJy/sr) of each column, and of course the frequency channel (FREQ). Where polarisation Q and U maps are provided, the ''COSMO'' polarisation convention (used in HEALPIX) is adopted, and it is specified in the ''POLCCONV'' keyword (see [[Sky_temperature_maps#Polarization_convention_used_in_the_Planck_project|this section]]. The COMMENT fields give a one-line summary of the product, and some other information useful for traceability within the DPCs. The original filename is also given in the ''FILENAME'' keyword. The ''BAD_DATA'' keyword gives the value used by Healpix to indicate pixels for which no signal is present (these will also have a hit-count value of 0). The main parameters are summarised below:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Sky map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'FREQ-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes I map<br />
|-<br />
|Q_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes Q map (optional)<br />
|-<br />
|U_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes U map (optional)<br />
|-<br />
|HITS || Int*4 || none || The hit-count map<br />
|-<br />
|II_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The II variance map<br />
|-<br />
|IQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|IU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|QQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QQ variance map (optional)<br />
|-<br />
|QU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QU variance map (optional)<br />
|-<br />
|UU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The UU variance map (optional)<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix <math>N_{side}</math> <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 12 <math>N_{side}</math><sup>2</sup> – 1 || Last pixel number<br />
|-<br />
|FREQ || string || nnn || The frequency channel <br />
|}<br />
<br />
<br />
The same structure applies to all ''SkyMap'' products, independent of whether they are full channel, survey of half-ring. The distinction between the types of maps is present in the FITS filename (and in the traceability comment fields).<br />
<br />
==Polarization convention used in the Planck project==<br />
<br />
The Planck collaboration used the COSMO convention for the polarization angle (as usually used in space based CMB missions), whereas other astronomical fields usually use the IAU convention. In the following document we report the difference between these two conventions, and the consequence if it is NOT taken into account correctly in the analysis.<br />
<br />
[[File:conventions.png|thumb|center|400px|'''Figure 1. COSMO convention (left) and IAU convention (right). The versor <math>\hat{z}</math> points outwards the pointing direction in COSMO, and inwards in IAU. The bottom panel refers to the plane tangent to the sphere.''']]<br />
<br />
Changing the orientation convention is equivalent to a transformation <math>\psi'=\pi-\psi</math> of the polarization angle (Figure 1). The consequence of this transformation is the inversion of the Stokes parameter <math>U</math>.<br />
The components of the polarization tensor in the helicity basis <math>\epsilon^{\pm}=1/\sqrt{2}(\hat{x}\pm i\hat{y})</math> are:<br />
<br />
<math><br />
(Q+iU)(\hat{n}) = \sum _{\ell m}a_{2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
\\(Q-iU)(\hat{n}) = \sum _{\ell m}a_{-2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where <math>{}_{2}Y_{\ell }^{m}(\hat{n})</math> are the spin weighted spherical harmonic functions.<br />
The <math>E</math> and <math>B</math> modes can be defined as:<br />
<math><br />
E(\hat{n}) = \sum_{\ell m}a_{E,\ell m}Y_{\ell }^{m}(\hat{n})<br />
\\B(\hat{n}) = \sum_{\ell m}a_{B,\ell m}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where the coefficients <math>a_{E,\ell m}</math> and <math>a_{B,\ell m}</math> are derived from linear combinations of the <math>a_{2,\ell m}</math> , <math>a_{-2,\ell m}</math> defined implicitly in the first equation (<math>Q\pm iU</math>).<br />
<br />
[[File:test_gradient.jpg|thumb|center|400px|]]<br />
[[File:test_curl.jpg|thumb|center|400px|'''Figure 2. Error on Planck-LFI 70 GHz <math>EE</math> (top) and <math>BB</math> (bottom) spectra, in case of wrong choice of the coordinate system convention (IAU instead of COSMO).''']]<br />
<br />
The effect of the sign inversion of <math>U</math> on the polarization spectra is a non trivial mixing of <math>E</math> and <math>B</math> modes. <br />
<br />
An example of the typical error on <math>EE</math> and <math>BB</math> auto-spectra in case of a wrong choice of the polarization basis is shown in Figure 2.<br />
<br />
BE CAREFUL about the polarization convention you are using. If the IAU convention is used in computing the power spectra, the sign of the <math>U</math> component of the Planck maps must be inverted before computing <math>E</math> and <math>B</math> modes.<br />
<br />
=== Note on the convention used by the Planck Catalog of Compact Sources (PCCS) ===<br />
For continuity with other compact sources catolgues, the Catalogue of Compact Sources provided by Planck follows the IAU convention, and the polarization angles are defined on an interval of [-90,90] degrees. To switch to the COSMO convention, the polarization angles listed in the catalogue have to be shifted by 90 degrees and multiplied by -1.<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:Mission products|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Sky_temperature_maps&diff=11276Sky temperature maps2015-02-04T18:22:33Z<p>Agregori: /* FITS file structure */</p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature and polarization maps}}<br />
==General description==<br />
<br />
Sky maps give the best estimate of the intensity and polarization (Stokes Q and U components), if available, of the signal from the sky after removal, as far as possible, of known systematic effects (mostly instrumental, but including also the solar and earth-motion dipole, Galactic strylight and the Zodiacal light). Sky maps are provided for the full Planck mission using all valid detectors in each frequency channel, and also for various subsets by splitting the mission in various time ranges or in subsets of the detectors in a given channel. These products are useful for the study of source variability, but they are especially interesting for characterisation purposes (see also the [[HFI-Validation | data validation]] section). The details of the start and end of the time ranges are given in the table below.<br />
<br />
To help in further processing, there are also masks of the Galactic Plane and of point sources, each provided for several different depths.<br />
<br />
All sky maps are in Healpix format, with Nside of 1024 (LFI 30, 44 and 70) and 2048 (LFI 70 and HFI), in Galactic coordinates, and Nested ordering. The signal is given in units of K<sub>cmb</sub> for 30-353 GHz, and of MJy/sr (for a constant <math>\nu F_\nu</math> energy distribution ) for 545 and 857 GHz. For each frequency channel, the intensity and polarization maps are packaged into a ''BINTABLE'' extension of a FITS file together with a hit-count map (or hit map, for short, giving the number of observation samples that are cumulated in a pixel, all detectors combined) and with the variance and covariance maps. Additional information is given in the FITS file header. The structure of the FITS file is given in the [[#Format | FITS file structure]] section below. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Ranges for mission and surveys'''<br />
|- bgcolor="ffdead" <br />
! Range || ODs || HFI rings || pointing-IDs || Comment<br />
|-<br />
|nominal mission || 91 - 563 || 240 - 14723 || 00004200 - 03180200 ||<br />
|-<br />
|full mission || 91 - 974 || 240 - 27005 || 00004200 - 05322620 || for HFI<br />
|-<br />
|full mission || 91 - 1543 || n/a || 00004200 - 06511160 || for LFI<br />
|-<br />
|Survey 1 || 91 - 270 || 240 - 5720 || 00004200 - 01059820 ||<br />
|-<br />
|Survey 2 || 270 - 456 || 5721 - 11194 || 01059830 - 02114520 ||<br />
|-<br />
|Survey 3 || 456 - 636 || 11195 - 16691 || 02114530 - 03193660 ||<br />
|-<br />
|Survey 4 || 636 - 807 || 16692 - 21720 || 03193670 - 04243900 ||<br />
|-<br />
|Survey 5 || 807 - 974 || 21721 - 27005 || 05267180 - 05322590 || end of mission for HFI<br />
|-<br />
|Survey 5 || 807 - 993 || n/a || 05267180 - 06344800 || end of survey for LFI<br />
|-<br />
|Survey 6 || 993 - 1177 || n/a || 06344810 - 06398120 || LFI only <br />
|-<br />
|Survey 7 || 1177 - 1358 || n/a || 06398130 - 06456410 || LFI only <br />
|-<br />
|Survey 8 || 1358 - 1543 || n/a || 06456420 - 06511160 || LFI only <br />
|-<br />
|Survey 9 || 1543 - 1604 || n/a || 06511170 - 06533320 || LFI only Not in this delivery<br />
|-<br />
|HFI mission-half-1 || 91 - 531 || 240 - 13471 || 00004200 - 03155580 ||<br />
|-<br />
|HFI mission-half-2 || 531 - 974 || 13472 - 27005 || 03155590 - 05322590 ||<br />
|-<br />
|LFI Year 1 || 91 - 456 || n/a || 00004200 - 02114520 ||<br />
|-<br />
|LFI Year 2 || 456 - 807 || n/a || 02114530 - 04243900 ||<br />
|-<br />
|LFI Year 3 || 807 - 1177 || n/a || 05267180 - 06398120 ||<br />
|-<br />
|LFI Year 4 || 1177 - 1543 || n/a || 06398130 - 06511160 ||<br />
|-<br />
|}<br />
<br />
==Production process==<br />
<br />
Sky maps are produced by combining appropriately the data of all working detectors in a frequency channel over some period of the mission. They give the best estimate of the signal from the sky (unpolarised) after removal, as far as possible, of known systematic effects and of the dipole signals induced by the motion of the solar system in the CMB and of the Planck satellite in the solar system. In particular, they include the Zodiacal light emission (Zodi for short) and also the scattering from the far-side lobes of the beams (FSL). More on this below.<br />
<br />
=== HFI processing ===<br />
<br />
The mapmaking and calibration process is described in detail in the [[Map-making_LFI | Map-making]] section and in the [[A08 paper| mapmaking]] paper, where detailed references are found. In brief it consists of:<br />
<br />
; binning the TOI data onto ''rings'' : Healpix rings (HPRs) are used here, each ring containing the combined data of one pointing period. <br />
; flux calibration : at 100-353 GHz, the flux calibration factors are determined by correlating the signal with the orbital dipole, which is determined very accurately from the Planck satellite orbital parameters provided by Flight Dynamics. This provides a single gain factor per bolometer. At 545 and 857 GHz the gain is determined from the observation of Uranus and Neptune (but not Jupiter which is too bright) and comparison to recent models made explicitly for this mission. A single gain is applied to all rings at these frequencies.<br />
; destriping : in order to remove low-frequency noise, an offset per ring is determined by minimizing the differences between HPRs at their crossings, and removed.<br />
; Zodiacal light correction : a Zodiacal light model is used to build HPRs of the the Zodi emission, which is subtracted from the calibrated HPRs.<br />
; projection onto the map : the offset-corrected, flux-calibrated, and Zodi-cleaned HPRs are projected onto Healpix maps, with the data of each bolometer weighted by a factor of 1/NET of that bolometer.<br />
<br />
These steps are followed by some post-processing which is designed to prepare the maps for the component separation work. This post processing consists of: <br />
<br />
; Dust bandpass leakage correction : the Q and U maps are corrected for the dust leakage due to the different bandpasses that is determined using the ''ground'' method as described [[MISSING REF| here]]<br />
; Far Side Lobe calibration correction : the 100-217 maps are multiplied by factors of 1.00087, 1.00046, and 1.00043, respectively, to compensate for the non-removal of the far-side lobes, and similarly the corresponding covariance maps have also been corrected by multiplication by the square of the factor.<br />
; Fill missing pixels : missing pixels are filled in with a value that is the mean of valid pixels within a given radius. A radius of 1 deg is used for the full channel maps, and 1.5 deg is used for the detset maps. This step is not applied to the single survey maps since they have large swaths of the sky that are not covered.<br />
<br />
These maps provide the main mission products. Together with signal maps, hit count, variance, and variance maps are also produced. The hit maps give the (integer) number of valid TOI-level samples that contribute to the signal of each pixel. All valid samples are counted in the same way, i.e., there is no weighting factor applied. The variance maps project the white noise estimate, provided by the NETs, in the sky domain.<br />
<br />
Note that the nominal mission maps have not had the post-processing applied, which makes them more easily comparable to the PR1 products.<br />
<br />
=== LFI processing ===<br />
Input timelines are cleaned by 4pi convolved dipole and Galactic Straylight obtained as convolution of the 4pi in band far sidelobes and Galactic Simulation<br />
<br />
LFI maps were constructed with the Madam map-making code, version 3.7.4. The code is based on generalized destriping technique, where the correlated noise component is modeled as a sequence of constant offset, called baselines. A noise filter was used to constrain the baseline solution allowing the use of 1 second baselines.<br />
<br />
Radiometers were combined according to the horn-uniform weighting scheme to minimize systematics. The used weights are listed in [[Map-making LFI#Map-making|Map-making]]. The flagged samples were excluded from the analysis by setting their weights to <math>C_{w}^{-1}</math> = 0. The galaxy region was masked out in the destriping phase, to reduce error arising from strong signal gradients. The polarization component was included in the analysis... <br />
<br />
A detailed description of the map-making procedure is given in {{PlanckPapers|planck2013-p02}} {{PlanckPapers|planck2014-a07||Planck-2015-A07}} and in section [[Map-making LFI#Map-making|Map-making]].<br />
<br />
==Types of maps ==<br />
<br />
=== Full mission, full channel maps (6 HFI, 4 LFI)===<br />
<br />
Full channel maps are built using all the valid detectors of a frequency channel and cover the either the full or the nominal mission. For HFI, the 143-8 and 545-3 bolometers are rejected entirely as they are seriously affected by RTS noise. For this release, HFI provides the Q and U components for the 353 GHz channel only. LFI provides the I, Q and U maps for all the channels. The I maps are displayed in the figures below. The color range is set using a histogram equalisation scheme (from HEALPIX) that is useful for these non-Gaussian data fields. The Q and U maps are not shown as they look like noise to the naked eye.<br />
The 70 GHz full map is available also at <math>N_{side}</math> 2048.<br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=260px heights=160px> <br />
File: SkyMap30e.png| '''Full mission, 30 GHz'''<br />
File: SkyMap44e.png | '''Full mission, 44 GHz'''<br />
File: SkyMap70e.png | '''Full mission, 70 GHz'''<br />
File: SkyMap100e.png | '''Full mission, 100 GHz'''<br />
File: SkyMap143e.png | '''Full mission, 143 GHz'''<br />
File: SkyMap217e.png | '''Full mission, 217 GHz'''<br />
File: SkyMap353e.png | '''Full mission, 353 GHz'''<br />
File: SkyMap545e.png | '''Full mission, 545 GHz'''<br />
File: SkyMap857e.png | '''Full mission, 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
=== Nominal mission, full channel maps (6 HFI)===<br />
<br />
These maps are similar to the ones above, but cover the nominal mission only. They are meant primarily to be compared to the PR1 products in order to see the level of improvements in the processing. Because of this, they are produced in Temperature only, and have not had the post-processing applied.<br />
<br />
=== Single survey, full channel maps (30 HFI, 35 LFI)===<br />
<br />
Single survey maps are built using all valid detectors of a frequency channel; they cover separately the different sky surveys. The surveys are defined as the times over which the satellite spin axis rotates but 180 degrees, which, due to the position of the detectors in the focal plane does not cover the full sky, but a fraction between ~80 and 90% depending on detector position. During adjacent surveys the sky is scanned in opposite directions. More precisely it is the ecliptic equator that is scanned in opposite directions. While these are useful to investigate variable sources, they are also used to study the systematics of the time-response of the detectors as they scan bright sources, like the Galactic Plane, in different directions during different survey. Note that the HFI and LFI missions cover 5 and 8 surveys, respectively, and in case of HFI the last survey in incomplete.<br />
The 70 GHz surveys maps are available also at <math>N_{side}</math> 2048.<br />
Note LFI provide a special surveys maps combination used in the low l analysis. This maps, available at the three LFI frequency 30, 44 and 70 GHz, was built using the combination of survey 1, 3, 5, 6, 7 and 8. <br />
<br />
=== Year maps, full channel maps (12 HFI, 16 LFI)===<br />
<br />
These maps are built using the data of surveys 1+2, surveys 3+4, and so forth. They are used to study long-term systematic effects.<br />
The 70 GHz years maps are available also at <math>N_{side}</math> 2048.<br />
<br />
===Half-mission maps, full channel maps (12 HFI, 12 LFI)===<br />
<br />
For HFI, the half mission is defined after eliminating those rings discarded for all bolometers. There are 347 such rings, may of which are during the 5th survey when the ''End-of-Life'' tests were performed. The remaining 26419 rings are divided in half (up to the odd ring) to define the two halves of the mission. This exercise is done for the full mission only.<br />
<br />
For LFI instead of the half-mission the following year combination has been created: Year 1+2, Year 1+3, Year 2+4, Year 3+4, <br />
<br />
===Full mission, single detector maps (18 HFI, 22 LFI)===<br />
<br />
IN case of HFI these maps are built only for the SWBs (non polarized) and contain only temperature data, of course. They are not built for the polarisation sensitive detectors because they are not fixed on the sky as the polarisation component depends on the position angle at the time of observation. Instead, we provide maps built by ''quads'' of polarisation-sensitive detectors (see next section), which have different polarisation angles and that can be used to built I, Q, and U maps<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''HFI Temperature sensitive bolometers'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Detector names<br />
|-<br />
|143 GHz || 143-5, 6, 7<br />
|-<br />
|217 GHz || 217-1, 2, 3, 4<br />
|-<br />
|353 GHz || 353-1, 2, 7, 8<br />
|-<br />
|545 GHz || 545-1, 2, 4<br />
|-<br />
|857 GHz || 857-1, 2 , 3, 4<br />
|}<br />
<br />
The 143-8 and 353-3 bolometer data are affected by strong RTS (random telegraphic signal) noise. They have not been used in the data processing, and are not delivered. For a figure showing the focal plane layout, see [[Detector_pointing#Introduction_and_Summary | this Introduction]] of the Detector Pointing chapter.<br />
<br />
In case of LFI, all the 22 Radiometers maps are available, those, obviously, are only in temperature.<br />
<br />
===Full mission, detector set or detector pairs maps (8 HFI, 8 LFI)===<br />
<br />
The objective here is to build independent temperature (I) and polarisation (Q and U) maps with the two pairs of polarisation sensitive detectors of each channel where they are available, i.e. in the 44-353 GHz channels. The table below indicates which detectors were used to built each detector set (detset).<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of HFI Detector Sets'''<br />
|- bgcolor="ffdead" <br />
!Frequency || DetSet1 || DetSet2 <br />
|-<br />
|100 GHz || 100-1a/b & 100-4a/b || 100-2a/b & 100-3a/b<br />
|-<br />
|143 GHz || 143-1a/b 1 & 43-3a/b || 143-2a/b & 143-4a/b<br />
|-<br />
|217 GHz || 217-5a/b & 217-7a/b || 217-6a/b & 217-8a/b<br />
|-<br />
|353 GHz || 353-3a/b & 353-5a/b || 353-4a/b & 353-6a/b<br />
|}<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of LFI Detector Pairs'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Horn Pair || Comment <br />
|-<br />
|44 GHz || 24 || This maps is only in temperature<br />
|-<br />
|44 GHz || 25 & 26 || <br />
|-<br />
|70 GHz || 18 & 23 || Available also at <math>N_{side}</math> = 2048<br />
|-<br />
|70 GHz || 19 & 22 || Available also at <math>N_{side}</math> = 2048<br />
|-<br />
|70 GHz || 20 & 21 || Available also at <math>N_{side}</math> = 2048<br />
|}<br />
<br />
<br />
===Half-ring maps (64 HFI, 62 LFI)===<br />
<br />
These maps are similar to the ones above, but are built using only the first or the second half of each ring (or pointing period). The HFI provides half-ring maps for the full mission only, and for the full channel, the detsets, and the single bolometers. The LFI provides half-rings maps for the channel full mission (70 GHz also at <math>N_{side}</math> 2048), for the radiometer full mission and the horn pairs full mission.<br />
<!----<br />
===Masks===<br />
<br />
Masks are provided of the Galactic Plane and of the point sources. For the Galactic Plane, eight masks are given covering different fractions of the sky, and for the points sources two masks are given, at the 5 and 10 sigma level, for each Planck HFI and LFI frequency channel. These are generic masks, specific masks applicable to other products are delivered with the products themselves.<br />
---><br />
<br />
=== The Zodiacal light correction maps ===<br />
<br />
The Zodiacal light signal depends on the location of the observer relative to the Zodiacal light bands, and thus it is not a fixed pattern on the sky but depends on the period of observation. The maps presented here are the difference between the uncorrected (and not delivered) and the corrected maps. <br />
<br />
<br />
<!---center><br />
<gallery perrow=3 widths=260px heights=170px><br />
File: ZodiRes100.png | '''zodi/FSL rediduals - 100 GHz'''<br />
File: ZodiRes143.png | '''zodi/FSL rediduals - 143 GHz''' <br />
File: ZodiRes217.png | '''zodi/FSL rediduals - 217 GHz'''<br />
File: ZodiRes353.png | '''zodi/FSL rediduals - 353 GHz'''<br />
File: ZodiRes545.png | '''zodi/FSL rediduals - 545 GHz'''<br />
File: ZodiRes857.png | '''zodi/FSL rediduals - 857 GHz'''<br />
</gallery><br />
</center ---><br />
<br />
=== Caveats and known issues ===<br />
<br />
TBW<br />
<br />
==== Map zero-level ====<br />
<br />
For the 100 to 857 GHz maps, the zero levels are set to their optimal levels for Galactic and CIB studies. A procedure for adjusting them to astrophysical values is given in the HFI Mapmaking and Calibration paper {{PlanckPapers|????}}.<br />
<br />
For the 30, 44 and 70 GHz, maps are corrected for zero level monopole by applying an offset correction, see LFI Calibration paper {{PlanckPapers|planck2013-p02b}} section 3.4 "Setting the zero levels in the maps" and {{PlanckPapers|planck2014-a06||Planck-2015-A06}}. Note that the offset applied is indicated in the header as a comment keyword.<br />
<br />
==Inputs==<br />
=== HFI inputs ===<br />
<br />
* The cleaned TOIs of signal of each detector, together with their flags, produced by the [[TOI processing|TOI processing]] pipeline<br />
* The TOIs of pointing (quaternions), described in [[Detector_pointing|Detector pointing]]<br />
* Bolometer-level characterization data, from the DPC's internal IMO (not distributed)<br />
* Planck orbit data used to compute and remove the earth dipole<br />
* Planck solar dipole information used to calibrate the CMB channels<br />
* Planet models used to calibrate the Galactic channels.<br />
<br />
=== LFI inputs ===<br />
<br />
The Madam map-maker takes as an input:<br />
<br />
* The calibrated timelines (for details see [[TOI processing LFI|TOI Processing]])<br />
* The detector pointings (for details see [[Detector_pointing|Detector pointing]])<br />
* The noise information in the form of three-parameter (white noise level (<math>\sigma</math>), slope, and knee frequency ($f_\mathrm{knee}$)) noise model (for details see [[The RIMO|RIMO]])<br />
<br />
==Related products==<br />
=== Masks ===<br />
<br />
This section presents the masks of the point sources and of the Galactic plane. These are ''general purpose'' masks. Other masks specific to certain products are packaged with the products.<br />
<br />
====Point source masks====<br />
<br />
For HFI and LFI two sets of masks are provided: <br />
* Intensity masks, which removes sources detected with SNR > 5. <br />
* Polarisation masks, which remove sources which have polarisation detection significance of 99.97 % or greater at the position of a source detected in intensity. They were derived from the polarisation maps with dust ground bandpass mismatch leakage correction applied. The cut around each source has a radius of 3σ (width) of the beam ~ 1.27 FWHM (for LFI the cut around each source has a radius of 32 arcmin at 30GHz, 27 arcmin at 44 GHz and 13 arcmin at 70 GHz).<br />
<br />
Both sets are found in the file ''HFI_Mask_PointSrc_2048_R2.00.fits'' in which the first extension contains the Intensity masks, and the second contains the Polarisation masks.<br />
<br />
====Galactic Plane masks====<br />
<br />
Eight masks are provided giving 20, 40, 60, 70, 80, 90, 97, and 99% sky coverage derived from the 353 GHz map, after CMB subtraction. They are independent of frequency channel. Three versions of these are given: not apodized, and apodized by 2 and 5 deg. The filenames are ''HFI_Mask_GalPlane-apoN_2048_R2.00.fits'', where N = 0, 2, 5.<br />
<br />
The masks are shows below. The 8 GalPlane masks are combined (added together) and shown in a single figure for each of the three apodization. While the result is quite clear for the case of no apodization, it is less so for the apodized case. The point source masks are shown separately for the Intensity case.<br />
<br />
<center><br />
<gallery perrow=3 widths=260px heights=160px ><br />
File: GalPlaneMask_apo0.png | '''Galactic Plane masks, no apod'''<br />
File: GalPlaneMask_apo2.png | '''Galactic Plane masks, apod 2 deg'''<br />
File: GalPlaneMask_apo5.png | '''Galactic Plane masks, apod 5 deg'''<br />
File: PointSrcMask_100.png | '''PointSource mask 100 GHz'''<br />
File: PointSrcMask_143.png | '''PointSource mask 143 GHz'''<br />
File: PointSrcMask_217.png | '''PointSource mask 217 GHz'''<br />
File: PointSrcMask_353.png | '''PointSource mask 343 GHz'''<br />
File: PointSrcMask_545.png | '''PointSource mask 545 GHz'''<br />
File: PointSrcMask_857.png | '''PointSource mask 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
== File names ==<br />
The FITS filenames are of the form ''{H|L}FI_SkyMap_fff{-tag}_Nside_R2.nn_{coverage}-{type}.fits'', where ''fff'' are three digits to indicate the Planck frequency band, ''tag'' indicates the single detector or the detset, ''Nside'' is the Healpix Nside of the map, ''coverage'' indicates which part of the mission is covered (full, half mission, survey, year, ...) , and the optional ''type'' indicates the subset of input data used. The table below lists the products by type, with the appropriate unix wildcards that form the full filename.<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=880px<br />
|+ '''HFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename <br />
|-<br />
| Full chan, full mission ||HFI_SkyMap_???_2048_R2.??_full.fits ||HFI_SkyMap_???_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
| Full channel, nominal mission ||HFI_SkyMap_???_2048_R2.??_nominal.fits || n/a<br />
|-<br />
| Full channel, single survey || HFI_SkyMap_???_2048_R2.??_survey-?.fits || n/a<br />
|-<br />
| Full channel, single year || HFI_SkyMap_???_2048_R2.??_year-?.fits || n/a<br />
|-<br />
| Full channel, half mission || HFI_SkyMap_???_2048_R2.??_halfmission*-?.fits || n/a<br />
|-<br />
| Det-set, full mission || HFI_SkyMap_???-ds?_2048_R2.??_full.fits || HFI_SkyMap_???-ds?_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
|Single SWB, full mission || HFI_SkyMap_???-?_2048_R2.??_full.fits || HFI_SkyMap_???-?_2048_R2.??_full-ringhalf-?.fits<br />
|}<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=1000px<br />
|+ '''LFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename || Comment<br />
|-<br />
| Full channel, full mission ||LFI_SkyMap_???_1024_R2.??_full.fits ||LFI_SkyMap_???_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Full channel, single survey || LFI_SkyMap_???_1024_R2.??_survey-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, survey combination || LFI_SkyMap_???_1024_R2.??_survey-1-3-5-6-7-8.fits || n/a || n/a<br />
|-<br />
| Full channel, single year || LFI_SkyMap_???_1024_R2.??_year-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, year combination || LFI_SkyMap_???_1024_R2.??_year?-?.fits || n/a || n/a<br />
|-<br />
| Horn pair, full mission || LFI_SkyMap_???-??-??_1024_R2.??_full.fits || LFI_SkyMap_???_??-??_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Single radiometer, full mission || LFI_SkyMap_???-???_1024_R2.??_full.fits || LFI_SkyMap_???-???_1024_R2.??_full-ringhalf-?.fits || n/a<br />
|}<br />
<br />
<br />
<br />
For the benefit of users who are only looking for the frequency maps with no additional information, we also provide a file combining the 9 frequency maps as separate columns in a single extension. The 9 columns in this file contain the intensity maps ONLY and no other information (hit maps and variance maps) is provided.<br />
<br />
<!---<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=500px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal.fits|link=LFI_SkyMap_030_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal.fits|link=LFI_SkyMap_044_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal.fits|link=LFI_SkyMap_070_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal.fits|link=LFI_SkyMap_070_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal.fits|link=HFI_SkyMap_100_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal.fits|link=HFI_SkyMap_143_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal.fits|link=HFI_SkyMap_217_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal.fits|link=HFI_SkyMap_353_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal.fits|link=HFI_SkyMap_545_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal.fits|link=HFI_SkyMap_857_2048_R1.10_nominal.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel, Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits}} <br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Combined frequency maps<br />
|-<br />
| '''All''' || {{PLASingleFile|fileType=file|name=COM_MapSet_I-allFreqs_R1.10_nominal.fits|link=COM_MapSet_I-allFreqs_R1.10_nominal.fits}} <br />
|}<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=850px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 maps || Survey 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_1.fits|link=LFI_SkyMap_030_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_2.fits|link=LFI_SkyMap_030_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_1.fits|link=LFI_SkyMap_044_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_2.fits|link=LFI_SkyMap_044_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_1.fits|link=LFI_SkyMap_070_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_2.fits|link=LFI_SkyMap_070_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_1.fits|link=LFI_SkyMap_070_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_2.fits|link=LFI_SkyMap_070_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 Zodi-corrected maps || Survey 2 Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Half-ring 1 maps ||Half-ring 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|}<br />
---><br />
<br />
== FITS file structure ==<br />
<br />
The FITS files for the sky maps contain a minimal primary header with no data, and a ''BINTABLE'' extension (EXTENSION 1, EXTNAME = ''FREQ-MAP'') containing the data. The structure is shows schematically in the figure below. The ''FREQ-MAP'' extension contains a 3- or a 10-column table that contain the signal, hit-count and variance maps, all in Healpix format. The 3-column case is for intensity only maps, the 10-column case is for polarisation. The number of rows is the number of map pixels, which is Npix = 12 <math>N_{side}</math><sup>2</sup> for Healpix maps, where <math>N_{side}</math> = 1024 or 2048 for most the maps presented in this chapter.<br />
<br />
[[File:FITS_FreqMap.png | 550px | center | thumb | '''FITS file structure''']]<br />
<br />
Note that file sizes are ~0.6 GB for I-only maps and ~1.9 GB for I,Q,U maps at <math>N_{side}</math> 2048 and ~0.14 GB for I-only maps and ~0.45 GB for I,Q,U maps at <math>N_{side}</math> 1024 .<br />
<br />
Keywords indicate the coordinate system (GALACTIC), the Healpix ordering scheme (NESTED), the units (K_cmb or MJy/sr) of each column, and of course the frequency channel (FREQ). Where polarisation Q and U maps are provided, the ''COSMO'' polarisation convention (used in HEALPIX) is adopted, and it is specified in the ''POLCCONV'' keyword (see [[Sky_temperature_maps#Polarization_convention_used_in_the_Planck_project|this section]]. The COMMENT fields give a one-line summary of the product, and some other information useful for traceability within the DPCs. The original filename is also given in the ''FILENAME'' keyword. The ''BAD_DATA'' keyword gives the value used by Healpix to indicate pixels for which no signal is present (these will also have a hit-count value of 0). The main parameters are summarised below:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Sky map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'FREQ-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes I map<br />
|-<br />
|Q_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes Q map (optional)<br />
|-<br />
|U_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes U map (optional)<br />
|-<br />
|HITS || Int*4 || none || The hit-count map<br />
|-<br />
|II_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The II variance map<br />
|-<br />
|IQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|IU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|QQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QQ variance map (optional)<br />
|-<br />
|QU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QU variance map (optional)<br />
|-<br />
|UU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The UU variance map (optional)<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix <math>N_{side}</math> <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 12 <math>N_{side}</math><sup>2</sup> – 1 || Last pixel number<br />
|-<br />
|FREQ || string || nnn || The frequency channel <br />
|}<br />
<br />
<br />
The same structure applies to all ''SkyMap'' products, independent of whether they are full channel, survey of half-ring. The distinction between the types of maps is present in the FITS filename (and in the traceability comment fields).<br />
<br />
==Polarization convention used in the Planck project==<br />
<br />
The Planck collaboration used the COSMO convention for the polarization angle (as usually used in space based CMB missions), whereas other astronomical fields usually use the IAU convention. In the following document we report the difference between these two conventions, and the consequence if it is NOT taken into account correctly in the analysis.<br />
<br />
[[File:conventions.png|thumb|center|400px|'''Figure 1. COSMO convention (left) and IAU convention (right). The versor <math>\hat{z}</math> points outwards the pointing direction in COSMO, and inwards in IAU. The bottom panel refers to the plane tangent to the sphere.''']]<br />
<br />
Changing the orientation convention is equivalent to a transformation <math>\psi'=\pi-\psi</math> of the polarization angle (Figure 1). The consequence of this transformation is the inversion of the Stokes parameter <math>U</math>.<br />
The components of the polarization tensor in the helicity basis <math>\epsilon^{\pm}=1/\sqrt{2}(\hat{x}\pm i\hat{y})</math> are:<br />
<br />
<math><br />
(Q+iU)(\hat{n}) = \sum _{\ell m}a_{2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
\\(Q-iU)(\hat{n}) = \sum _{\ell m}a_{-2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where <math>{}_{2}Y_{\ell }^{m}(\hat{n})</math> are the spin weighted spherical harmonic functions.<br />
The <math>E</math> and <math>B</math> modes can be defined as:<br />
<math><br />
E(\hat{n}) = \sum_{\ell m}a_{E,\ell m}Y_{\ell }^{m}(\hat{n})<br />
\\B(\hat{n}) = \sum_{\ell m}a_{B,\ell m}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where the coefficients <math>a_{E,\ell m}</math> and <math>a_{B,\ell m}</math> are derived from linear combinations of the <math>a_{2,\ell m}</math> , <math>a_{-2,\ell m}</math> defined implicitly in the first equation (<math>Q\pm iU</math>).<br />
<br />
[[File:test_gradient.jpg|thumb|center|400px|]]<br />
[[File:test_curl.jpg|thumb|center|400px|'''Figure 2. Error on Planck-LFI 70 GHz <math>EE</math> (top) and <math>BB</math> (bottom) spectra, in case of wrong choice of the coordinate system convention (IAU instead of COSMO).''']]<br />
<br />
The effect of the sign inversion of <math>U</math> on the polarization spectra is a non trivial mixing of <math>E</math> and <math>B</math> modes. <br />
<br />
An example of the typical error on <math>EE</math> and <math>BB</math> auto-spectra in case of a wrong choice of the polarization basis is shown in Figure 2.<br />
<br />
BE CAREFUL about the polarization convention you are using. If the IAU convention is used in computing the power spectra, the sign of the <math>U</math> component of the Planck maps must be inverted before computing <math>E</math> and <math>B</math> modes.<br />
<br />
=== Note on the convention used by the Planck Catalog of Compact Sources (PCCS) ===<br />
For continuity with other compact sources catolgues, the Catalogue of Compact Sources provided by Planck follows the IAU convention, and the polarization angles are defined on an interval of [-90,90] degrees. To switch to the COSMO convention, the polarization angles listed in the catalogue have to be shifted by 90 degrees and multiplied by -1.<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:Mission products|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Sky_temperature_maps&diff=11275Sky temperature maps2015-02-04T18:19:54Z<p>Agregori: /* Types of maps */</p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature and polarization maps}}<br />
==General description==<br />
<br />
Sky maps give the best estimate of the intensity and polarization (Stokes Q and U components), if available, of the signal from the sky after removal, as far as possible, of known systematic effects (mostly instrumental, but including also the solar and earth-motion dipole, Galactic strylight and the Zodiacal light). Sky maps are provided for the full Planck mission using all valid detectors in each frequency channel, and also for various subsets by splitting the mission in various time ranges or in subsets of the detectors in a given channel. These products are useful for the study of source variability, but they are especially interesting for characterisation purposes (see also the [[HFI-Validation | data validation]] section). The details of the start and end of the time ranges are given in the table below.<br />
<br />
To help in further processing, there are also masks of the Galactic Plane and of point sources, each provided for several different depths.<br />
<br />
All sky maps are in Healpix format, with Nside of 1024 (LFI 30, 44 and 70) and 2048 (LFI 70 and HFI), in Galactic coordinates, and Nested ordering. The signal is given in units of K<sub>cmb</sub> for 30-353 GHz, and of MJy/sr (for a constant <math>\nu F_\nu</math> energy distribution ) for 545 and 857 GHz. For each frequency channel, the intensity and polarization maps are packaged into a ''BINTABLE'' extension of a FITS file together with a hit-count map (or hit map, for short, giving the number of observation samples that are cumulated in a pixel, all detectors combined) and with the variance and covariance maps. Additional information is given in the FITS file header. The structure of the FITS file is given in the [[#Format | FITS file structure]] section below. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Ranges for mission and surveys'''<br />
|- bgcolor="ffdead" <br />
! Range || ODs || HFI rings || pointing-IDs || Comment<br />
|-<br />
|nominal mission || 91 - 563 || 240 - 14723 || 00004200 - 03180200 ||<br />
|-<br />
|full mission || 91 - 974 || 240 - 27005 || 00004200 - 05322620 || for HFI<br />
|-<br />
|full mission || 91 - 1543 || n/a || 00004200 - 06511160 || for LFI<br />
|-<br />
|Survey 1 || 91 - 270 || 240 - 5720 || 00004200 - 01059820 ||<br />
|-<br />
|Survey 2 || 270 - 456 || 5721 - 11194 || 01059830 - 02114520 ||<br />
|-<br />
|Survey 3 || 456 - 636 || 11195 - 16691 || 02114530 - 03193660 ||<br />
|-<br />
|Survey 4 || 636 - 807 || 16692 - 21720 || 03193670 - 04243900 ||<br />
|-<br />
|Survey 5 || 807 - 974 || 21721 - 27005 || 05267180 - 05322590 || end of mission for HFI<br />
|-<br />
|Survey 5 || 807 - 993 || n/a || 05267180 - 06344800 || end of survey for LFI<br />
|-<br />
|Survey 6 || 993 - 1177 || n/a || 06344810 - 06398120 || LFI only <br />
|-<br />
|Survey 7 || 1177 - 1358 || n/a || 06398130 - 06456410 || LFI only <br />
|-<br />
|Survey 8 || 1358 - 1543 || n/a || 06456420 - 06511160 || LFI only <br />
|-<br />
|Survey 9 || 1543 - 1604 || n/a || 06511170 - 06533320 || LFI only Not in this delivery<br />
|-<br />
|HFI mission-half-1 || 91 - 531 || 240 - 13471 || 00004200 - 03155580 ||<br />
|-<br />
|HFI mission-half-2 || 531 - 974 || 13472 - 27005 || 03155590 - 05322590 ||<br />
|-<br />
|LFI Year 1 || 91 - 456 || n/a || 00004200 - 02114520 ||<br />
|-<br />
|LFI Year 2 || 456 - 807 || n/a || 02114530 - 04243900 ||<br />
|-<br />
|LFI Year 3 || 807 - 1177 || n/a || 05267180 - 06398120 ||<br />
|-<br />
|LFI Year 4 || 1177 - 1543 || n/a || 06398130 - 06511160 ||<br />
|-<br />
|}<br />
<br />
==Production process==<br />
<br />
Sky maps are produced by combining appropriately the data of all working detectors in a frequency channel over some period of the mission. They give the best estimate of the signal from the sky (unpolarised) after removal, as far as possible, of known systematic effects and of the dipole signals induced by the motion of the solar system in the CMB and of the Planck satellite in the solar system. In particular, they include the Zodiacal light emission (Zodi for short) and also the scattering from the far-side lobes of the beams (FSL). More on this below.<br />
<br />
=== HFI processing ===<br />
<br />
The mapmaking and calibration process is described in detail in the [[Map-making_LFI | Map-making]] section and in the [[A08 paper| mapmaking]] paper, where detailed references are found. In brief it consists of:<br />
<br />
; binning the TOI data onto ''rings'' : Healpix rings (HPRs) are used here, each ring containing the combined data of one pointing period. <br />
; flux calibration : at 100-353 GHz, the flux calibration factors are determined by correlating the signal with the orbital dipole, which is determined very accurately from the Planck satellite orbital parameters provided by Flight Dynamics. This provides a single gain factor per bolometer. At 545 and 857 GHz the gain is determined from the observation of Uranus and Neptune (but not Jupiter which is too bright) and comparison to recent models made explicitly for this mission. A single gain is applied to all rings at these frequencies.<br />
; destriping : in order to remove low-frequency noise, an offset per ring is determined by minimizing the differences between HPRs at their crossings, and removed.<br />
; Zodiacal light correction : a Zodiacal light model is used to build HPRs of the the Zodi emission, which is subtracted from the calibrated HPRs.<br />
; projection onto the map : the offset-corrected, flux-calibrated, and Zodi-cleaned HPRs are projected onto Healpix maps, with the data of each bolometer weighted by a factor of 1/NET of that bolometer.<br />
<br />
These steps are followed by some post-processing which is designed to prepare the maps for the component separation work. This post processing consists of: <br />
<br />
; Dust bandpass leakage correction : the Q and U maps are corrected for the dust leakage due to the different bandpasses that is determined using the ''ground'' method as described [[MISSING REF| here]]<br />
; Far Side Lobe calibration correction : the 100-217 maps are multiplied by factors of 1.00087, 1.00046, and 1.00043, respectively, to compensate for the non-removal of the far-side lobes, and similarly the corresponding covariance maps have also been corrected by multiplication by the square of the factor.<br />
; Fill missing pixels : missing pixels are filled in with a value that is the mean of valid pixels within a given radius. A radius of 1 deg is used for the full channel maps, and 1.5 deg is used for the detset maps. This step is not applied to the single survey maps since they have large swaths of the sky that are not covered.<br />
<br />
These maps provide the main mission products. Together with signal maps, hit count, variance, and variance maps are also produced. The hit maps give the (integer) number of valid TOI-level samples that contribute to the signal of each pixel. All valid samples are counted in the same way, i.e., there is no weighting factor applied. The variance maps project the white noise estimate, provided by the NETs, in the sky domain.<br />
<br />
Note that the nominal mission maps have not had the post-processing applied, which makes them more easily comparable to the PR1 products.<br />
<br />
=== LFI processing ===<br />
Input timelines are cleaned by 4pi convolved dipole and Galactic Straylight obtained as convolution of the 4pi in band far sidelobes and Galactic Simulation<br />
<br />
LFI maps were constructed with the Madam map-making code, version 3.7.4. The code is based on generalized destriping technique, where the correlated noise component is modeled as a sequence of constant offset, called baselines. A noise filter was used to constrain the baseline solution allowing the use of 1 second baselines.<br />
<br />
Radiometers were combined according to the horn-uniform weighting scheme to minimize systematics. The used weights are listed in [[Map-making LFI#Map-making|Map-making]]. The flagged samples were excluded from the analysis by setting their weights to <math>C_{w}^{-1}</math> = 0. The galaxy region was masked out in the destriping phase, to reduce error arising from strong signal gradients. The polarization component was included in the analysis... <br />
<br />
A detailed description of the map-making procedure is given in {{PlanckPapers|planck2013-p02}} {{PlanckPapers|planck2014-a07||Planck-2015-A07}} and in section [[Map-making LFI#Map-making|Map-making]].<br />
<br />
==Types of maps ==<br />
<br />
=== Full mission, full channel maps (6 HFI, 4 LFI)===<br />
<br />
Full channel maps are built using all the valid detectors of a frequency channel and cover the either the full or the nominal mission. For HFI, the 143-8 and 545-3 bolometers are rejected entirely as they are seriously affected by RTS noise. For this release, HFI provides the Q and U components for the 353 GHz channel only. LFI provides the I, Q and U maps for all the channels. The I maps are displayed in the figures below. The color range is set using a histogram equalisation scheme (from HEALPIX) that is useful for these non-Gaussian data fields. The Q and U maps are not shown as they look like noise to the naked eye.<br />
The 70 GHz full map is available also at <math>N_{side}</math> 2048.<br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=260px heights=160px> <br />
File: SkyMap30e.png| '''Full mission, 30 GHz'''<br />
File: SkyMap44e.png | '''Full mission, 44 GHz'''<br />
File: SkyMap70e.png | '''Full mission, 70 GHz'''<br />
File: SkyMap100e.png | '''Full mission, 100 GHz'''<br />
File: SkyMap143e.png | '''Full mission, 143 GHz'''<br />
File: SkyMap217e.png | '''Full mission, 217 GHz'''<br />
File: SkyMap353e.png | '''Full mission, 353 GHz'''<br />
File: SkyMap545e.png | '''Full mission, 545 GHz'''<br />
File: SkyMap857e.png | '''Full mission, 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
=== Nominal mission, full channel maps (6 HFI)===<br />
<br />
These maps are similar to the ones above, but cover the nominal mission only. They are meant primarily to be compared to the PR1 products in order to see the level of improvements in the processing. Because of this, they are produced in Temperature only, and have not had the post-processing applied.<br />
<br />
=== Single survey, full channel maps (30 HFI, 35 LFI)===<br />
<br />
Single survey maps are built using all valid detectors of a frequency channel; they cover separately the different sky surveys. The surveys are defined as the times over which the satellite spin axis rotates but 180 degrees, which, due to the position of the detectors in the focal plane does not cover the full sky, but a fraction between ~80 and 90% depending on detector position. During adjacent surveys the sky is scanned in opposite directions. More precisely it is the ecliptic equator that is scanned in opposite directions. While these are useful to investigate variable sources, they are also used to study the systematics of the time-response of the detectors as they scan bright sources, like the Galactic Plane, in different directions during different survey. Note that the HFI and LFI missions cover 5 and 8 surveys, respectively, and in case of HFI the last survey in incomplete.<br />
The 70 GHz surveys maps are available also at <math>N_{side}</math> 2048.<br />
Note LFI provide a special surveys maps combination used in the low l analysis. This maps, available at the three LFI frequency 30, 44 and 70 GHz, was built using the combination of survey 1, 3, 5, 6, 7 and 8. <br />
<br />
=== Year maps, full channel maps (12 HFI, 16 LFI)===<br />
<br />
These maps are built using the data of surveys 1+2, surveys 3+4, and so forth. They are used to study long-term systematic effects.<br />
The 70 GHz years maps are available also at <math>N_{side}</math> 2048.<br />
<br />
===Half-mission maps, full channel maps (12 HFI, 12 LFI)===<br />
<br />
For HFI, the half mission is defined after eliminating those rings discarded for all bolometers. There are 347 such rings, may of which are during the 5th survey when the ''End-of-Life'' tests were performed. The remaining 26419 rings are divided in half (up to the odd ring) to define the two halves of the mission. This exercise is done for the full mission only.<br />
<br />
For LFI instead of the half-mission the following year combination has been created: Year 1+2, Year 1+3, Year 2+4, Year 3+4, <br />
<br />
===Full mission, single detector maps (18 HFI, 22 LFI)===<br />
<br />
IN case of HFI these maps are built only for the SWBs (non polarized) and contain only temperature data, of course. They are not built for the polarisation sensitive detectors because they are not fixed on the sky as the polarisation component depends on the position angle at the time of observation. Instead, we provide maps built by ''quads'' of polarisation-sensitive detectors (see next section), which have different polarisation angles and that can be used to built I, Q, and U maps<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''HFI Temperature sensitive bolometers'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Detector names<br />
|-<br />
|143 GHz || 143-5, 6, 7<br />
|-<br />
|217 GHz || 217-1, 2, 3, 4<br />
|-<br />
|353 GHz || 353-1, 2, 7, 8<br />
|-<br />
|545 GHz || 545-1, 2, 4<br />
|-<br />
|857 GHz || 857-1, 2 , 3, 4<br />
|}<br />
<br />
The 143-8 and 353-3 bolometer data are affected by strong RTS (random telegraphic signal) noise. They have not been used in the data processing, and are not delivered. For a figure showing the focal plane layout, see [[Detector_pointing#Introduction_and_Summary | this Introduction]] of the Detector Pointing chapter.<br />
<br />
In case of LFI, all the 22 Radiometers maps are available, those, obviously, are only in temperature.<br />
<br />
===Full mission, detector set or detector pairs maps (8 HFI, 8 LFI)===<br />
<br />
The objective here is to build independent temperature (I) and polarisation (Q and U) maps with the two pairs of polarisation sensitive detectors of each channel where they are available, i.e. in the 44-353 GHz channels. The table below indicates which detectors were used to built each detector set (detset).<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of HFI Detector Sets'''<br />
|- bgcolor="ffdead" <br />
!Frequency || DetSet1 || DetSet2 <br />
|-<br />
|100 GHz || 100-1a/b & 100-4a/b || 100-2a/b & 100-3a/b<br />
|-<br />
|143 GHz || 143-1a/b 1 & 43-3a/b || 143-2a/b & 143-4a/b<br />
|-<br />
|217 GHz || 217-5a/b & 217-7a/b || 217-6a/b & 217-8a/b<br />
|-<br />
|353 GHz || 353-3a/b & 353-5a/b || 353-4a/b & 353-6a/b<br />
|}<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of LFI Detector Pairs'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Horn Pair || Comment <br />
|-<br />
|44 GHz || 24 || This maps is only in temperature<br />
|-<br />
|44 GHz || 25 & 26 || <br />
|-<br />
|70 GHz || 18 & 23 || Available also at <math>N_{side}</math> = 2048<br />
|-<br />
|70 GHz || 19 & 22 || Available also at <math>N_{side}</math> = 2048<br />
|-<br />
|70 GHz || 20 & 21 || Available also at <math>N_{side}</math> = 2048<br />
|}<br />
<br />
<br />
===Half-ring maps (64 HFI, 62 LFI)===<br />
<br />
These maps are similar to the ones above, but are built using only the first or the second half of each ring (or pointing period). The HFI provides half-ring maps for the full mission only, and for the full channel, the detsets, and the single bolometers. The LFI provides half-rings maps for the channel full mission (70 GHz also at <math>N_{side}</math> 2048), for the radiometer full mission and the horn pairs full mission.<br />
<!----<br />
===Masks===<br />
<br />
Masks are provided of the Galactic Plane and of the point sources. For the Galactic Plane, eight masks are given covering different fractions of the sky, and for the points sources two masks are given, at the 5 and 10 sigma level, for each Planck HFI and LFI frequency channel. These are generic masks, specific masks applicable to other products are delivered with the products themselves.<br />
---><br />
<br />
=== The Zodiacal light correction maps ===<br />
<br />
The Zodiacal light signal depends on the location of the observer relative to the Zodiacal light bands, and thus it is not a fixed pattern on the sky but depends on the period of observation. The maps presented here are the difference between the uncorrected (and not delivered) and the corrected maps. <br />
<br />
<br />
<!---center><br />
<gallery perrow=3 widths=260px heights=170px><br />
File: ZodiRes100.png | '''zodi/FSL rediduals - 100 GHz'''<br />
File: ZodiRes143.png | '''zodi/FSL rediduals - 143 GHz''' <br />
File: ZodiRes217.png | '''zodi/FSL rediduals - 217 GHz'''<br />
File: ZodiRes353.png | '''zodi/FSL rediduals - 353 GHz'''<br />
File: ZodiRes545.png | '''zodi/FSL rediduals - 545 GHz'''<br />
File: ZodiRes857.png | '''zodi/FSL rediduals - 857 GHz'''<br />
</gallery><br />
</center ---><br />
<br />
=== Caveats and known issues ===<br />
<br />
TBW<br />
<br />
==== Map zero-level ====<br />
<br />
For the 100 to 857 GHz maps, the zero levels are set to their optimal levels for Galactic and CIB studies. A procedure for adjusting them to astrophysical values is given in the HFI Mapmaking and Calibration paper {{PlanckPapers|????}}.<br />
<br />
For the 30, 44 and 70 GHz, maps are corrected for zero level monopole by applying an offset correction, see LFI Calibration paper {{PlanckPapers|planck2013-p02b}} section 3.4 "Setting the zero levels in the maps" and {{PlanckPapers|planck2014-a06||Planck-2015-A06}}. Note that the offset applied is indicated in the header as a comment keyword.<br />
<br />
==Inputs==<br />
=== HFI inputs ===<br />
<br />
* The cleaned TOIs of signal of each detector, together with their flags, produced by the [[TOI processing|TOI processing]] pipeline<br />
* The TOIs of pointing (quaternions), described in [[Detector_pointing|Detector pointing]]<br />
* Bolometer-level characterization data, from the DPC's internal IMO (not distributed)<br />
* Planck orbit data used to compute and remove the earth dipole<br />
* Planck solar dipole information used to calibrate the CMB channels<br />
* Planet models used to calibrate the Galactic channels.<br />
<br />
=== LFI inputs ===<br />
<br />
The Madam map-maker takes as an input:<br />
<br />
* The calibrated timelines (for details see [[TOI processing LFI|TOI Processing]])<br />
* The detector pointings (for details see [[Detector_pointing|Detector pointing]])<br />
* The noise information in the form of three-parameter (white noise level (<math>\sigma</math>), slope, and knee frequency ($f_\mathrm{knee}$)) noise model (for details see [[The RIMO|RIMO]])<br />
<br />
==Related products==<br />
=== Masks ===<br />
<br />
This section presents the masks of the point sources and of the Galactic plane. These are ''general purpose'' masks. Other masks specific to certain products are packaged with the products.<br />
<br />
====Point source masks====<br />
<br />
For HFI and LFI two sets of masks are provided: <br />
* Intensity masks, which removes sources detected with SNR > 5. <br />
* Polarisation masks, which remove sources which have polarisation detection significance of 99.97 % or greater at the position of a source detected in intensity. They were derived from the polarisation maps with dust ground bandpass mismatch leakage correction applied. The cut around each source has a radius of 3σ (width) of the beam ~ 1.27 FWHM (for LFI the cut around each source has a radius of 32 arcmin at 30GHz, 27 arcmin at 44 GHz and 13 arcmin at 70 GHz).<br />
<br />
Both sets are found in the file ''HFI_Mask_PointSrc_2048_R2.00.fits'' in which the first extension contains the Intensity masks, and the second contains the Polarisation masks.<br />
<br />
====Galactic Plane masks====<br />
<br />
Eight masks are provided giving 20, 40, 60, 70, 80, 90, 97, and 99% sky coverage derived from the 353 GHz map, after CMB subtraction. They are independent of frequency channel. Three versions of these are given: not apodized, and apodized by 2 and 5 deg. The filenames are ''HFI_Mask_GalPlane-apoN_2048_R2.00.fits'', where N = 0, 2, 5.<br />
<br />
The masks are shows below. The 8 GalPlane masks are combined (added together) and shown in a single figure for each of the three apodization. While the result is quite clear for the case of no apodization, it is less so for the apodized case. The point source masks are shown separately for the Intensity case.<br />
<br />
<center><br />
<gallery perrow=3 widths=260px heights=160px ><br />
File: GalPlaneMask_apo0.png | '''Galactic Plane masks, no apod'''<br />
File: GalPlaneMask_apo2.png | '''Galactic Plane masks, apod 2 deg'''<br />
File: GalPlaneMask_apo5.png | '''Galactic Plane masks, apod 5 deg'''<br />
File: PointSrcMask_100.png | '''PointSource mask 100 GHz'''<br />
File: PointSrcMask_143.png | '''PointSource mask 143 GHz'''<br />
File: PointSrcMask_217.png | '''PointSource mask 217 GHz'''<br />
File: PointSrcMask_353.png | '''PointSource mask 343 GHz'''<br />
File: PointSrcMask_545.png | '''PointSource mask 545 GHz'''<br />
File: PointSrcMask_857.png | '''PointSource mask 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
== File names ==<br />
The FITS filenames are of the form ''{H|L}FI_SkyMap_fff{-tag}_Nside_R2.nn_{coverage}-{type}.fits'', where ''fff'' are three digits to indicate the Planck frequency band, ''tag'' indicates the single detector or the detset, ''Nside'' is the Healpix Nside of the map, ''coverage'' indicates which part of the mission is covered (full, half mission, survey, year, ...) , and the optional ''type'' indicates the subset of input data used. The table below lists the products by type, with the appropriate unix wildcards that form the full filename.<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=880px<br />
|+ '''HFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename <br />
|-<br />
| Full chan, full mission ||HFI_SkyMap_???_2048_R2.??_full.fits ||HFI_SkyMap_???_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
| Full channel, nominal mission ||HFI_SkyMap_???_2048_R2.??_nominal.fits || n/a<br />
|-<br />
| Full channel, single survey || HFI_SkyMap_???_2048_R2.??_survey-?.fits || n/a<br />
|-<br />
| Full channel, single year || HFI_SkyMap_???_2048_R2.??_year-?.fits || n/a<br />
|-<br />
| Full channel, half mission || HFI_SkyMap_???_2048_R2.??_halfmission*-?.fits || n/a<br />
|-<br />
| Det-set, full mission || HFI_SkyMap_???-ds?_2048_R2.??_full.fits || HFI_SkyMap_???-ds?_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
|Single SWB, full mission || HFI_SkyMap_???-?_2048_R2.??_full.fits || HFI_SkyMap_???-?_2048_R2.??_full-ringhalf-?.fits<br />
|}<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=1000px<br />
|+ '''LFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename || Comment<br />
|-<br />
| Full channel, full mission ||LFI_SkyMap_???_1024_R2.??_full.fits ||LFI_SkyMap_???_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Full channel, single survey || LFI_SkyMap_???_1024_R2.??_survey-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, survey combination || LFI_SkyMap_???_1024_R2.??_survey-1-3-5-6-7-8.fits || n/a || n/a<br />
|-<br />
| Full channel, single year || LFI_SkyMap_???_1024_R2.??_year-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, year combination || LFI_SkyMap_???_1024_R2.??_year?-?.fits || n/a || n/a<br />
|-<br />
| Horn pair, full mission || LFI_SkyMap_???-??-??_1024_R2.??_full.fits || LFI_SkyMap_???_??-??_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Single radiometer, full mission || LFI_SkyMap_???-???_1024_R2.??_full.fits || LFI_SkyMap_???-???_1024_R2.??_full-ringhalf-?.fits || n/a<br />
|}<br />
<br />
<br />
<br />
For the benefit of users who are only looking for the frequency maps with no additional information, we also provide a file combining the 9 frequency maps as separate columns in a single extension. The 9 columns in this file contain the intensity maps ONLY and no other information (hit maps and variance maps) is provided.<br />
<br />
<!---<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=500px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal.fits|link=LFI_SkyMap_030_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal.fits|link=LFI_SkyMap_044_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal.fits|link=LFI_SkyMap_070_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal.fits|link=LFI_SkyMap_070_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal.fits|link=HFI_SkyMap_100_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal.fits|link=HFI_SkyMap_143_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal.fits|link=HFI_SkyMap_217_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal.fits|link=HFI_SkyMap_353_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal.fits|link=HFI_SkyMap_545_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal.fits|link=HFI_SkyMap_857_2048_R1.10_nominal.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel, Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits}} <br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Combined frequency maps<br />
|-<br />
| '''All''' || {{PLASingleFile|fileType=file|name=COM_MapSet_I-allFreqs_R1.10_nominal.fits|link=COM_MapSet_I-allFreqs_R1.10_nominal.fits}} <br />
|}<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=850px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 maps || Survey 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_1.fits|link=LFI_SkyMap_030_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_2.fits|link=LFI_SkyMap_030_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_1.fits|link=LFI_SkyMap_044_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_2.fits|link=LFI_SkyMap_044_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_1.fits|link=LFI_SkyMap_070_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_2.fits|link=LFI_SkyMap_070_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_1.fits|link=LFI_SkyMap_070_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_2.fits|link=LFI_SkyMap_070_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 Zodi-corrected maps || Survey 2 Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Half-ring 1 maps ||Half-ring 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|}<br />
---><br />
<br />
== FITS file structure ==<br />
<br />
The FITS files for the sky maps contain a minimal primary header with no data, and a ''BINTABLE'' extension (EXTENSION 1, EXTNAME = ''FREQ-MAP'') containing the data. The structure is shows schematically in the figure below. The ''FREQ-MAP'' extension contains a 3- or a 10-column table that contain the signal, hit-count and variance maps, all in Healpix format. The 3-column case is for intensity only maps, the 10-column case is for polarisation. The number of rows is the number of map pixels, which is Npix = 12 Nside<sup>2</sup> for Healpix maps, where Nside = 1024 or 2048 for most the maps presented in this chapter.<br />
<br />
[[File:FITS_FreqMap.png | 550px | center | thumb | '''FITS file structure''']]<br />
<br />
Note that file sizes are ~0.6 GB for I-only maps and ~1.9 GB for I,Q,U maps at Nside 2048 and ~0.14 GB for I-only maps and ~0.45 GB for I,Q,U maps at Nside 1024 .<br />
<br />
Keywords indicate the coordinate system (GALACTIC), the Healpix ordering scheme (NESTED), the units (K_cmb or MJy/sr) of each column, and of course the frequency channel (FREQ). Where polarisation Q and U maps are provided, the ''COSMO'' polarisation convention (used in HEALPIX) is adopted, and it is specified in the ''POLCCONV'' keyword (see [[Sky_temperature_maps#Polarization_convention_used_in_the_Planck_project|this section]]. The COMMENT fields give a one-line summary of the product, and some other information useful for traceability within the DPCs. The original filename is also given in the ''FILENAME'' keyword. The ''BAD_DATA'' keyword gives the value used by Healpix to indicate pixels for which no signal is present (these will also have a hit-count value of 0). The main parameters are summarised below:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Sky map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'FREQ-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes I map<br />
|-<br />
|Q_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes Q map (optional)<br />
|-<br />
|U_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes U map (optional)<br />
|-<br />
|HITS || Int*4 || none || The hit-count map<br />
|-<br />
|II_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The II variance map<br />
|-<br />
|IQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|IU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|QQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QQ variance map (optional)<br />
|-<br />
|QU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QU variance map (optional)<br />
|-<br />
|UU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The UU variance map (optional)<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 12 Nside<sup>2</sup> – 1 || Last pixel number<br />
|-<br />
|FREQ || string || nnn || The frequency channel <br />
|}<br />
<br />
<br />
The same structure applies to all ''SkyMap'' products, independent of whether they are full channel, survey of half-ring. The distinction between the types of maps is present in the FITS filename (and in the traceability comment fields).<br />
<br />
==Polarization convention used in the Planck project==<br />
<br />
The Planck collaboration used the COSMO convention for the polarization angle (as usually used in space based CMB missions), whereas other astronomical fields usually use the IAU convention. In the following document we report the difference between these two conventions, and the consequence if it is NOT taken into account correctly in the analysis.<br />
<br />
[[File:conventions.png|thumb|center|400px|'''Figure 1. COSMO convention (left) and IAU convention (right). The versor <math>\hat{z}</math> points outwards the pointing direction in COSMO, and inwards in IAU. The bottom panel refers to the plane tangent to the sphere.''']]<br />
<br />
Changing the orientation convention is equivalent to a transformation <math>\psi'=\pi-\psi</math> of the polarization angle (Figure 1). The consequence of this transformation is the inversion of the Stokes parameter <math>U</math>.<br />
The components of the polarization tensor in the helicity basis <math>\epsilon^{\pm}=1/\sqrt{2}(\hat{x}\pm i\hat{y})</math> are:<br />
<br />
<math><br />
(Q+iU)(\hat{n}) = \sum _{\ell m}a_{2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
\\(Q-iU)(\hat{n}) = \sum _{\ell m}a_{-2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where <math>{}_{2}Y_{\ell }^{m}(\hat{n})</math> are the spin weighted spherical harmonic functions.<br />
The <math>E</math> and <math>B</math> modes can be defined as:<br />
<math><br />
E(\hat{n}) = \sum_{\ell m}a_{E,\ell m}Y_{\ell }^{m}(\hat{n})<br />
\\B(\hat{n}) = \sum_{\ell m}a_{B,\ell m}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where the coefficients <math>a_{E,\ell m}</math> and <math>a_{B,\ell m}</math> are derived from linear combinations of the <math>a_{2,\ell m}</math> , <math>a_{-2,\ell m}</math> defined implicitly in the first equation (<math>Q\pm iU</math>).<br />
<br />
[[File:test_gradient.jpg|thumb|center|400px|]]<br />
[[File:test_curl.jpg|thumb|center|400px|'''Figure 2. Error on Planck-LFI 70 GHz <math>EE</math> (top) and <math>BB</math> (bottom) spectra, in case of wrong choice of the coordinate system convention (IAU instead of COSMO).''']]<br />
<br />
The effect of the sign inversion of <math>U</math> on the polarization spectra is a non trivial mixing of <math>E</math> and <math>B</math> modes. <br />
<br />
An example of the typical error on <math>EE</math> and <math>BB</math> auto-spectra in case of a wrong choice of the polarization basis is shown in Figure 2.<br />
<br />
BE CAREFUL about the polarization convention you are using. If the IAU convention is used in computing the power spectra, the sign of the <math>U</math> component of the Planck maps must be inverted before computing <math>E</math> and <math>B</math> modes.<br />
<br />
=== Note on the convention used by the Planck Catalog of Compact Sources (PCCS) ===<br />
For continuity with other compact sources catolgues, the Catalogue of Compact Sources provided by Planck follows the IAU convention, and the polarization angles are defined on an interval of [-90,90] degrees. To switch to the COSMO convention, the polarization angles listed in the catalogue have to be shifted by 90 degrees and multiplied by -1.<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:Mission products|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Sky_temperature_maps&diff=11274Sky temperature maps2015-02-04T18:18:31Z<p>Agregori: /* Full mission, full channel maps (6 HFI, 4 LFI) */</p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature and polarization maps}}<br />
==General description==<br />
<br />
Sky maps give the best estimate of the intensity and polarization (Stokes Q and U components), if available, of the signal from the sky after removal, as far as possible, of known systematic effects (mostly instrumental, but including also the solar and earth-motion dipole, Galactic strylight and the Zodiacal light). Sky maps are provided for the full Planck mission using all valid detectors in each frequency channel, and also for various subsets by splitting the mission in various time ranges or in subsets of the detectors in a given channel. These products are useful for the study of source variability, but they are especially interesting for characterisation purposes (see also the [[HFI-Validation | data validation]] section). The details of the start and end of the time ranges are given in the table below.<br />
<br />
To help in further processing, there are also masks of the Galactic Plane and of point sources, each provided for several different depths.<br />
<br />
All sky maps are in Healpix format, with Nside of 1024 (LFI 30, 44 and 70) and 2048 (LFI 70 and HFI), in Galactic coordinates, and Nested ordering. The signal is given in units of K<sub>cmb</sub> for 30-353 GHz, and of MJy/sr (for a constant <math>\nu F_\nu</math> energy distribution ) for 545 and 857 GHz. For each frequency channel, the intensity and polarization maps are packaged into a ''BINTABLE'' extension of a FITS file together with a hit-count map (or hit map, for short, giving the number of observation samples that are cumulated in a pixel, all detectors combined) and with the variance and covariance maps. Additional information is given in the FITS file header. The structure of the FITS file is given in the [[#Format | FITS file structure]] section below. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Ranges for mission and surveys'''<br />
|- bgcolor="ffdead" <br />
! Range || ODs || HFI rings || pointing-IDs || Comment<br />
|-<br />
|nominal mission || 91 - 563 || 240 - 14723 || 00004200 - 03180200 ||<br />
|-<br />
|full mission || 91 - 974 || 240 - 27005 || 00004200 - 05322620 || for HFI<br />
|-<br />
|full mission || 91 - 1543 || n/a || 00004200 - 06511160 || for LFI<br />
|-<br />
|Survey 1 || 91 - 270 || 240 - 5720 || 00004200 - 01059820 ||<br />
|-<br />
|Survey 2 || 270 - 456 || 5721 - 11194 || 01059830 - 02114520 ||<br />
|-<br />
|Survey 3 || 456 - 636 || 11195 - 16691 || 02114530 - 03193660 ||<br />
|-<br />
|Survey 4 || 636 - 807 || 16692 - 21720 || 03193670 - 04243900 ||<br />
|-<br />
|Survey 5 || 807 - 974 || 21721 - 27005 || 05267180 - 05322590 || end of mission for HFI<br />
|-<br />
|Survey 5 || 807 - 993 || n/a || 05267180 - 06344800 || end of survey for LFI<br />
|-<br />
|Survey 6 || 993 - 1177 || n/a || 06344810 - 06398120 || LFI only <br />
|-<br />
|Survey 7 || 1177 - 1358 || n/a || 06398130 - 06456410 || LFI only <br />
|-<br />
|Survey 8 || 1358 - 1543 || n/a || 06456420 - 06511160 || LFI only <br />
|-<br />
|Survey 9 || 1543 - 1604 || n/a || 06511170 - 06533320 || LFI only Not in this delivery<br />
|-<br />
|HFI mission-half-1 || 91 - 531 || 240 - 13471 || 00004200 - 03155580 ||<br />
|-<br />
|HFI mission-half-2 || 531 - 974 || 13472 - 27005 || 03155590 - 05322590 ||<br />
|-<br />
|LFI Year 1 || 91 - 456 || n/a || 00004200 - 02114520 ||<br />
|-<br />
|LFI Year 2 || 456 - 807 || n/a || 02114530 - 04243900 ||<br />
|-<br />
|LFI Year 3 || 807 - 1177 || n/a || 05267180 - 06398120 ||<br />
|-<br />
|LFI Year 4 || 1177 - 1543 || n/a || 06398130 - 06511160 ||<br />
|-<br />
|}<br />
<br />
==Production process==<br />
<br />
Sky maps are produced by combining appropriately the data of all working detectors in a frequency channel over some period of the mission. They give the best estimate of the signal from the sky (unpolarised) after removal, as far as possible, of known systematic effects and of the dipole signals induced by the motion of the solar system in the CMB and of the Planck satellite in the solar system. In particular, they include the Zodiacal light emission (Zodi for short) and also the scattering from the far-side lobes of the beams (FSL). More on this below.<br />
<br />
=== HFI processing ===<br />
<br />
The mapmaking and calibration process is described in detail in the [[Map-making_LFI | Map-making]] section and in the [[A08 paper| mapmaking]] paper, where detailed references are found. In brief it consists of:<br />
<br />
; binning the TOI data onto ''rings'' : Healpix rings (HPRs) are used here, each ring containing the combined data of one pointing period. <br />
; flux calibration : at 100-353 GHz, the flux calibration factors are determined by correlating the signal with the orbital dipole, which is determined very accurately from the Planck satellite orbital parameters provided by Flight Dynamics. This provides a single gain factor per bolometer. At 545 and 857 GHz the gain is determined from the observation of Uranus and Neptune (but not Jupiter which is too bright) and comparison to recent models made explicitly for this mission. A single gain is applied to all rings at these frequencies.<br />
; destriping : in order to remove low-frequency noise, an offset per ring is determined by minimizing the differences between HPRs at their crossings, and removed.<br />
; Zodiacal light correction : a Zodiacal light model is used to build HPRs of the the Zodi emission, which is subtracted from the calibrated HPRs.<br />
; projection onto the map : the offset-corrected, flux-calibrated, and Zodi-cleaned HPRs are projected onto Healpix maps, with the data of each bolometer weighted by a factor of 1/NET of that bolometer.<br />
<br />
These steps are followed by some post-processing which is designed to prepare the maps for the component separation work. This post processing consists of: <br />
<br />
; Dust bandpass leakage correction : the Q and U maps are corrected for the dust leakage due to the different bandpasses that is determined using the ''ground'' method as described [[MISSING REF| here]]<br />
; Far Side Lobe calibration correction : the 100-217 maps are multiplied by factors of 1.00087, 1.00046, and 1.00043, respectively, to compensate for the non-removal of the far-side lobes, and similarly the corresponding covariance maps have also been corrected by multiplication by the square of the factor.<br />
; Fill missing pixels : missing pixels are filled in with a value that is the mean of valid pixels within a given radius. A radius of 1 deg is used for the full channel maps, and 1.5 deg is used for the detset maps. This step is not applied to the single survey maps since they have large swaths of the sky that are not covered.<br />
<br />
These maps provide the main mission products. Together with signal maps, hit count, variance, and variance maps are also produced. The hit maps give the (integer) number of valid TOI-level samples that contribute to the signal of each pixel. All valid samples are counted in the same way, i.e., there is no weighting factor applied. The variance maps project the white noise estimate, provided by the NETs, in the sky domain.<br />
<br />
Note that the nominal mission maps have not had the post-processing applied, which makes them more easily comparable to the PR1 products.<br />
<br />
=== LFI processing ===<br />
Input timelines are cleaned by 4pi convolved dipole and Galactic Straylight obtained as convolution of the 4pi in band far sidelobes and Galactic Simulation<br />
<br />
LFI maps were constructed with the Madam map-making code, version 3.7.4. The code is based on generalized destriping technique, where the correlated noise component is modeled as a sequence of constant offset, called baselines. A noise filter was used to constrain the baseline solution allowing the use of 1 second baselines.<br />
<br />
Radiometers were combined according to the horn-uniform weighting scheme to minimize systematics. The used weights are listed in [[Map-making LFI#Map-making|Map-making]]. The flagged samples were excluded from the analysis by setting their weights to <math>C_{w}^{-1}</math> = 0. The galaxy region was masked out in the destriping phase, to reduce error arising from strong signal gradients. The polarization component was included in the analysis... <br />
<br />
A detailed description of the map-making procedure is given in {{PlanckPapers|planck2013-p02}} {{PlanckPapers|planck2014-a07||Planck-2015-A07}} and in section [[Map-making LFI#Map-making|Map-making]].<br />
<br />
==Types of maps ==<br />
<br />
=== Full mission, full channel maps (6 HFI, 4 LFI)===<br />
<br />
Full channel maps are built using all the valid detectors of a frequency channel and cover the either the full or the nominal mission. For HFI, the 143-8 and 545-3 bolometers are rejected entirely as they are seriously affected by RTS noise. For this release, HFI provides the Q and U components for the 353 GHz channel only. LFI provides the I, Q and U maps for all the channels. The I maps are displayed in the figures below. The color range is set using a histogram equalisation scheme (from HEALPIX) that is useful for these non-Gaussian data fields. The Q and U maps are not shown as they look like noise to the naked eye.<br />
The 70 GHz full map is available also at <math>N_{side}</math> 2048.<br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=260px heights=160px> <br />
File: SkyMap30e.png| '''Full mission, 30 GHz'''<br />
File: SkyMap44e.png | '''Full mission, 44 GHz'''<br />
File: SkyMap70e.png | '''Full mission, 70 GHz'''<br />
File: SkyMap100e.png | '''Full mission, 100 GHz'''<br />
File: SkyMap143e.png | '''Full mission, 143 GHz'''<br />
File: SkyMap217e.png | '''Full mission, 217 GHz'''<br />
File: SkyMap353e.png | '''Full mission, 353 GHz'''<br />
File: SkyMap545e.png | '''Full mission, 545 GHz'''<br />
File: SkyMap857e.png | '''Full mission, 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
=== Nominal mission, full channel maps (6 HFI)===<br />
<br />
These maps are similar to the ones above, but cover the nominal mission only. They are meant primarily to be compared to the PR1 products in order to see the level of improvements in the processing. Because of this, they are produced in Temperature only, and have not had the post-processing applied.<br />
<br />
=== Single survey, full channel maps (30 HFI, 35 LFI)===<br />
<br />
Single survey maps are built using all valid detectors of a frequency channel; they cover separately the different sky surveys. The surveys are defined as the times over which the satellite spin axis rotates but 180 degrees, which, due to the position of the detectors in the focal plane does not cover the full sky, but a fraction between ~80 and 90% depending on detector position. During adjacent surveys the sky is scanned in opposite directions. More precisely it is the ecliptic equator that is scanned in opposite directions. While these are useful to investigate variable sources, they are also used to study the systematics of the time-response of the detectors as they scan bright sources, like the Galactic Plane, in different directions during different survey. Note that the HFI and LFI missions cover 5 and 8 surveys, respectively, and in case of HFI the last survey in incomplete.<br />
The 70 GHz surveys maps are available also at Nside 2048.<br />
Note LFI provide a special surveys maps combination used in the low l analysis. This maps, available at the three LFI frequency 30, 44 and 70 GHz, was built using the combination of survey 1, 3, 5, 6, 7 and 8. <br />
<br />
=== Year maps, full channel maps (12 HFI, 16 LFI)===<br />
<br />
These maps are built using the data of surveys 1+2, surveys 3+4, and so forth. They are used to study long-term systematic effects.<br />
The 70 GHz years maps are available also at Nside 2048.<br />
<br />
===Half-mission maps, full channel maps (12 HFI, 12 LFI)===<br />
<br />
For HFI, the half mission is defined after eliminating those rings discarded for all bolometers. There are 347 such rings, may of which are during the 5th survey when the ''End-of-Life'' tests were performed. The remaining 26419 rings are divided in half (up to the odd ring) to define the two halves of the mission. This exercise is done for the full mission only.<br />
<br />
For LFI instead of the half-mission the following year combination has been created: Year 1+2, Year 1+3, Year 2+4, Year 3+4, <br />
<br />
===Full mission, single detector maps (18 HFI, 22 LFI)===<br />
<br />
IN case of HFI these maps are built only for the SWBs (non polarized) and contain only temperature data, of course. They are not built for the polarisation sensitive detectors because they are not fixed on the sky as the polarisation component depends on the position angle at the time of observation. Instead, we provide maps built by ''quads'' of polarisation-sensitive detectors (see next section), which have different polarisation angles and that can be used to built I, Q, and U maps<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''HFI Temperature sensitive bolometers'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Detector names<br />
|-<br />
|143 GHz || 143-5, 6, 7<br />
|-<br />
|217 GHz || 217-1, 2, 3, 4<br />
|-<br />
|353 GHz || 353-1, 2, 7, 8<br />
|-<br />
|545 GHz || 545-1, 2, 4<br />
|-<br />
|857 GHz || 857-1, 2 , 3, 4<br />
|}<br />
<br />
The 143-8 and 353-3 bolometer data are affected by strong RTS (random telegraphic signal) noise. They have not been used in the data processing, and are not delivered. For a figure showing the focal plane layout, see [[Detector_pointing#Introduction_and_Summary | this Introduction]] of the Detector Pointing chapter.<br />
<br />
In case of LFI, all the 22 Radiometers maps are available, those, obviously, are only in temperature.<br />
<br />
===Full mission, detector set or detector pairs maps (8 HFI, 8 LFI)===<br />
<br />
The objective here is to build independent temperature (I) and polarisation (Q and U) maps with the two pairs of polarisation sensitive detectors of each channel where they are available, i.e. in the 44-353 GHz channels. The table below indicates which detectors were used to built each detector set (detset).<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of HFI Detector Sets'''<br />
|- bgcolor="ffdead" <br />
!Frequency || DetSet1 || DetSet2 <br />
|-<br />
|100 GHz || 100-1a/b & 100-4a/b || 100-2a/b & 100-3a/b<br />
|-<br />
|143 GHz || 143-1a/b 1 & 43-3a/b || 143-2a/b & 143-4a/b<br />
|-<br />
|217 GHz || 217-5a/b & 217-7a/b || 217-6a/b & 217-8a/b<br />
|-<br />
|353 GHz || 353-3a/b & 353-5a/b || 353-4a/b & 353-6a/b<br />
|}<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=600px<br />
|+ '''Definition of LFI Detector Pairs'''<br />
|- bgcolor="ffdead" <br />
!Frequency || Horn Pair || Comment <br />
|-<br />
|44 GHz || 24 || This maps is only in temperature<br />
|-<br />
|44 GHz || 25 & 26 || <br />
|-<br />
|70 GHz || 18 & 23 || Available also at Nside = 2048<br />
|-<br />
|70 GHz || 19 & 22 || Available also at Nside = 2048<br />
|-<br />
|70 GHz || 20 & 21 || Available also at Nside = 2048<br />
|}<br />
<br />
<br />
===Half-ring maps (64 HFI, 62 LFI)===<br />
<br />
These maps are similar to the ones above, but are built using only the first or the second half of each ring (or pointing period). The HFI provides half-ring maps for the full mission only, and for the full channel, the detsets, and the single bolometers. The LFI provides half-rings maps for the channel full mission (70 GHz also at Nside 2048), for the radiometer full mission and the horn pairs full mission.<br />
<!----<br />
===Masks===<br />
<br />
Masks are provided of the Galactic Plane and of the point sources. For the Galactic Plane, eight masks are given covering different fractions of the sky, and for the points sources two masks are given, at the 5 and 10 sigma level, for each Planck HFI and LFI frequency channel. These are generic masks, specific masks applicable to other products are delivered with the products themselves.<br />
---><br />
<br />
=== The Zodiacal light correction maps ===<br />
<br />
The Zodiacal light signal depends on the location of the observer relative to the Zodiacal light bands, and thus it is not a fixed pattern on the sky but depends on the period of observation. The maps presented here are the difference between the uncorrected (and not delivered) and the corrected maps. <br />
<br />
<br />
<!---center><br />
<gallery perrow=3 widths=260px heights=170px><br />
File: ZodiRes100.png | '''zodi/FSL rediduals - 100 GHz'''<br />
File: ZodiRes143.png | '''zodi/FSL rediduals - 143 GHz''' <br />
File: ZodiRes217.png | '''zodi/FSL rediduals - 217 GHz'''<br />
File: ZodiRes353.png | '''zodi/FSL rediduals - 353 GHz'''<br />
File: ZodiRes545.png | '''zodi/FSL rediduals - 545 GHz'''<br />
File: ZodiRes857.png | '''zodi/FSL rediduals - 857 GHz'''<br />
</gallery><br />
</center ---><br />
<br />
=== Caveats and known issues ===<br />
<br />
TBW<br />
<br />
==== Map zero-level ====<br />
<br />
For the 100 to 857 GHz maps, the zero levels are set to their optimal levels for Galactic and CIB studies. A procedure for adjusting them to astrophysical values is given in the HFI Mapmaking and Calibration paper {{PlanckPapers|????}}.<br />
<br />
For the 30, 44 and 70 GHz, maps are corrected for zero level monopole by applying an offset correction, see LFI Calibration paper {{PlanckPapers|planck2013-p02b}} section 3.4 "Setting the zero levels in the maps" and {{PlanckPapers|planck2014-a06||Planck-2015-A06}}. Note that the offset applied is indicated in the header as a comment keyword.<br />
<br />
==Inputs==<br />
=== HFI inputs ===<br />
<br />
* The cleaned TOIs of signal of each detector, together with their flags, produced by the [[TOI processing|TOI processing]] pipeline<br />
* The TOIs of pointing (quaternions), described in [[Detector_pointing|Detector pointing]]<br />
* Bolometer-level characterization data, from the DPC's internal IMO (not distributed)<br />
* Planck orbit data used to compute and remove the earth dipole<br />
* Planck solar dipole information used to calibrate the CMB channels<br />
* Planet models used to calibrate the Galactic channels.<br />
<br />
=== LFI inputs ===<br />
<br />
The Madam map-maker takes as an input:<br />
<br />
* The calibrated timelines (for details see [[TOI processing LFI|TOI Processing]])<br />
* The detector pointings (for details see [[Detector_pointing|Detector pointing]])<br />
* The noise information in the form of three-parameter (white noise level (<math>\sigma</math>), slope, and knee frequency ($f_\mathrm{knee}$)) noise model (for details see [[The RIMO|RIMO]])<br />
<br />
==Related products==<br />
=== Masks ===<br />
<br />
This section presents the masks of the point sources and of the Galactic plane. These are ''general purpose'' masks. Other masks specific to certain products are packaged with the products.<br />
<br />
====Point source masks====<br />
<br />
For HFI and LFI two sets of masks are provided: <br />
* Intensity masks, which removes sources detected with SNR > 5. <br />
* Polarisation masks, which remove sources which have polarisation detection significance of 99.97 % or greater at the position of a source detected in intensity. They were derived from the polarisation maps with dust ground bandpass mismatch leakage correction applied. The cut around each source has a radius of 3σ (width) of the beam ~ 1.27 FWHM (for LFI the cut around each source has a radius of 32 arcmin at 30GHz, 27 arcmin at 44 GHz and 13 arcmin at 70 GHz).<br />
<br />
Both sets are found in the file ''HFI_Mask_PointSrc_2048_R2.00.fits'' in which the first extension contains the Intensity masks, and the second contains the Polarisation masks.<br />
<br />
====Galactic Plane masks====<br />
<br />
Eight masks are provided giving 20, 40, 60, 70, 80, 90, 97, and 99% sky coverage derived from the 353 GHz map, after CMB subtraction. They are independent of frequency channel. Three versions of these are given: not apodized, and apodized by 2 and 5 deg. The filenames are ''HFI_Mask_GalPlane-apoN_2048_R2.00.fits'', where N = 0, 2, 5.<br />
<br />
The masks are shows below. The 8 GalPlane masks are combined (added together) and shown in a single figure for each of the three apodization. While the result is quite clear for the case of no apodization, it is less so for the apodized case. The point source masks are shown separately for the Intensity case.<br />
<br />
<center><br />
<gallery perrow=3 widths=260px heights=160px ><br />
File: GalPlaneMask_apo0.png | '''Galactic Plane masks, no apod'''<br />
File: GalPlaneMask_apo2.png | '''Galactic Plane masks, apod 2 deg'''<br />
File: GalPlaneMask_apo5.png | '''Galactic Plane masks, apod 5 deg'''<br />
File: PointSrcMask_100.png | '''PointSource mask 100 GHz'''<br />
File: PointSrcMask_143.png | '''PointSource mask 143 GHz'''<br />
File: PointSrcMask_217.png | '''PointSource mask 217 GHz'''<br />
File: PointSrcMask_353.png | '''PointSource mask 343 GHz'''<br />
File: PointSrcMask_545.png | '''PointSource mask 545 GHz'''<br />
File: PointSrcMask_857.png | '''PointSource mask 857 GHz'''<br />
</gallery><br />
</center><br />
<br />
== File names ==<br />
The FITS filenames are of the form ''{H|L}FI_SkyMap_fff{-tag}_Nside_R2.nn_{coverage}-{type}.fits'', where ''fff'' are three digits to indicate the Planck frequency band, ''tag'' indicates the single detector or the detset, ''Nside'' is the Healpix Nside of the map, ''coverage'' indicates which part of the mission is covered (full, half mission, survey, year, ...) , and the optional ''type'' indicates the subset of input data used. The table below lists the products by type, with the appropriate unix wildcards that form the full filename.<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=880px<br />
|+ '''HFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename <br />
|-<br />
| Full chan, full mission ||HFI_SkyMap_???_2048_R2.??_full.fits ||HFI_SkyMap_???_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
| Full channel, nominal mission ||HFI_SkyMap_???_2048_R2.??_nominal.fits || n/a<br />
|-<br />
| Full channel, single survey || HFI_SkyMap_???_2048_R2.??_survey-?.fits || n/a<br />
|-<br />
| Full channel, single year || HFI_SkyMap_???_2048_R2.??_year-?.fits || n/a<br />
|-<br />
| Full channel, half mission || HFI_SkyMap_???_2048_R2.??_halfmission*-?.fits || n/a<br />
|-<br />
| Det-set, full mission || HFI_SkyMap_???-ds?_2048_R2.??_full.fits || HFI_SkyMap_???-ds?_2048_R2.??_full-ringhalf-?.fits<br />
|-<br />
|Single SWB, full mission || HFI_SkyMap_???-?_2048_R2.??_full.fits || HFI_SkyMap_???-?_2048_R2.??_full-ringhalf-?.fits<br />
|}<br />
<br />
{| class="wikitable" align="center" style="text-align"left" border="1" cellpadding="15" cellspacing="20" width=1000px<br />
|+ '''LFI FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Coverage || filename || half-ring filename || Comment<br />
|-<br />
| Full channel, full mission ||LFI_SkyMap_???_1024_R2.??_full.fits ||LFI_SkyMap_???_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Full channel, single survey || LFI_SkyMap_???_1024_R2.??_survey-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, survey combination || LFI_SkyMap_???_1024_R2.??_survey-1-3-5-6-7-8.fits || n/a || n/a<br />
|-<br />
| Full channel, single year || LFI_SkyMap_???_1024_R2.??_year-?.fits || n/a || Available also at Nside = 2048<br />
|-<br />
| Full channel, year combination || LFI_SkyMap_???_1024_R2.??_year?-?.fits || n/a || n/a<br />
|-<br />
| Horn pair, full mission || LFI_SkyMap_???-??-??_1024_R2.??_full.fits || LFI_SkyMap_???_??-??_1024_R2.??_full-ringhalf-?.fits || Available also at Nside = 2048<br />
|-<br />
| Single radiometer, full mission || LFI_SkyMap_???-???_1024_R2.??_full.fits || LFI_SkyMap_???-???_1024_R2.??_full-ringhalf-?.fits || n/a<br />
|}<br />
<br />
<br />
<br />
For the benefit of users who are only looking for the frequency maps with no additional information, we also provide a file combining the 9 frequency maps as separate columns in a single extension. The 9 columns in this file contain the intensity maps ONLY and no other information (hit maps and variance maps) is provided.<br />
<br />
<!---<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=500px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal.fits|link=LFI_SkyMap_030_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal.fits|link=LFI_SkyMap_044_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal.fits|link=LFI_SkyMap_070_1024_R1.10_nominal.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal.fits|link=LFI_SkyMap_070_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal.fits|link=HFI_SkyMap_100_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal.fits|link=HFI_SkyMap_143_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal.fits|link=HFI_SkyMap_217_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal.fits|link=HFI_SkyMap_353_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal.fits|link=HFI_SkyMap_545_2048_R1.10_nominal.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal.fits|link=HFI_SkyMap_857_2048_R1.10_nominal.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Full channel, Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ZodiCorrected.fits}} <br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Combined frequency maps<br />
|-<br />
| '''All''' || {{PLASingleFile|fileType=file|name=COM_MapSet_I-allFreqs_R1.10_nominal.fits|link=COM_MapSet_I-allFreqs_R1.10_nominal.fits}} <br />
|}<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:center" border="1" cellpadding="3" cellspacing="0" width=850px<br />
|+ '''FITS filenames'''<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 maps || Survey 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_1.fits|link=LFI_SkyMap_030_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_survey_2.fits|link=LFI_SkyMap_030_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_1.fits|link=LFI_SkyMap_044_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_survey_2.fits|link=LFI_SkyMap_044_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_1.fits|link=LFI_SkyMap_070_1024_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_survey_2.fits|link=LFI_SkyMap_070_1024_R1.10_survey_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_1.fits|link=LFI_SkyMap_070_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_survey_2.fits|link=LFI_SkyMap_070_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Survey 1 Zodi-corrected maps || Survey 2 Zodi-corrected maps<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_100_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_143_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_217_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_353_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_545_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_1_ZodiCorrected.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits|link=HFI_SkyMap_857_2048_R1.10_survey_2_ZodiCorrected.fits}}<br />
|- bgcolor="ffdead"<br />
! Frequency || Half-ring 1 maps ||Half-ring 2 maps<br />
|-<br />
| '''30GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_030_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''44GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_044_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_1024_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''70GHz''' || {{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits|link=LFI_SkyMap_070_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''100GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_100_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''143GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_143_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''217GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_217_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''353GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_353_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''545GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_545_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|-<br />
| '''857GHz''' || {{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_1.fits}} ||<br />
{{PLASingleFile|fileType=map|name=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits|link=HFI_SkyMap_857_2048_R1.10_nominal_ringhalf_2.fits}}<br />
|}<br />
---><br />
<br />
== FITS file structure ==<br />
<br />
The FITS files for the sky maps contain a minimal primary header with no data, and a ''BINTABLE'' extension (EXTENSION 1, EXTNAME = ''FREQ-MAP'') containing the data. The structure is shows schematically in the figure below. The ''FREQ-MAP'' extension contains a 3- or a 10-column table that contain the signal, hit-count and variance maps, all in Healpix format. The 3-column case is for intensity only maps, the 10-column case is for polarisation. The number of rows is the number of map pixels, which is Npix = 12 Nside<sup>2</sup> for Healpix maps, where Nside = 1024 or 2048 for most the maps presented in this chapter.<br />
<br />
[[File:FITS_FreqMap.png | 550px | center | thumb | '''FITS file structure''']]<br />
<br />
Note that file sizes are ~0.6 GB for I-only maps and ~1.9 GB for I,Q,U maps at Nside 2048 and ~0.14 GB for I-only maps and ~0.45 GB for I,Q,U maps at Nside 1024 .<br />
<br />
Keywords indicate the coordinate system (GALACTIC), the Healpix ordering scheme (NESTED), the units (K_cmb or MJy/sr) of each column, and of course the frequency channel (FREQ). Where polarisation Q and U maps are provided, the ''COSMO'' polarisation convention (used in HEALPIX) is adopted, and it is specified in the ''POLCCONV'' keyword (see [[Sky_temperature_maps#Polarization_convention_used_in_the_Planck_project|this section]]. The COMMENT fields give a one-line summary of the product, and some other information useful for traceability within the DPCs. The original filename is also given in the ''FILENAME'' keyword. The ''BAD_DATA'' keyword gives the value used by Healpix to indicate pixels for which no signal is present (these will also have a hit-count value of 0). The main parameters are summarised below:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Sky map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'FREQ-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes I map<br />
|-<br />
|Q_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes Q map (optional)<br />
|-<br />
|U_STOKES || Real*4 || K_cmb or MJy/sr || The Stokes U map (optional)<br />
|-<br />
|HITS || Int*4 || none || The hit-count map<br />
|-<br />
|II_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The II variance map<br />
|-<br />
|IQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|IU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The IQ variance map (optional)<br />
|-<br />
|QQ_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QQ variance map (optional)<br />
|-<br />
|QU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The QU variance map (optional)<br />
|-<br />
|UU_COV || Real*4 || K_cmb<sup>2</sup> or (MJy/sr)<sup>2</sup> || The UU variance map (optional)<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 12 Nside<sup>2</sup> – 1 || Last pixel number<br />
|-<br />
|FREQ || string || nnn || The frequency channel <br />
|}<br />
<br />
<br />
The same structure applies to all ''SkyMap'' products, independent of whether they are full channel, survey of half-ring. The distinction between the types of maps is present in the FITS filename (and in the traceability comment fields).<br />
<br />
==Polarization convention used in the Planck project==<br />
<br />
The Planck collaboration used the COSMO convention for the polarization angle (as usually used in space based CMB missions), whereas other astronomical fields usually use the IAU convention. In the following document we report the difference between these two conventions, and the consequence if it is NOT taken into account correctly in the analysis.<br />
<br />
[[File:conventions.png|thumb|center|400px|'''Figure 1. COSMO convention (left) and IAU convention (right). The versor <math>\hat{z}</math> points outwards the pointing direction in COSMO, and inwards in IAU. The bottom panel refers to the plane tangent to the sphere.''']]<br />
<br />
Changing the orientation convention is equivalent to a transformation <math>\psi'=\pi-\psi</math> of the polarization angle (Figure 1). The consequence of this transformation is the inversion of the Stokes parameter <math>U</math>.<br />
The components of the polarization tensor in the helicity basis <math>\epsilon^{\pm}=1/\sqrt{2}(\hat{x}\pm i\hat{y})</math> are:<br />
<br />
<math><br />
(Q+iU)(\hat{n}) = \sum _{\ell m}a_{2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
\\(Q-iU)(\hat{n}) = \sum _{\ell m}a_{-2,lm}{}_{2}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where <math>{}_{2}Y_{\ell }^{m}(\hat{n})</math> are the spin weighted spherical harmonic functions.<br />
The <math>E</math> and <math>B</math> modes can be defined as:<br />
<math><br />
E(\hat{n}) = \sum_{\ell m}a_{E,\ell m}Y_{\ell }^{m}(\hat{n})<br />
\\B(\hat{n}) = \sum_{\ell m}a_{B,\ell m}Y_{\ell }^{m}(\hat{n})<br />
</math><br />
<br />
where the coefficients <math>a_{E,\ell m}</math> and <math>a_{B,\ell m}</math> are derived from linear combinations of the <math>a_{2,\ell m}</math> , <math>a_{-2,\ell m}</math> defined implicitly in the first equation (<math>Q\pm iU</math>).<br />
<br />
[[File:test_gradient.jpg|thumb|center|400px|]]<br />
[[File:test_curl.jpg|thumb|center|400px|'''Figure 2. Error on Planck-LFI 70 GHz <math>EE</math> (top) and <math>BB</math> (bottom) spectra, in case of wrong choice of the coordinate system convention (IAU instead of COSMO).''']]<br />
<br />
The effect of the sign inversion of <math>U</math> on the polarization spectra is a non trivial mixing of <math>E</math> and <math>B</math> modes. <br />
<br />
An example of the typical error on <math>EE</math> and <math>BB</math> auto-spectra in case of a wrong choice of the polarization basis is shown in Figure 2.<br />
<br />
BE CAREFUL about the polarization convention you are using. If the IAU convention is used in computing the power spectra, the sign of the <math>U</math> component of the Planck maps must be inverted before computing <math>E</math> and <math>B</math> modes.<br />
<br />
=== Note on the convention used by the Planck Catalog of Compact Sources (PCCS) ===<br />
For continuity with other compact sources catolgues, the Catalogue of Compact Sources provided by Planck follows the IAU convention, and the polarization angles are defined on an interval of [-90,90] degrees. To switch to the COSMO convention, the polarization angles listed in the catalogue have to be shifted by 90 degrees and multiplied by -1.<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:Mission products|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=C2&diff=11272C22015-02-04T18:14:12Z<p>Agregori: </p>
<hr />
<div>{{DISPLAYTITLE:CMB power spectra}}<br />
<br />
<br />
The main product to express cosmological constraints posed by Planck data is a likelihood code. One of its by-product is the derived maximum-likelihood CMB spectrum, which is available for plotting purposes; see product page. <br />
<br />
The likelihood code itself will be released together with the corresponding "CMB power spectra and likelihood" paper {{PlanckPapers|planck2014-a13||Planck-2015-A13}}; however, a short summary of the approach (similar to that used in 2013) is already available in the 2015 release parameter paper. <br />
<br />
== References ==<br />
<references /><br />
<br />
[[Category:HFI/LFI joint data processing|004]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Astrophysical_component_separation&diff=11271Astrophysical component separation2015-02-04T18:08:07Z<p>Agregori: /* Commander-Ruler */</p>
<hr />
<div>==CMB and foreground separation==<br />
<br />
See the Component Separation paper {{PlanckPapers|planck2013-p06}} {{PlanckPapers|planck2014-a11||Planck-2015-A11}} for details.<br />
===NILC===<br />
NILC is a linear method for combining the input frequency channels. It implements an ILC with weighting coefficients varying over the sky and over the multipole range up to <math>\ell=3200</math> and it does so using 'needlets' which are spherical wavelets. A special procedure is used for processing the coarsest needlet scale<br />
which contains the large scale multipoles.<br />
<br />
In practice, our NILC processing depends on several implementation choices, as follows:<br />
; Input channels<br />
: In this work, the NILC algorithm is applied to all Planck channels from 44 to 857 GHz omitting only the 30 GHz channel.<br />
; Pre-processing of point sources<br />
: Identical to the SMICA pre-processing.<br />
; Masking and inpainting<br />
: The NILC CMB map is actually produced in a three-step process. In a first step, the NILC weights are computed from covariance matrices evaluated using a Galactic mask removing about 2 % of the sky (and is apodized at 1◦). In a second step, those NILC weights are applied to needlet coefficients computed over the complete sky (except for point source masking/subtraction), yielding a NILC CMB estimate over the full sky (except for the point source mask). In short, the weights are computed over a masked sky but are applied to a full sky (excluding point sources). In a final step, the pixels masked due to point source processing are replaced by the values of a constrained Gaussian realization (inpainting).<br />
; Spatial localization<br />
: The boundaries of the zones used for spatial localisation are obtained as iso-level curves of a low resolution map of Galactic emission.<br />
; Beam control and transfer function<br />
: As in the SMICA processing, the input maps are internally re-beamed to a 5′ resolution, so the resulting CMB map is automatically synthesized with an effective Gaussian beam of five arcminutes, according to the unbiased nature of the ILC.<br />
; Using SMICA recalibration<br />
: In our current implementation, the NILC solution uses the values determined by SMICA for the CMB spectrum.<br />
<br />
===SEVEM===<br />
The aim of Sevem is to produce clean CMB maps at one or several frequencies by using a procedure based on template fitting. The templates are internal, i.e., they are constructed from Planck data, avoiding the need for external data sets, which usually complicates the analyses and may introduce inconsistencies. The method has been successfully applied to Planck simulations (Leach et al., 2008{{BibCite|leach2008}}) and to WMAP polarisation data (Fernandez-Cobos et al., 2012{{BibCite|fernandezcobos2012}}). In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<br />
<br />
The input maps used are all the Planck frequency channels. In particular, for intensity, we have cleaned the 100, 143 GHz and 217 GHz maps using four templates. Three or them are constructed as the difference of the following Planck channels (smoothed to a common resolution to remove the CMB contribution): (30-44) GHz, (44-70) GHz, (545-353) GHz and a fourth template given by the 857 GHz channel (smoothed at the resolution of the 545 GHz channel). For polarization we clean maps at frequencies of 70, 100 and 143 GHz using three templates for each channel. In particular, we use (30-44) GHz smoothed to a common resolution, (353-217) at 10', and (217-143) GHz at 1 degree resolution to clean the 70 and 100 GHz maps. To clean the 143 GHz channel, the last template is replaced by (217-100) GHz at 1 degree resolution. Before constructing the templates, for both intensity and polarization, we perform inpainting in the positions of detected point sources to reduce their contamination of the final map. <br />
<br />
A linear combination of the templates is then subtracted from the Planck sky map at the considered frequency, in order to produce the clean CMB map. The coefficients of the linear combination are obtained by minimising the variance of the clean map outside a given mask. Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although we expect that foreground residuals are present in the excluded areas). Inpainting of point sources is also carried out in the clean maps.<br />
<br />
The final CMB intensity map has then been constructed by combining the 143 and 217 GHz cleaned maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of FWHM=5 arcminutes at <math>N_{side}</math>=2048. The final CMB polarization map has been obtained by combining the 100 and 143 GHz clean maps at <math>N_{side}</math>=1024 and has a resolution of 10 arc minutes.<br />
<br />
===SMICA===<br />
<br />
<br />
A linear method, SMICA reconstructs a CMB map as a linear combination<br />
in the harmonic domain of <math>N_{chan}</math> input frequency maps<br />
with weights that depend on multipole <math>\ell</math>. Given the<br />
<math>N_{chan} × 1</math> vector <math>\mathbf{x}_{\ell m}</math> of<br />
spherical harmonic coefficients for the input maps, it computes<br />
coefficients <math>s_{\ell m}</math> for the CMB map as<br />
<br />
: <math>\label{eq:smica:shat} <br />
\hat{s}_{\ell m} = \mathbf{w}^†_\ell \mathbf{x}_{\ell m}</math><br />
<br />
where the <math>N_{chan} × 1</math> vector <math>\mathbf{w}_\ell<br />
</math> which contains the multipole-dependent weights is built to<br />
offer unit gain to the CMB with minimum variance. This is achieved<br />
with<br />
<br />
: <math>\label{eq:smica:w} <br />
\mathbf{w}_\ell = \frac{\mathbf{R}_\ell ^{-1} \mathbf{a}}{\mathbf{a}^† \mathbf{R}_\ell ^{-1} \mathbf{a}} </math><br />
<br />
where vector <math>\mathbf{a}</math> is the emission spectrum of the<br />
CMB evaluated at each channel (allowing for possible inter-channel<br />
recalibration factors) and <math> \mathbf{R}_\ell </math> is the<br />
<math>N_{chan} × N_{chan}</math> spectral covariance matrix of<br />
<math>\mathbf{x}_{\ell m}</math>. Taking <math>\mathbf{R}_\ell </math><br />
in the second equation<br />
<!-- Eq. \ref{eq:smica:w} --><br />
to be the sample spectral covariance matrix<br />
<math>\mathbf{\hat{R}}_\ell </math> of the observations:<br />
<br />
: <math>\label{eq:smica:Rhat} <br />
\mathbf{\hat{R}}_\ell = \frac{1}{2 \ell + 1} \sum_m \mathbf{x}_{ \ell m} \mathbf{x}_{\ell m}^†</math> <br />
<br />
would implement a simple harmonic-domain ILC. This is not what SMICA<br />
does. As discussed below, we instead use a model <math>\mathbf{R}_\ell<br />
(θ)</math> and determine the covariance matrix to be used in the second equation<br />
<!-- Eq. \ref{eq:smica:w} --><br />
by fitting <math>\mathbf{R}_\ell (θ)</math> to<br />
<math>\mathbf{\hat{R}}_\ell </math>. This is done in the maximum<br />
likelihood sense for stationary Gaussian fields, yielding the best fit<br />
model parameters θ as<br />
<br />
: <math>\label{eq:smica:thetahat}<br />
\hat{θ} = \rm{arg \, min}_θ \sum_\ell (2\ell + 1) ( \mathbf{\hat{R}}_\ell \mathbf{R}_\ell (θ)^{-1} \, +\, log \, det \, \mathbf{R}_\ell (θ)).</math><br />
<br />
<br />
SMICA models the data is a superposition of CMB, noise and<br />
foregrounds. The latter are not parametrically modelled; instead, we<br />
represent the total foreground emission by <math>d</math> templates<br />
with arbitrary frequency spectra, angular spectra and correlations:<br />
<br />
: <math> \label{eq:smica:Rmodel}<br />
\mathbf{R}_\ell (θ) = \mathbf{aa}^† \, C_\ell \, + \, \mathbf{A P}_\ell \mathbf{A}^† \, + \, \mathbf{N}_\ell <br />
</math> <br />
<br />
where <math>C_\ell </math> is the angular power spectrum of the CMB,<br />
<math>\mathbf{A}</math> is a <math>N_{chan} ×d</math> matrix,<br />
<math>\mathbf{P}_\ell </math> is a positive <math>d×d</math> matrix,<br />
and <math>\mathbf{N}_\ell </math> is a diagonal matrix representing<br />
the noise power spectrum. The parameter vector <math>θ</math> contains<br />
all or part of the quantities in the above equation.<br />
<br />
<br />
The above equations summarize the founding principles of SMICA; its<br />
actual operation depends on a choice for the spectral model<br />
<math>\mathbf{R}_\ell (θ)</math> and on several<br />
implementation-specific details.<br />
<br />
<br />
<br />
The actual implementation of SMICA includes the following steps:<br />
; Inputs<br />
: All nine Planck frequency channels from 30 to 857 GHz, harmonically transformed up to <math>\ell = 4000 </math>.<br />
; Fit<br />
: In practice, the SMICA fit, i.e. the minimization of the fourth equation, is conducted in three successive steps: We first estimate the CMB spectral law by fitting all model parameters over a clean fraction of sky in the range <math> 100 ≤ \ell ≤ 680</math> and retaining the best fit value for vector <math> \mathbf{a}</math>. In the second step, we estimate the foreground emissivity by fixing a to its value from the previous step and fitting all the other parameters over a large fraction of sky in the range <math> 4 ≤ \ell ≤ 150</math> and retaining the best fit values for the matrix <math> \mathbf{A}</math>. In the last step, we fit all power spectrum parameters; that is, we fix <math>\mathbf{a}</math> and <math>\mathbf{A}</math> to their previously found values and fit for each <math> C_\ell </math> and <math>\mathbf{P}_\ell </math> at each <math>\ell</math>. <br />
;Beams<br />
: The discussion thus far assumes that all input maps have the same resolution and effective beam. Since the observed maps actually vary in resolution, we process the input maps in the following way. To the <math>i</math>-th input map with effective beam <math>b_i(\ell)</math> and sampled on an HEALPix grid with <math>N^i_{side}</math>, the CMB sky multipole <math>s_{\ell m}</math> actually contributes <math>s_{\ell m}a_i b_i(\ell) p_i(\ell)</math>, where <math>p_i(\ell)</math> is the pixel window function for the grid at <math>N^i_{side}</math>. Seeking a final CMB map at 5-arcmin resolution, the highest resolution of Planck, we work with input spherical harmonics re-beamed to 5 arcmins, <math>\mathbf{\tilde{x}}_{\ell m} </math>; that is, SMICA operates on vectors with entries <math>x ̃^i_{\ell m} = x^i_{\ell m} b_5(\ell) / b_i(\ell) / p_i(\ell)</math>, where <math>b_5(\ell)</math> is a 5 arcmin Gaussian beam function. By construction, SMICA then produces an CMB map with an effective Gaussian beam of 5 arcmin (without the pixel window function).<br />
; Pre-processing<br />
: We start by fitting point sources with SNR > 5 in the PCCS catalogue in each input map. If the fit is successful, the fitted point source is removed from the map; otherwise it is masked and the hole in-painted. This is done at all frequencies but 545 and 857 GHz, where all point sources with SNR > 7.5 are masked and in-painted. <br />
; Masking and in-painting<br />
: In practice, SMICA uses a small Galactic mask leaving 97% of the sky. We deliver a full-sky CMB map in which the masked pixels (Galactic and point-source) are replaced by a constrained Gaussian realization.<br />
; Binning<br />
: In our implementation, we use binned spectra.<br />
; High <math>\ell</math><br />
: Since there is little point trying to model the spectral covariance at high multipoles, because the sample estimate is sufficient, SMICA implements a simple harmonic ILC at <math>\ell > 1500</math>; that is, it applies the filter (second equation) with <math>\mathbf{R}_\ell = \mathbf{\hat{R}}_\ell</math>.<br />
<br />
Viewed as a filter, SMICA can be summarized by the weights <math>\mathbf{w}_\ell</math> applied to each input map as a function of multipole. In this sense, SMICA is strictly equivalent to co-adding the input maps after convolution by specific axi-symmetric kernels directly related to the corresponding entry of <math>\mathbf{w}_\ell</math>. The SMICA weights used here are shown in figure below for input maps in units of K<math>_\rm{RJ}</math>. They show, in particular, the (expected) progressive attenuation of the lowest resolution channels with increasing multipole.<br />
<br />
[[File:smica.jpg|thumb|center|600px|'''Weights <math>w_\ell</math> given by SMICA to the input maps, after they are re-beamed to 5 arcmin and expressed in K<math>_\rm{RJ}</math>, as a function of multipole.''']]<br />
<br />
===Commander-Ruler===<br />
<br />
The Commander-Ruler (C-R) approach implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters. For computational reasons, the fit is performed in a two-step procedure: First, both foreground amplitudes and spectral parameters are found at low-resolution using MCMC/Gibbs sampling algorithms (Jewell et al. 2004<!--{{BibCite|jewell2004}}-->; Wandelt et al. 2004<!--{{BibCite|wandelt2004}}-->; Eriksen et al. 2004, 2007, 2008<!--{{BibCite|eriksen2004}}{{BibCite|eriksen2007}}{{BibCite|eriksen2008}}-->). Second, the amplitudes are recalculated at high resolution by solving the generalized least squares system (GLSS) per pixel with the spectral parameters fixed to their values from the low-resolution run.<br />
For the CMB-oriented analysis presented in this paper, we use only the seven lowest Planck frequencies, i.e., from 30 to 353 GHz. We first downgrade each frequency map from its native angular resolution to a common resolution of 40 arcminutes and re-pixelize at HEALPix N<math>_\rm{side}</math> = 256. Second, we set the monopoles and dipoles for each frequency band using a method that locally conserves spectral indices (Wehus et al. 2013<!--{{BibCite|wehus2013}}-->, in preparation). We approximate the effective instrumental noise as white with an RMS per pixel given by the Planck scanning pattern and an amplitude calibrated by smoothing simulations of the instrumental noise including correlations to the same resolution. For the high-resolution analysis, the important pre-processing step is the upgrading of the effective low-resolution mixing matrices to full Planck resolution: this is done by repixelizing from N<math>_\rm{side}</math> = 256 to 2048 in harmonic space, ensuring that potential pixelization effects from the low-resolution map do not introduce sharp boundaries in the high-resolution map.<br />
<br />
<!--<br />
TBW.<br />
--><br />
<br />
== References ==<br />
<br />
<References /><br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Astrophysical_component_separation&diff=11270Astrophysical component separation2015-02-04T18:07:05Z<p>Agregori: /* Commander-Ruler */</p>
<hr />
<div>==CMB and foreground separation==<br />
<br />
See the Component Separation paper {{PlanckPapers|planck2013-p06}} {{PlanckPapers|planck2014-a11||Planck-2015-A11}} for details.<br />
===NILC===<br />
NILC is a linear method for combining the input frequency channels. It implements an ILC with weighting coefficients varying over the sky and over the multipole range up to <math>\ell=3200</math> and it does so using 'needlets' which are spherical wavelets. A special procedure is used for processing the coarsest needlet scale<br />
which contains the large scale multipoles.<br />
<br />
In practice, our NILC processing depends on several implementation choices, as follows:<br />
; Input channels<br />
: In this work, the NILC algorithm is applied to all Planck channels from 44 to 857 GHz omitting only the 30 GHz channel.<br />
; Pre-processing of point sources<br />
: Identical to the SMICA pre-processing.<br />
; Masking and inpainting<br />
: The NILC CMB map is actually produced in a three-step process. In a first step, the NILC weights are computed from covariance matrices evaluated using a Galactic mask removing about 2 % of the sky (and is apodized at 1◦). In a second step, those NILC weights are applied to needlet coefficients computed over the complete sky (except for point source masking/subtraction), yielding a NILC CMB estimate over the full sky (except for the point source mask). In short, the weights are computed over a masked sky but are applied to a full sky (excluding point sources). In a final step, the pixels masked due to point source processing are replaced by the values of a constrained Gaussian realization (inpainting).<br />
; Spatial localization<br />
: The boundaries of the zones used for spatial localisation are obtained as iso-level curves of a low resolution map of Galactic emission.<br />
; Beam control and transfer function<br />
: As in the SMICA processing, the input maps are internally re-beamed to a 5′ resolution, so the resulting CMB map is automatically synthesized with an effective Gaussian beam of five arcminutes, according to the unbiased nature of the ILC.<br />
; Using SMICA recalibration<br />
: In our current implementation, the NILC solution uses the values determined by SMICA for the CMB spectrum.<br />
<br />
===SEVEM===<br />
The aim of Sevem is to produce clean CMB maps at one or several frequencies by using a procedure based on template fitting. The templates are internal, i.e., they are constructed from Planck data, avoiding the need for external data sets, which usually complicates the analyses and may introduce inconsistencies. The method has been successfully applied to Planck simulations (Leach et al., 2008{{BibCite|leach2008}}) and to WMAP polarisation data (Fernandez-Cobos et al., 2012{{BibCite|fernandezcobos2012}}). In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<br />
<br />
The input maps used are all the Planck frequency channels. In particular, for intensity, we have cleaned the 100, 143 GHz and 217 GHz maps using four templates. Three or them are constructed as the difference of the following Planck channels (smoothed to a common resolution to remove the CMB contribution): (30-44) GHz, (44-70) GHz, (545-353) GHz and a fourth template given by the 857 GHz channel (smoothed at the resolution of the 545 GHz channel). For polarization we clean maps at frequencies of 70, 100 and 143 GHz using three templates for each channel. In particular, we use (30-44) GHz smoothed to a common resolution, (353-217) at 10', and (217-143) GHz at 1 degree resolution to clean the 70 and 100 GHz maps. To clean the 143 GHz channel, the last template is replaced by (217-100) GHz at 1 degree resolution. Before constructing the templates, for both intensity and polarization, we perform inpainting in the positions of detected point sources to reduce their contamination of the final map. <br />
<br />
A linear combination of the templates is then subtracted from the Planck sky map at the considered frequency, in order to produce the clean CMB map. The coefficients of the linear combination are obtained by minimising the variance of the clean map outside a given mask. Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although we expect that foreground residuals are present in the excluded areas). Inpainting of point sources is also carried out in the clean maps.<br />
<br />
The final CMB intensity map has then been constructed by combining the 143 and 217 GHz cleaned maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of FWHM=5 arcminutes at <math>N_{side}</math>=2048. The final CMB polarization map has been obtained by combining the 100 and 143 GHz clean maps at <math>N_{side}</math>=1024 and has a resolution of 10 arc minutes.<br />
<br />
===SMICA===<br />
<br />
<br />
A linear method, SMICA reconstructs a CMB map as a linear combination<br />
in the harmonic domain of <math>N_{chan}</math> input frequency maps<br />
with weights that depend on multipole <math>\ell</math>. Given the<br />
<math>N_{chan} × 1</math> vector <math>\mathbf{x}_{\ell m}</math> of<br />
spherical harmonic coefficients for the input maps, it computes<br />
coefficients <math>s_{\ell m}</math> for the CMB map as<br />
<br />
: <math>\label{eq:smica:shat} <br />
\hat{s}_{\ell m} = \mathbf{w}^†_\ell \mathbf{x}_{\ell m}</math><br />
<br />
where the <math>N_{chan} × 1</math> vector <math>\mathbf{w}_\ell<br />
</math> which contains the multipole-dependent weights is built to<br />
offer unit gain to the CMB with minimum variance. This is achieved<br />
with<br />
<br />
: <math>\label{eq:smica:w} <br />
\mathbf{w}_\ell = \frac{\mathbf{R}_\ell ^{-1} \mathbf{a}}{\mathbf{a}^† \mathbf{R}_\ell ^{-1} \mathbf{a}} </math><br />
<br />
where vector <math>\mathbf{a}</math> is the emission spectrum of the<br />
CMB evaluated at each channel (allowing for possible inter-channel<br />
recalibration factors) and <math> \mathbf{R}_\ell </math> is the<br />
<math>N_{chan} × N_{chan}</math> spectral covariance matrix of<br />
<math>\mathbf{x}_{\ell m}</math>. Taking <math>\mathbf{R}_\ell </math><br />
in the second equation<br />
<!-- Eq. \ref{eq:smica:w} --><br />
to be the sample spectral covariance matrix<br />
<math>\mathbf{\hat{R}}_\ell </math> of the observations:<br />
<br />
: <math>\label{eq:smica:Rhat} <br />
\mathbf{\hat{R}}_\ell = \frac{1}{2 \ell + 1} \sum_m \mathbf{x}_{ \ell m} \mathbf{x}_{\ell m}^†</math> <br />
<br />
would implement a simple harmonic-domain ILC. This is not what SMICA<br />
does. As discussed below, we instead use a model <math>\mathbf{R}_\ell<br />
(θ)</math> and determine the covariance matrix to be used in the second equation<br />
<!-- Eq. \ref{eq:smica:w} --><br />
by fitting <math>\mathbf{R}_\ell (θ)</math> to<br />
<math>\mathbf{\hat{R}}_\ell </math>. This is done in the maximum<br />
likelihood sense for stationary Gaussian fields, yielding the best fit<br />
model parameters θ as<br />
<br />
: <math>\label{eq:smica:thetahat}<br />
\hat{θ} = \rm{arg \, min}_θ \sum_\ell (2\ell + 1) ( \mathbf{\hat{R}}_\ell \mathbf{R}_\ell (θ)^{-1} \, +\, log \, det \, \mathbf{R}_\ell (θ)).</math><br />
<br />
<br />
SMICA models the data is a superposition of CMB, noise and<br />
foregrounds. The latter are not parametrically modelled; instead, we<br />
represent the total foreground emission by <math>d</math> templates<br />
with arbitrary frequency spectra, angular spectra and correlations:<br />
<br />
: <math> \label{eq:smica:Rmodel}<br />
\mathbf{R}_\ell (θ) = \mathbf{aa}^† \, C_\ell \, + \, \mathbf{A P}_\ell \mathbf{A}^† \, + \, \mathbf{N}_\ell <br />
</math> <br />
<br />
where <math>C_\ell </math> is the angular power spectrum of the CMB,<br />
<math>\mathbf{A}</math> is a <math>N_{chan} ×d</math> matrix,<br />
<math>\mathbf{P}_\ell </math> is a positive <math>d×d</math> matrix,<br />
and <math>\mathbf{N}_\ell </math> is a diagonal matrix representing<br />
the noise power spectrum. The parameter vector <math>θ</math> contains<br />
all or part of the quantities in the above equation.<br />
<br />
<br />
The above equations summarize the founding principles of SMICA; its<br />
actual operation depends on a choice for the spectral model<br />
<math>\mathbf{R}_\ell (θ)</math> and on several<br />
implementation-specific details.<br />
<br />
<br />
<br />
The actual implementation of SMICA includes the following steps:<br />
; Inputs<br />
: All nine Planck frequency channels from 30 to 857 GHz, harmonically transformed up to <math>\ell = 4000 </math>.<br />
; Fit<br />
: In practice, the SMICA fit, i.e. the minimization of the fourth equation, is conducted in three successive steps: We first estimate the CMB spectral law by fitting all model parameters over a clean fraction of sky in the range <math> 100 ≤ \ell ≤ 680</math> and retaining the best fit value for vector <math> \mathbf{a}</math>. In the second step, we estimate the foreground emissivity by fixing a to its value from the previous step and fitting all the other parameters over a large fraction of sky in the range <math> 4 ≤ \ell ≤ 150</math> and retaining the best fit values for the matrix <math> \mathbf{A}</math>. In the last step, we fit all power spectrum parameters; that is, we fix <math>\mathbf{a}</math> and <math>\mathbf{A}</math> to their previously found values and fit for each <math> C_\ell </math> and <math>\mathbf{P}_\ell </math> at each <math>\ell</math>. <br />
;Beams<br />
: The discussion thus far assumes that all input maps have the same resolution and effective beam. Since the observed maps actually vary in resolution, we process the input maps in the following way. To the <math>i</math>-th input map with effective beam <math>b_i(\ell)</math> and sampled on an HEALPix grid with <math>N^i_{side}</math>, the CMB sky multipole <math>s_{\ell m}</math> actually contributes <math>s_{\ell m}a_i b_i(\ell) p_i(\ell)</math>, where <math>p_i(\ell)</math> is the pixel window function for the grid at <math>N^i_{side}</math>. Seeking a final CMB map at 5-arcmin resolution, the highest resolution of Planck, we work with input spherical harmonics re-beamed to 5 arcmins, <math>\mathbf{\tilde{x}}_{\ell m} </math>; that is, SMICA operates on vectors with entries <math>x ̃^i_{\ell m} = x^i_{\ell m} b_5(\ell) / b_i(\ell) / p_i(\ell)</math>, where <math>b_5(\ell)</math> is a 5 arcmin Gaussian beam function. By construction, SMICA then produces an CMB map with an effective Gaussian beam of 5 arcmin (without the pixel window function).<br />
; Pre-processing<br />
: We start by fitting point sources with SNR > 5 in the PCCS catalogue in each input map. If the fit is successful, the fitted point source is removed from the map; otherwise it is masked and the hole in-painted. This is done at all frequencies but 545 and 857 GHz, where all point sources with SNR > 7.5 are masked and in-painted. <br />
; Masking and in-painting<br />
: In practice, SMICA uses a small Galactic mask leaving 97% of the sky. We deliver a full-sky CMB map in which the masked pixels (Galactic and point-source) are replaced by a constrained Gaussian realization.<br />
; Binning<br />
: In our implementation, we use binned spectra.<br />
; High <math>\ell</math><br />
: Since there is little point trying to model the spectral covariance at high multipoles, because the sample estimate is sufficient, SMICA implements a simple harmonic ILC at <math>\ell > 1500</math>; that is, it applies the filter (second equation) with <math>\mathbf{R}_\ell = \mathbf{\hat{R}}_\ell</math>.<br />
<br />
Viewed as a filter, SMICA can be summarized by the weights <math>\mathbf{w}_\ell</math> applied to each input map as a function of multipole. In this sense, SMICA is strictly equivalent to co-adding the input maps after convolution by specific axi-symmetric kernels directly related to the corresponding entry of <math>\mathbf{w}_\ell</math>. The SMICA weights used here are shown in figure below for input maps in units of K<math>_\rm{RJ}</math>. They show, in particular, the (expected) progressive attenuation of the lowest resolution channels with increasing multipole.<br />
<br />
[[File:smica.jpg|thumb|center|600px|'''Weights <math>w_\ell</math> given by SMICA to the input maps, after they are re-beamed to 5 arcmin and expressed in K<math>_\rm{RJ}</math>, as a function of multipole.''']]<br />
<br />
===Commander-Ruler===<br />
<br />
The Commander-Ruler (C-R) approach implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters. For computational reasons, the fit is performed in a two-step procedure: First, both foreground amplitudes and spectral parameters are found at low-resolution using MCMC/Gibbs sampling algorithms (Jewell et al. 2004<!--{{BibCite|jewell2004}}-->; Wandelt et al. 2004<!--{{BibCite|wandelt2004}}-->; Eriksen et al. 2004, 2007, 2008<!--{{BibCite|eriksen2004}}{{BibCite|eriksen2007}}{{BibCite|eriksen2008}}-->). Second, the amplitudes are recalculated at high resolution by solving the generalized least squares system (GLSS) per pixel with the spectral parameters fixed to their values from the low-resolution run.<br />
For the CMB-oriented analysis presented in this paper, we use only the seven lowest Planck frequencies, i.e., from 30 to 353 GHz. We first downgrade each frequency map from its native angular resolution to a common resolution of 40 arcminutes and re-pixelize at HEALPix N<math>_\rm{side}</math> = 256. Second, we set the monopoles and dipoles for each frequency band using a method that locally conserves spectral indices (Wehus et al. 2013{{BibCite|wehus2013}}, in preparation). We approximate the effective instrumental noise as white with an RMS per pixel given by the Planck scanning pattern and an amplitude calibrated by smoothing simulations of the instrumental noise including correlations to the same resolution. For the high-resolution analysis, the important pre-processing step is the upgrading of the effective low-resolution mixing matrices to full Planck resolution: this is done by repixelizing from N<math>_\rm{side}</math> = 256 to 2048 in harmonic space, ensuring that potential pixelization effects from the low-resolution map do not introduce sharp boundaries in the high-resolution map.<br />
<br />
<!--<br />
TBW.<br />
--><br />
<br />
== References ==<br />
<br />
<References /><br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Compact_Source_catalogues&diff=11268Compact Source catalogues2015-02-04T18:04:30Z<p>Agregori: /* Catalogue of Planck Galactic Cold Clumps */</p>
<hr />
<div>==Planck Catalogue of Compact Sources==<br />
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps. <br />
<br />
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between August 13 2009 and November 26 2010, as described in {{PlanckPapers|planck2013-p05}}. It consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between August 13 2009 and August 3 2013, as described in {{PlanckPapers|planck2014-a35||Planck-2015-A35}}, it consists of eighteen lists of sources, two lists per channel.<br />
<br />
The are three main differences between the PCCS and the PCCS2: <br />
<br />
<ol><br />
<li>The amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data).</li><br />
<li>The inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities.</li><br />
<li>The division of the PCCS2 into two sets of catalogues, PCCS2 and PCCS2E, depending on our ability to validate their contents.</li><br />
</ol><br />
<br />
Both the 2013 PCCS and the 2014 PCCS2 can be downloaded from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive].<br />
<br />
=== Detection procedure ===<br />
The Mexican Hat Wavelet 2{{BibCite|nuevo2006}} {{BibCite|lopezcaniego2006}} is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (IFCAMEX and HFI-MHW), the results are compatible at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency Matrix Multi-filters{{BibCite|herranz2009}} (MTXF) and the Bayesian PowellSnakes {{BibCite|carvalho2009}}. Both of them have been used both in PCCS and PCCS2 for the validation of the results obtained by the MHW2 in total intensity. <br />
<br />
In addition, two maximum likelihood methods have been used to do the anlysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the Filter Fusion technique {{BibCite|argueso2009}} and has been applied to WMAP maps {{BibCite|lopezcaniego2009}}. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source catalogue {{PlanckPapers|planck2011-1-10}}. In practice, both of them are filtering methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each. <br />
<br />
The detection of the compact sources is done locally on small flat patches to improve the efficiency of the process. The reason for this being that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimised to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centered at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into accoun the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large scale diffuse emission and the small scale noise fluctuation.<br />
<br />
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.<br />
<br />
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4. <br />
<br />
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone. The S/N thresholds are given in [[Catalogues|Table 1]].<br />
<br />
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag has been added to the catalogues for this purpose.<br />
<br />
In this version of the Planck catalogue of compact sources, we have split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources. For the lower frequencies, between 30 and 70 GHz, we still use a S/N threshold of 4, although some of the unvalidated sources are in the 4-4.5 S/N threshold regime. Moreover, as will be explained below, we use external catalogues and a multifrequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic masks and cirrus masks.<br />
<br />
=== Photometry ===<br />
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples.<br />
These additional flux density estimations are based on aperture photometry, PSF fitting and Gaussian fitting (see {{PlanckPapers|planck2013-p05}} for a detailed description of these additional photometries). The native flux density estimation is the only one that is obtained directly from the projected filtered maps while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Section 7.4 of the LFI DPC paper {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and Section of the HFI DPC paper {{PlanckPapers|planck2014-a08||Planck-2015-A08}}, and can be applied by the user.<br />
<br />
=== Validation process ===<br />
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be done with a large number of existing catalogues, whereas the validation of thermal sources is mostly done with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.<br />
<br />
==== Internal validation ====<br />
The catalogues have been validated through an internal Monte-Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N) and location, while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte-Carlo quality assesments injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 Ghz and above, maps from the Full Focal Plane 8 simulations have been used.<br />
<br />
==== External validation ====<br />
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy and flux density accuracy using external data sets, particularly large-area radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometries, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, but one additional excercise has been done. Simulatenous observations of a sample of 92 sources has been carried out in the Very Large Array, the Australia Compact Array and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level. <br />
<br />
At higher frequencies, surveys as the South-Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by the Galactic cirrus at high frequencies.<br />
<br />
=== Cautionary notes ===<br />
We list here some cautionary notes for users of the PCCS.<br />
<br />
* Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns {{PlanckPapers|planck2013-p02}}{{PlanckPapers|planck2013-p03}}. Follow-up observations of these sources might show significant differences in flux density compared to the values in the data products. Although the maps used for the PCCS are based on 2.6 sky coverages, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.<br />
<br />
* Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see {{PlanckPapers|planck2013-p03a}}). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.<br />
<br />
* Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.<br />
<br />
* Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, especially in regions of high non-Gaussian background emission, but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds.<br />
<br />
* Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in {{PlanckPapers|planck2013-p02}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and {{PlanckPapers|planck2013-p03}}, {{PlanckPapers|planck2014-a08||Planck-2015-A08}}.<br />
<br />
* Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium features (ISM) or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters which could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20◦, we can use the RIIFSCz {{BibCite|wang2014}} to provide a guide to the likely nature of sources. We cross match the PCCS2 857 GHz catalogue and the PCCS2E 857 GHz catalogue to the IRAS sources in the RIIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857 GHz catalogue 3094 have plausible IRAS counterparts while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy.sr−1. The non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy.sr−1 and a second peak at about 2.6 MJy.sr−1 . Both distributions have a long tail, but the non-IRAS-Identified tail is much longer. On this basis sources with SKY BRIGHTNESS > 4 MJy.sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy.sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8 but many non- matched sources do. These should be treated with caution. The PCCS2E 857 GHz catalogue contains 10470 sources with |b| > 20◦ of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy.sr−1 , but the non-matched sources have brightnesses extending to >55MJy.sr−1. Similarly hardly any of the IRAS-matched sources have CIRRUS N > 8 but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, be it inside the filament mask (WHICH ZONE=1), the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857GHz sources that do not match an IRAS source and that lie in the region, |b| > 20◦, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2 and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20◦ , where 2.47 % is in the filament mask, 23.15 % in the Galactic region and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20◦, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extra-galactic sources that are extended at Planck spatial resolution will also meet this criterion.<br />
<br />
<!--- ---------------------------------------><br />
<br />
==Planck Sunyaev-Zeldovich catalogue==<br />
<br />
The Planck SZ catalogue is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in {{PlanckPapers|planck2013-p05a}}, {{PlanckPapers|planck2014-a36||Planck-2015-A36}}. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (SNR >= 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from {{BibCite|arnaud2010}}, in the detection.<br />
<br />
* MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.<br />
<br />
* PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.<br />
<br />
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.<br />
<br />
== Catalogue of ''Planck'' Galactic Cold Clumps ==<br />
<br />
The catalogue of ''Planck'' Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in {{PlanckPapers|planck2014-a37||Planck-2015-A37}}. The sources are extracted with the CoCoCoDeT algorithm (Montier, 2010<!--{{BibCite|Montier2010}}-->), using Planck-HFI 857, 545, and 353 GHz maps and the 3 THz IRIS map <br />
(Miville 2005)<!--{{BibCite|Miville2005}}-->, an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.<br />
<br />
The CoCoCoDeT detection algorithm uses the 3 THz map as a spatial template of a warm background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857, 545, and 353 GHz maps of the cold residual component map over the full sky. A point source detection algorithm is applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin to other detections.<br />
<br />
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:<br />
* FLUX_QUALITY=1 : sources with flux density estimates at S/N > 1 in all bands ;<br />
* FLUX_QUALITY=2 : sources with flux density estimates at S/N > 1 only in 857, 545, and 353 GHz Planck bands, considered as very cold source candidates ;<br />
* FLUX_QUALITY=3 : sources without any reliable flux density estimates, listed as poor candidates.<br />
We also raise a flag on the blending between sources which can be used to quantify the reliability of the aperture photometry processing.<br />
<br />
To estimate possible contamination by extragalactic sources we (1) cross-correlated the positions with catalogues of extragalactic sources, (2) rejected detections with SED [in colour-colour plots] consistent with radio sources, and (3) rejected detections with clear association to extragalactic sources visible in DSS images. Compared to the original number of sources, these only resulted in a small number of rejections.<br />
<br />
Distance estimates, combining seven different methods, have been obtained for 5574 sources with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for infrared dark clouds (IRDCs), optical and near-infrared extinction using SDSS and 2MASS data, respectively, association with molecular clouds with known distances, and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.<br />
<br />
The derived physical properties of the PGCC sources are: temperature, column density, physical size, mass, density and luminosity.<br />
PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass and density) covering a large varety of objects, from dense cold cores to large molecular clouds.<br />
<br />
The validation of this catalogue has been performed with a Monte Carlo Quality Assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2' and 0.8' for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1<math>\sigma</math>. This kind of analysis is also very powerful to characterize the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detection has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.<br />
<br />
We computed the cross-correlation between the PGCC catalogue and the other internal ''Planck'' catalogues: PCCS2, PCCS2E, PSZ and PH''z''. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A few sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting a dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), that require further analysis to elucidate.<br />
<br />
The PGCC catalogue contains also 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies which are so close that we can identify individual clumps in them.<br />
<br />
<br />
<!--- ---------------------------------------><br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Compact_Source_catalogues&diff=11266Compact Source catalogues2015-02-04T18:02:06Z<p>Agregori: /* Catalogue of Planck Galactic Cold Clumps */</p>
<hr />
<div>==Planck Catalogue of Compact Sources==<br />
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps. <br />
<br />
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between August 13 2009 and November 26 2010, as described in {{PlanckPapers|planck2013-p05}}. It consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between August 13 2009 and August 3 2013, as described in {{PlanckPapers|planck2014-a35||Planck-2015-A35}}, it consists of eighteen lists of sources, two lists per channel.<br />
<br />
The are three main differences between the PCCS and the PCCS2: <br />
<br />
<ol><br />
<li>The amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data).</li><br />
<li>The inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities.</li><br />
<li>The division of the PCCS2 into two sets of catalogues, PCCS2 and PCCS2E, depending on our ability to validate their contents.</li><br />
</ol><br />
<br />
Both the 2013 PCCS and the 2014 PCCS2 can be downloaded from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive].<br />
<br />
=== Detection procedure ===<br />
The Mexican Hat Wavelet 2{{BibCite|nuevo2006}} {{BibCite|lopezcaniego2006}} is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (IFCAMEX and HFI-MHW), the results are compatible at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency Matrix Multi-filters{{BibCite|herranz2009}} (MTXF) and the Bayesian PowellSnakes {{BibCite|carvalho2009}}. Both of them have been used both in PCCS and PCCS2 for the validation of the results obtained by the MHW2 in total intensity. <br />
<br />
In addition, two maximum likelihood methods have been used to do the anlysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the Filter Fusion technique {{BibCite|argueso2009}} and has been applied to WMAP maps {{BibCite|lopezcaniego2009}}. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source catalogue {{PlanckPapers|planck2011-1-10}}. In practice, both of them are filtering methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each. <br />
<br />
The detection of the compact sources is done locally on small flat patches to improve the efficiency of the process. The reason for this being that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimised to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centered at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into accoun the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large scale diffuse emission and the small scale noise fluctuation.<br />
<br />
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.<br />
<br />
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4. <br />
<br />
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone. The S/N thresholds are given in [[Catalogues|Table 1]].<br />
<br />
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag has been added to the catalogues for this purpose.<br />
<br />
In this version of the Planck catalogue of compact sources, we have split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources. For the lower frequencies, between 30 and 70 GHz, we still use a S/N threshold of 4, although some of the unvalidated sources are in the 4-4.5 S/N threshold regime. Moreover, as will be explained below, we use external catalogues and a multifrequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic masks and cirrus masks.<br />
<br />
=== Photometry ===<br />
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples.<br />
These additional flux density estimations are based on aperture photometry, PSF fitting and Gaussian fitting (see {{PlanckPapers|planck2013-p05}} for a detailed description of these additional photometries). The native flux density estimation is the only one that is obtained directly from the projected filtered maps while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Section 7.4 of the LFI DPC paper {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and Section of the HFI DPC paper {{PlanckPapers|planck2014-a08||Planck-2015-A08}}, and can be applied by the user.<br />
<br />
=== Validation process ===<br />
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be done with a large number of existing catalogues, whereas the validation of thermal sources is mostly done with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.<br />
<br />
==== Internal validation ====<br />
The catalogues have been validated through an internal Monte-Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N) and location, while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte-Carlo quality assesments injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 Ghz and above, maps from the Full Focal Plane 8 simulations have been used.<br />
<br />
==== External validation ====<br />
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy and flux density accuracy using external data sets, particularly large-area radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometries, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, but one additional excercise has been done. Simulatenous observations of a sample of 92 sources has been carried out in the Very Large Array, the Australia Compact Array and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level. <br />
<br />
At higher frequencies, surveys as the South-Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by the Galactic cirrus at high frequencies.<br />
<br />
=== Cautionary notes ===<br />
We list here some cautionary notes for users of the PCCS.<br />
<br />
* Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns {{PlanckPapers|planck2013-p02}}{{PlanckPapers|planck2013-p03}}. Follow-up observations of these sources might show significant differences in flux density compared to the values in the data products. Although the maps used for the PCCS are based on 2.6 sky coverages, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.<br />
<br />
* Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see {{PlanckPapers|planck2013-p03a}}). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.<br />
<br />
* Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.<br />
<br />
* Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, especially in regions of high non-Gaussian background emission, but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds.<br />
<br />
* Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in {{PlanckPapers|planck2013-p02}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and {{PlanckPapers|planck2013-p03}}, {{PlanckPapers|planck2014-a08||Planck-2015-A08}}.<br />
<br />
* Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium features (ISM) or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters which could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20◦, we can use the RIIFSCz {{BibCite|wang2014}} to provide a guide to the likely nature of sources. We cross match the PCCS2 857 GHz catalogue and the PCCS2E 857 GHz catalogue to the IRAS sources in the RIIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857 GHz catalogue 3094 have plausible IRAS counterparts while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy.sr−1. The non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy.sr−1 and a second peak at about 2.6 MJy.sr−1 . Both distributions have a long tail, but the non-IRAS-Identified tail is much longer. On this basis sources with SKY BRIGHTNESS > 4 MJy.sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy.sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8 but many non- matched sources do. These should be treated with caution. The PCCS2E 857 GHz catalogue contains 10470 sources with |b| > 20◦ of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy.sr−1 , but the non-matched sources have brightnesses extending to >55MJy.sr−1. Similarly hardly any of the IRAS-matched sources have CIRRUS N > 8 but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, be it inside the filament mask (WHICH ZONE=1), the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857GHz sources that do not match an IRAS source and that lie in the region, |b| > 20◦, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2 and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20◦ , where 2.47 % is in the filament mask, 23.15 % in the Galactic region and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20◦, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extra-galactic sources that are extended at Planck spatial resolution will also meet this criterion.<br />
<br />
<!--- ---------------------------------------><br />
<br />
==Planck Sunyaev-Zeldovich catalogue==<br />
<br />
The Planck SZ catalogue is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in {{PlanckPapers|planck2013-p05a}}, {{PlanckPapers|planck2014-a36||Planck-2015-A36}}. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (SNR >= 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from {{BibCite|arnaud2010}}, in the detection.<br />
<br />
* MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.<br />
<br />
* PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.<br />
<br />
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.<br />
<br />
== Catalogue of ''Planck'' Galactic Cold Clumps ==<br />
<br />
The catalogue of ''Planck'' Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in {{PlanckPapers|planck2014-a37||Planck-2015-A37}}. The sources are extracted with the CoCoCoDeT algorithm {{BibCite|Montier2010}}, using Planck-HFI 857, 545, and 353 GHz maps and the 3 THz IRIS map <br />
{{BibCite|Miville2005}}, an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.<br />
<br />
The CoCoCoDeT detection algorithm uses the 3 THz map as a spatial template of a warm background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857, 545, and 353 GHz maps of the cold residual component map over the full sky. A point source detection algorithm is applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin to other detections.<br />
<br />
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:<br />
* FLUX_QUALITY=1 : sources with flux density estimates at S/N > 1 in all bands ;<br />
* FLUX_QUALITY=2 : sources with flux density estimates at S/N > 1 only in 857, 545, and 353 GHz Planck bands, considered as very cold source candidates ;<br />
* FLUX_QUALITY=3 : sources without any reliable flux density estimates, listed as poor candidates.<br />
We also raise a flag on the blending between sources which can be used to quantify the reliability of the aperture photometry processing.<br />
<br />
To estimate possible contamination by extragalactic sources we (1) cross-correlated the positions with catalogues of extragalactic sources, (2) rejected detections with SED [in colour-colour plots] consistent with radio sources, and (3) rejected detections with clear association to extragalactic sources visible in DSS images. Compared to the original number of sources, these only resulted in a small number of rejections.<br />
<br />
Distance estimates, combining seven different methods, have been obtained for 5574 sources with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for infrared dark clouds (IRDCs), optical and near-infrared extinction using SDSS and 2MASS data, respectively, association with molecular clouds with known distances, and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.<br />
<br />
The derived physical properties of the PGCC sources are: temperature, column density, physical size, mass, density and luminosity.<br />
PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass and density) covering a large varety of objects, from dense cold cores to large molecular clouds.<br />
<br />
The validation of this catalogue has been performed with a Monte Carlo Quality Assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2' and 0.8' for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1<math>\sigma</math>. This kind of analysis is also very powerful to characterize the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detection has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.<br />
<br />
We computed the cross-correlation between the PGCC catalogue and the other internal ''Planck'' catalogues: PCCS2, PCCS2E, PSZ and PH''z''. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A few sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting a dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), that require further analysis to elucidate.<br />
<br />
The PGCC catalogue contains also 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies which are so close that we can identify individual clumps in them.<br />
<br />
<br />
<!--- ---------------------------------------><br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Compact_Source_catalogues&diff=11265Compact Source catalogues2015-02-04T18:01:11Z<p>Agregori: /* Planck Sunyaev-Zeldovich catalogue */</p>
<hr />
<div>==Planck Catalogue of Compact Sources==<br />
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps. <br />
<br />
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between August 13 2009 and November 26 2010, as described in {{PlanckPapers|planck2013-p05}}. It consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between August 13 2009 and August 3 2013, as described in {{PlanckPapers|planck2014-a35||Planck-2015-A35}}, it consists of eighteen lists of sources, two lists per channel.<br />
<br />
The are three main differences between the PCCS and the PCCS2: <br />
<br />
<ol><br />
<li>The amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data).</li><br />
<li>The inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities.</li><br />
<li>The division of the PCCS2 into two sets of catalogues, PCCS2 and PCCS2E, depending on our ability to validate their contents.</li><br />
</ol><br />
<br />
Both the 2013 PCCS and the 2014 PCCS2 can be downloaded from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive].<br />
<br />
=== Detection procedure ===<br />
The Mexican Hat Wavelet 2{{BibCite|nuevo2006}} {{BibCite|lopezcaniego2006}} is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (IFCAMEX and HFI-MHW), the results are compatible at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency Matrix Multi-filters{{BibCite|herranz2009}} (MTXF) and the Bayesian PowellSnakes {{BibCite|carvalho2009}}. Both of them have been used both in PCCS and PCCS2 for the validation of the results obtained by the MHW2 in total intensity. <br />
<br />
In addition, two maximum likelihood methods have been used to do the anlysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the Filter Fusion technique {{BibCite|argueso2009}} and has been applied to WMAP maps {{BibCite|lopezcaniego2009}}. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source catalogue {{PlanckPapers|planck2011-1-10}}. In practice, both of them are filtering methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each. <br />
<br />
The detection of the compact sources is done locally on small flat patches to improve the efficiency of the process. The reason for this being that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimised to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centered at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into accoun the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large scale diffuse emission and the small scale noise fluctuation.<br />
<br />
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.<br />
<br />
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4. <br />
<br />
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone. The S/N thresholds are given in [[Catalogues|Table 1]].<br />
<br />
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag has been added to the catalogues for this purpose.<br />
<br />
In this version of the Planck catalogue of compact sources, we have split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources. For the lower frequencies, between 30 and 70 GHz, we still use a S/N threshold of 4, although some of the unvalidated sources are in the 4-4.5 S/N threshold regime. Moreover, as will be explained below, we use external catalogues and a multifrequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic masks and cirrus masks.<br />
<br />
=== Photometry ===<br />
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples.<br />
These additional flux density estimations are based on aperture photometry, PSF fitting and Gaussian fitting (see {{PlanckPapers|planck2013-p05}} for a detailed description of these additional photometries). The native flux density estimation is the only one that is obtained directly from the projected filtered maps while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Section 7.4 of the LFI DPC paper {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and Section of the HFI DPC paper {{PlanckPapers|planck2014-a08||Planck-2015-A08}}, and can be applied by the user.<br />
<br />
=== Validation process ===<br />
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be done with a large number of existing catalogues, whereas the validation of thermal sources is mostly done with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.<br />
<br />
==== Internal validation ====<br />
The catalogues have been validated through an internal Monte-Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N) and location, while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte-Carlo quality assesments injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 Ghz and above, maps from the Full Focal Plane 8 simulations have been used.<br />
<br />
==== External validation ====<br />
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy and flux density accuracy using external data sets, particularly large-area radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometries, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, but one additional excercise has been done. Simulatenous observations of a sample of 92 sources has been carried out in the Very Large Array, the Australia Compact Array and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level. <br />
<br />
At higher frequencies, surveys as the South-Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by the Galactic cirrus at high frequencies.<br />
<br />
=== Cautionary notes ===<br />
We list here some cautionary notes for users of the PCCS.<br />
<br />
* Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns {{PlanckPapers|planck2013-p02}}{{PlanckPapers|planck2013-p03}}. Follow-up observations of these sources might show significant differences in flux density compared to the values in the data products. Although the maps used for the PCCS are based on 2.6 sky coverages, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.<br />
<br />
* Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see {{PlanckPapers|planck2013-p03a}}). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.<br />
<br />
* Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.<br />
<br />
* Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, especially in regions of high non-Gaussian background emission, but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds.<br />
<br />
* Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in {{PlanckPapers|planck2013-p02}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and {{PlanckPapers|planck2013-p03}}, {{PlanckPapers|planck2014-a08||Planck-2015-A08}}.<br />
<br />
* Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium features (ISM) or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters which could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20◦, we can use the RIIFSCz {{BibCite|wang2014}} to provide a guide to the likely nature of sources. We cross match the PCCS2 857 GHz catalogue and the PCCS2E 857 GHz catalogue to the IRAS sources in the RIIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857 GHz catalogue 3094 have plausible IRAS counterparts while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy.sr−1. The non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy.sr−1 and a second peak at about 2.6 MJy.sr−1 . Both distributions have a long tail, but the non-IRAS-Identified tail is much longer. On this basis sources with SKY BRIGHTNESS > 4 MJy.sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy.sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8 but many non- matched sources do. These should be treated with caution. The PCCS2E 857 GHz catalogue contains 10470 sources with |b| > 20◦ of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy.sr−1 , but the non-matched sources have brightnesses extending to >55MJy.sr−1. Similarly hardly any of the IRAS-matched sources have CIRRUS N > 8 but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, be it inside the filament mask (WHICH ZONE=1), the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857GHz sources that do not match an IRAS source and that lie in the region, |b| > 20◦, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2 and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20◦ , where 2.47 % is in the filament mask, 23.15 % in the Galactic region and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20◦, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extra-galactic sources that are extended at Planck spatial resolution will also meet this criterion.<br />
<br />
<!--- ---------------------------------------><br />
<br />
==Planck Sunyaev-Zeldovich catalogue==<br />
<br />
The Planck SZ catalogue is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in {{PlanckPapers|planck2013-p05a}}, {{PlanckPapers|planck2014-a36||Planck-2015-A36}}. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (SNR >= 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from {{BibCite|arnaud2010}}, in the detection.<br />
<br />
* MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.<br />
<br />
* PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.<br />
<br />
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.<br />
<br />
== Catalogue of ''Planck'' Galactic Cold Clumps ==<br />
<br />
The catalogue of ''Planck'' Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in {{PlanckPapers|planck2014-a37}}. The sources are extracted with the CoCoCoDeT algorithm {{BibCite|Montier2010}}, using Planck-HFI 857, 545, and 353 GHz maps and the 3 THz IRIS map <br />
{{BibCite|Miville2005}}, an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.<br />
<br />
The CoCoCoDeT detection algorithm uses the 3 THz map as a spatial template of a warm background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857, 545, and 353 GHz maps of the cold residual component map over the full sky. A point source detection algorithm is applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin to other detections.<br />
<br />
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:<br />
* FLUX_QUALITY=1 : sources with flux density estimates at S/N > 1 in all bands ;<br />
* FLUX_QUALITY=2 : sources with flux density estimates at S/N > 1 only in 857, 545, and 353 GHz Planck bands, considered as very cold source candidates ;<br />
* FLUX_QUALITY=3 : sources without any reliable flux density estimates, listed as poor candidates.<br />
We also raise a flag on the blending between sources which can be used to quantify the reliability of the aperture photometry processing.<br />
<br />
To estimate possible contamination by extragalactic sources we (1) cross-correlated the positions with catalogues of extragalactic sources, (2) rejected detections with SED [in colour-colour plots] consistent with radio sources, and (3) rejected detections with clear association to extragalactic sources visible in DSS images. Compared to the original number of sources, these only resulted in a small number of rejections.<br />
<br />
Distance estimates, combining seven different methods, have been obtained for 5574 sources with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for infrared dark clouds (IRDCs), optical and near-infrared extinction using SDSS and 2MASS data, respectively, association with molecular clouds with known distances, and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.<br />
<br />
The derived physical properties of the PGCC sources are: temperature, column density, physical size, mass, density and luminosity.<br />
PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass and density) covering a large varety of objects, from dense cold cores to large molecular clouds.<br />
<br />
The validation of this catalogue has been performed with a Monte Carlo Quality Assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2' and 0.8' for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1<math>\sigma</math>. This kind of analysis is also very powerful to characterize the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detection has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.<br />
<br />
We computed the cross-correlation between the PGCC catalogue and the other internal ''Planck'' catalogues: PCCS2, PCCS2E, PSZ and PH''z''. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A few sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting a dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), that require further analysis to elucidate.<br />
<br />
The PGCC catalogue contains also 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies which are so close that we can identify individual clumps in them.<br />
<br />
<br />
<!--- ---------------------------------------><br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Compact_Source_catalogues&diff=11263Compact Source catalogues2015-02-04T18:00:15Z<p>Agregori: /* Cautionary notes */</p>
<hr />
<div>==Planck Catalogue of Compact Sources==<br />
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps. <br />
<br />
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between August 13 2009 and November 26 2010, as described in {{PlanckPapers|planck2013-p05}}. It consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between August 13 2009 and August 3 2013, as described in {{PlanckPapers|planck2014-a35||Planck-2015-A35}}, it consists of eighteen lists of sources, two lists per channel.<br />
<br />
The are three main differences between the PCCS and the PCCS2: <br />
<br />
<ol><br />
<li>The amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data).</li><br />
<li>The inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities.</li><br />
<li>The division of the PCCS2 into two sets of catalogues, PCCS2 and PCCS2E, depending on our ability to validate their contents.</li><br />
</ol><br />
<br />
Both the 2013 PCCS and the 2014 PCCS2 can be downloaded from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive].<br />
<br />
=== Detection procedure ===<br />
The Mexican Hat Wavelet 2{{BibCite|nuevo2006}} {{BibCite|lopezcaniego2006}} is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (IFCAMEX and HFI-MHW), the results are compatible at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency Matrix Multi-filters{{BibCite|herranz2009}} (MTXF) and the Bayesian PowellSnakes {{BibCite|carvalho2009}}. Both of them have been used both in PCCS and PCCS2 for the validation of the results obtained by the MHW2 in total intensity. <br />
<br />
In addition, two maximum likelihood methods have been used to do the anlysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the Filter Fusion technique {{BibCite|argueso2009}} and has been applied to WMAP maps {{BibCite|lopezcaniego2009}}. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source catalogue {{PlanckPapers|planck2011-1-10}}. In practice, both of them are filtering methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each. <br />
<br />
The detection of the compact sources is done locally on small flat patches to improve the efficiency of the process. The reason for this being that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimised to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centered at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into accoun the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large scale diffuse emission and the small scale noise fluctuation.<br />
<br />
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.<br />
<br />
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4. <br />
<br />
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone. The S/N thresholds are given in [[Catalogues|Table 1]].<br />
<br />
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag has been added to the catalogues for this purpose.<br />
<br />
In this version of the Planck catalogue of compact sources, we have split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources. For the lower frequencies, between 30 and 70 GHz, we still use a S/N threshold of 4, although some of the unvalidated sources are in the 4-4.5 S/N threshold regime. Moreover, as will be explained below, we use external catalogues and a multifrequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic masks and cirrus masks.<br />
<br />
=== Photometry ===<br />
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples.<br />
These additional flux density estimations are based on aperture photometry, PSF fitting and Gaussian fitting (see {{PlanckPapers|planck2013-p05}} for a detailed description of these additional photometries). The native flux density estimation is the only one that is obtained directly from the projected filtered maps while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Section 7.4 of the LFI DPC paper {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and Section of the HFI DPC paper {{PlanckPapers|planck2014-a08||Planck-2015-A08}}, and can be applied by the user.<br />
<br />
=== Validation process ===<br />
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be done with a large number of existing catalogues, whereas the validation of thermal sources is mostly done with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.<br />
<br />
==== Internal validation ====<br />
The catalogues have been validated through an internal Monte-Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N) and location, while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte-Carlo quality assesments injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 Ghz and above, maps from the Full Focal Plane 8 simulations have been used.<br />
<br />
==== External validation ====<br />
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy and flux density accuracy using external data sets, particularly large-area radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometries, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, but one additional excercise has been done. Simulatenous observations of a sample of 92 sources has been carried out in the Very Large Array, the Australia Compact Array and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level. <br />
<br />
At higher frequencies, surveys as the South-Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by the Galactic cirrus at high frequencies.<br />
<br />
=== Cautionary notes ===<br />
We list here some cautionary notes for users of the PCCS.<br />
<br />
* Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns {{PlanckPapers|planck2013-p02}}{{PlanckPapers|planck2013-p03}}. Follow-up observations of these sources might show significant differences in flux density compared to the values in the data products. Although the maps used for the PCCS are based on 2.6 sky coverages, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.<br />
<br />
* Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see {{PlanckPapers|planck2013-p03a}}). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.<br />
<br />
* Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.<br />
<br />
* Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, especially in regions of high non-Gaussian background emission, but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds.<br />
<br />
* Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in {{PlanckPapers|planck2013-p02}}, {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and {{PlanckPapers|planck2013-p03}}, {{PlanckPapers|planck2014-a08||Planck-2015-A08}}.<br />
<br />
* Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium features (ISM) or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters which could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20◦, we can use the RIIFSCz {{BibCite|wang2014}} to provide a guide to the likely nature of sources. We cross match the PCCS2 857 GHz catalogue and the PCCS2E 857 GHz catalogue to the IRAS sources in the RIIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857 GHz catalogue 3094 have plausible IRAS counterparts while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy.sr−1. The non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy.sr−1 and a second peak at about 2.6 MJy.sr−1 . Both distributions have a long tail, but the non-IRAS-Identified tail is much longer. On this basis sources with SKY BRIGHTNESS > 4 MJy.sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy.sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8 but many non- matched sources do. These should be treated with caution. The PCCS2E 857 GHz catalogue contains 10470 sources with |b| > 20◦ of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy.sr−1 , but the non-matched sources have brightnesses extending to >55MJy.sr−1. Similarly hardly any of the IRAS-matched sources have CIRRUS N > 8 but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, be it inside the filament mask (WHICH ZONE=1), the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857GHz sources that do not match an IRAS source and that lie in the region, |b| > 20◦, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2 and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20◦ , where 2.47 % is in the filament mask, 23.15 % in the Galactic region and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20◦, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extra-galactic sources that are extended at Planck spatial resolution will also meet this criterion.<br />
<br />
<!--- ---------------------------------------><br />
<br />
==Planck Sunyaev-Zeldovich catalogue==<br />
<br />
The Planck SZ catalogue is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in {{PlanckPapers|planck2013-p05a}}. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (SNR >= 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from {{BibCite|arnaud2010}}, in the detection.<br />
<br />
* MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.<br />
<br />
* PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.<br />
<br />
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.<br />
<br />
<br />
== Catalogue of ''Planck'' Galactic Cold Clumps ==<br />
<br />
The catalogue of ''Planck'' Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in {{PlanckPapers|planck2014-a37}}. The sources are extracted with the CoCoCoDeT algorithm {{BibCite|Montier2010}}, using Planck-HFI 857, 545, and 353 GHz maps and the 3 THz IRIS map <br />
{{BibCite|Miville2005}}, an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.<br />
<br />
The CoCoCoDeT detection algorithm uses the 3 THz map as a spatial template of a warm background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857, 545, and 353 GHz maps of the cold residual component map over the full sky. A point source detection algorithm is applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin to other detections.<br />
<br />
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:<br />
* FLUX_QUALITY=1 : sources with flux density estimates at S/N > 1 in all bands ;<br />
* FLUX_QUALITY=2 : sources with flux density estimates at S/N > 1 only in 857, 545, and 353 GHz Planck bands, considered as very cold source candidates ;<br />
* FLUX_QUALITY=3 : sources without any reliable flux density estimates, listed as poor candidates.<br />
We also raise a flag on the blending between sources which can be used to quantify the reliability of the aperture photometry processing.<br />
<br />
To estimate possible contamination by extragalactic sources we (1) cross-correlated the positions with catalogues of extragalactic sources, (2) rejected detections with SED [in colour-colour plots] consistent with radio sources, and (3) rejected detections with clear association to extragalactic sources visible in DSS images. Compared to the original number of sources, these only resulted in a small number of rejections.<br />
<br />
Distance estimates, combining seven different methods, have been obtained for 5574 sources with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for infrared dark clouds (IRDCs), optical and near-infrared extinction using SDSS and 2MASS data, respectively, association with molecular clouds with known distances, and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.<br />
<br />
The derived physical properties of the PGCC sources are: temperature, column density, physical size, mass, density and luminosity.<br />
PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass and density) covering a large varety of objects, from dense cold cores to large molecular clouds.<br />
<br />
The validation of this catalogue has been performed with a Monte Carlo Quality Assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2' and 0.8' for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1<math>\sigma</math>. This kind of analysis is also very powerful to characterize the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detection has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.<br />
<br />
We computed the cross-correlation between the PGCC catalogue and the other internal ''Planck'' catalogues: PCCS2, PCCS2E, PSZ and PH''z''. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A few sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting a dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), that require further analysis to elucidate.<br />
<br />
The PGCC catalogue contains also 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies which are so close that we can identify individual clumps in them.<br />
<br />
<br />
<!--- ---------------------------------------><br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Compact_Source_catalogues&diff=11262Compact Source catalogues2015-02-04T17:56:51Z<p>Agregori: /* Photometry */</p>
<hr />
<div>==Planck Catalogue of Compact Sources==<br />
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps. <br />
<br />
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between August 13 2009 and November 26 2010, as described in {{PlanckPapers|planck2013-p05}}. It consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between August 13 2009 and August 3 2013, as described in {{PlanckPapers|planck2014-a35||Planck-2015-A35}}, it consists of eighteen lists of sources, two lists per channel.<br />
<br />
The are three main differences between the PCCS and the PCCS2: <br />
<br />
<ol><br />
<li>The amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data).</li><br />
<li>The inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities.</li><br />
<li>The division of the PCCS2 into two sets of catalogues, PCCS2 and PCCS2E, depending on our ability to validate their contents.</li><br />
</ol><br />
<br />
Both the 2013 PCCS and the 2014 PCCS2 can be downloaded from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive].<br />
<br />
=== Detection procedure ===<br />
The Mexican Hat Wavelet 2{{BibCite|nuevo2006}} {{BibCite|lopezcaniego2006}} is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (IFCAMEX and HFI-MHW), the results are compatible at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency Matrix Multi-filters{{BibCite|herranz2009}} (MTXF) and the Bayesian PowellSnakes {{BibCite|carvalho2009}}. Both of them have been used both in PCCS and PCCS2 for the validation of the results obtained by the MHW2 in total intensity. <br />
<br />
In addition, two maximum likelihood methods have been used to do the anlysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the Filter Fusion technique {{BibCite|argueso2009}} and has been applied to WMAP maps {{BibCite|lopezcaniego2009}}. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source catalogue {{PlanckPapers|planck2011-1-10}}. In practice, both of them are filtering methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each. <br />
<br />
The detection of the compact sources is done locally on small flat patches to improve the efficiency of the process. The reason for this being that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimised to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centered at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into accoun the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large scale diffuse emission and the small scale noise fluctuation.<br />
<br />
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.<br />
<br />
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4. <br />
<br />
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone. The S/N thresholds are given in [[Catalogues|Table 1]].<br />
<br />
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag has been added to the catalogues for this purpose.<br />
<br />
In this version of the Planck catalogue of compact sources, we have split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources. For the lower frequencies, between 30 and 70 GHz, we still use a S/N threshold of 4, although some of the unvalidated sources are in the 4-4.5 S/N threshold regime. Moreover, as will be explained below, we use external catalogues and a multifrequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic masks and cirrus masks.<br />
<br />
=== Photometry ===<br />
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples.<br />
These additional flux density estimations are based on aperture photometry, PSF fitting and Gaussian fitting (see {{PlanckPapers|planck2013-p05}} for a detailed description of these additional photometries). The native flux density estimation is the only one that is obtained directly from the projected filtered maps while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Section 7.4 of the LFI DPC paper {{PlanckPapers|planck2014-a03||Planck-2015-A03}} and Section of the HFI DPC paper {{PlanckPapers|planck2014-a08||Planck-2015-A08}}, and can be applied by the user.<br />
<br />
=== Validation process ===<br />
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be done with a large number of existing catalogues, whereas the validation of thermal sources is mostly done with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.<br />
<br />
==== Internal validation ====<br />
The catalogues have been validated through an internal Monte-Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N) and location, while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte-Carlo quality assesments injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 Ghz and above, maps from the Full Focal Plane 8 simulations have been used.<br />
<br />
==== External validation ====<br />
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy and flux density accuracy using external data sets, particularly large-area radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometries, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, but one additional excercise has been done. Simulatenous observations of a sample of 92 sources has been carried out in the Very Large Array, the Australia Compact Array and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level. <br />
<br />
At higher frequencies, surveys as the South-Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by the Galactic cirrus at high frequencies.<br />
<br />
=== Cautionary notes ===<br />
We list here some cautionary notes for users of the PCCS.<br />
<br />
* Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns {{PlanckPapers|planck2013-p02}}{{PlanckPapers|planck2013-p03}}. Follow-up observations of these sources might show significant differences in flux density compared to the values in the data products. Although the maps used for the PCCS are based on 2.6 sky coverages, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.<br />
<br />
* Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see {{PlanckPapers|planck2013-p03a}}). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.<br />
<br />
* Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.<br />
<br />
* Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, especially in regions of high non-Gaussian background emission, but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds.<br />
<br />
* Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in {{PlanckPapers|planck2013-p02}} and {{PlanckPapers|planck2013-p03}}.<br />
<br />
* Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium features (ISM) or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters which could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20◦, we can use the RIIFSCz {{BibCite|wang2014}} to provide a guide to the likely nature of sources. We cross match the PCCS2 857 GHz catalogue and the PCCS2E 857 GHz catalogue to the IRAS sources in the RIIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857 GHz catalogue 3094 have plausible IRAS counterparts while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy.sr−1. The non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy.sr−1 and a second peak at about 2.6 MJy.sr−1 . Both distributions have a long tail, but the non-IRAS-Identified tail is much longer. On this basis sources with SKY BRIGHTNESS > 4 MJy.sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy.sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8 but many non- matched sources do. These should be treated with caution. The PCCS2E 857 GHz catalogue contains 10470 sources with |b| > 20◦ of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy.sr−1 , but the non-matched sources have brightnesses extending to >55MJy.sr−1. Similarly hardly any of the IRAS-matched sources have CIRRUS N > 8 but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, be it inside the filament mask (WHICH ZONE=1), the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857GHz sources that do not match an IRAS source and that lie in the region, |b| > 20◦, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2 and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20◦ , where 2.47 % is in the filament mask, 23.15 % in the Galactic region and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20◦, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extra-galactic sources that are extended at Planck spatial resolution will also meet this criterion.<br />
<br />
<!--- ---------------------------------------><br />
<br />
==Planck Sunyaev-Zeldovich catalogue==<br />
<br />
The Planck SZ catalogue is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in {{PlanckPapers|planck2013-p05a}}. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (SNR >= 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from {{BibCite|arnaud2010}}, in the detection.<br />
<br />
* MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.<br />
<br />
* PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.<br />
<br />
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.<br />
<br />
<br />
== Catalogue of ''Planck'' Galactic Cold Clumps ==<br />
<br />
The catalogue of ''Planck'' Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in {{PlanckPapers|planck2014-a37}}. The sources are extracted with the CoCoCoDeT algorithm {{BibCite|Montier2010}}, using Planck-HFI 857, 545, and 353 GHz maps and the 3 THz IRIS map <br />
{{BibCite|Miville2005}}, an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.<br />
<br />
The CoCoCoDeT detection algorithm uses the 3 THz map as a spatial template of a warm background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857, 545, and 353 GHz maps of the cold residual component map over the full sky. A point source detection algorithm is applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin to other detections.<br />
<br />
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:<br />
* FLUX_QUALITY=1 : sources with flux density estimates at S/N > 1 in all bands ;<br />
* FLUX_QUALITY=2 : sources with flux density estimates at S/N > 1 only in 857, 545, and 353 GHz Planck bands, considered as very cold source candidates ;<br />
* FLUX_QUALITY=3 : sources without any reliable flux density estimates, listed as poor candidates.<br />
We also raise a flag on the blending between sources which can be used to quantify the reliability of the aperture photometry processing.<br />
<br />
To estimate possible contamination by extragalactic sources we (1) cross-correlated the positions with catalogues of extragalactic sources, (2) rejected detections with SED [in colour-colour plots] consistent with radio sources, and (3) rejected detections with clear association to extragalactic sources visible in DSS images. Compared to the original number of sources, these only resulted in a small number of rejections.<br />
<br />
Distance estimates, combining seven different methods, have been obtained for 5574 sources with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for infrared dark clouds (IRDCs), optical and near-infrared extinction using SDSS and 2MASS data, respectively, association with molecular clouds with known distances, and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.<br />
<br />
The derived physical properties of the PGCC sources are: temperature, column density, physical size, mass, density and luminosity.<br />
PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass and density) covering a large varety of objects, from dense cold cores to large molecular clouds.<br />
<br />
The validation of this catalogue has been performed with a Monte Carlo Quality Assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2' and 0.8' for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1<math>\sigma</math>. This kind of analysis is also very powerful to characterize the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detection has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.<br />
<br />
We computed the cross-correlation between the PGCC catalogue and the other internal ''Planck'' catalogues: PCCS2, PCCS2E, PSZ and PH''z''. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A few sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting a dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), that require further analysis to elucidate.<br />
<br />
The PGCC catalogue contains also 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies which are so close that we can identify individual clumps in them.<br />
<br />
<br />
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<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Compact_Source_catalogues&diff=11261Compact Source catalogues2015-02-04T17:54:50Z<p>Agregori: /* Planck Catalogue of Compact Sources */</p>
<hr />
<div>==Planck Catalogue of Compact Sources==<br />
The Planck Catalogue of Compact Sources is a set of single frequency lists of sources, both Galactic and extragalactic, extracted from the Planck maps. <br />
<br />
The first public version of the PCCS was derived from the nominal mission data acquired by Planck between August 13 2009 and November 26 2010, as described in {{PlanckPapers|planck2013-p05}}. It consisted of nine lists of sources, one per channel between 30 and 857 GHz. The second public version of the catalogue (PCCS2) has been produced using the full mission data obtained between August 13 2009 and August 3 2013, as described in {{PlanckPapers|planck2014-a35||Planck-2015-A35}}, it consists of eighteen lists of sources, two lists per channel.<br />
<br />
The are three main differences between the PCCS and the PCCS2: <br />
<br />
<ol><br />
<li>The amount of data used to build the PCCS (Nominal Mission with 15.5 months) and PCCS2 (Full Mission with 48 months of LFI data and 29 months of HFI data).</li><br />
<li>The inclusion of polarization information between 30 and 353 GHz, the seven Planck channels with polarization capabilities.</li><br />
<li>The division of the PCCS2 into two sets of catalogues, PCCS2 and PCCS2E, depending on our ability to validate their contents.</li><br />
</ol><br />
<br />
Both the 2013 PCCS and the 2014 PCCS2 can be downloaded from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive Planck Legacy Archive].<br />
<br />
=== Detection procedure ===<br />
The Mexican Hat Wavelet 2{{BibCite|nuevo2006}} {{BibCite|lopezcaniego2006}} is the base algorithm used to produce the single channel catalogues of the PCCS and the PCCS2. Although each DPC has is own implementation of this algorithm (IFCAMEX and HFI-MHW), the results are compatible at least at the statistical uncertainty level. Additional algorithms are also implemented, like the multi-frequency Matrix Multi-filters{{BibCite|herranz2009}} (MTXF) and the Bayesian PowellSnakes {{BibCite|carvalho2009}}. Both of them have been used both in PCCS and PCCS2 for the validation of the results obtained by the MHW2 in total intensity. <br />
<br />
In addition, two maximum likelihood methods have been used to do the anlysis in polarization. Both of them can be used to blindly dectect sources in polarization maps. However, the PCCS2 analysis has been performed in a non-blind fashion, looking at the positions of the sources already detected in total intensity and providing an estimation of the polarized flux density. As for total intensity, each DPC has its own implementation of this code (IFCAPOL and PwSPOL). The IFCAPOL algorithm is based on the Filter Fusion technique {{BibCite|argueso2009}} and has been applied to WMAP maps {{BibCite|lopezcaniego2009}}. The PwSPOL algortihm is a modified version of PwS, the code used in the Early Release Compact Source catalogue {{PlanckPapers|planck2011-1-10}}. In practice, both of them are filtering methods based on matched filters, that filter the Q and U maps before attempting to estimate the flux density from each. <br />
<br />
The detection of the compact sources is done locally on small flat patches to improve the efficiency of the process. The reason for this being that the filters can be optimized taking into accont the statistical properties of the background in the vicinity of the sources. In order to perform this local analysis, the full-sky maps are divided into a sufficient number of overlapping flat patches in such a way that 100% of the sky is covered. Each patch is then filtered by the MHW2 with a scale that is optimised to provide the maximum signal-to-noise ratio in the filtered maps. A sub-catalogue of objects is produced for each patch and then, at the end of the process, all the sub-catalogues are merged together, removing repetitions. Similarly, in polarization a flat patch centered at the position of the source detected in total intensity is obtained from the all-sky Q and U maps. Then a matched filter is computed taking into accoun the beam profile at each frequency and the power spectrum of each of the projected flat patches. In both cases, the filters are normalized in such a way that they preserve the amplitude of the sources after filtering, while removing the large scale diffuse emission and the small scale noise fluctuation.<br />
<br />
The primary goal of the ERCSC was reliability greater than 90%. In order to increase completeness and explore possibly interesting new sources at fainter flux density levels, however, the initial overall reliability goal of the PCCS was reduced to 80%. The S/N thresholds applied to each frequency channel were determined, as far as possible, to meet this goal. The reliability of the PCCS catalogues has been assessed using the internal and external validation described below.<br />
<br />
At 30, 44, and 70 GHz, the reliability goal alone would permit S/N thresholds below 4. A secondary goal of minimizing the upward bias on flux densities led to the imposition of an S/N threshold of 4. <br />
<br />
At higher frequencies, where the confusion caused by the Galactic emission starts to become an issue, the sky was divided into two zones, one Galactic (52% of the sky) and one extragalactic (48% of the sky). At 100, 143, and 217 GHz, the S/N threshold needed to achieve the target reliability is determined in the extragalactic zone, but applied uniformly on sky. At 353, 545, and 857 GHz, the need to control confusion from Galactic cirrus emission led to the adoption of different S/N thresholds in the two zones. The extragalactic zone has a lower threshold than the Galactic zone. The S/N thresholds are given in [[Catalogues|Table 1]].<br />
<br />
In the PCCS2 we still have an 80% reliability goal, but a new approach has been followed. There was a demand for the possibility of producing an even higher reliability catalogue from Planck, and a new reliability flag has been added to the catalogues for this purpose.<br />
<br />
In this version of the Planck catalogue of compact sources, we have split the catalogue into two, PCCS2 and PCCS2E, based on our ability to validate each of the sources. For the lower frequencies, between 30 and 70 GHz, we still use a S/N threshold of 4, although some of the unvalidated sources are in the 4-4.5 S/N threshold regime. Moreover, as will be explained below, we use external catalogues and a multifrequency analysis to validate the sources. For the higher frequency channels, at 100 GHz and above, there is very little external information available to validate the catalogues and the validation has instead been done statistically and by applying Galactic masks and cirrus masks.<br />
<br />
=== Photometry ===<br />
In addition of the native flux density estimation provided by the detection algorithm, three additional measurements are obtained for each of the sources in the parent samples.<br />
These additional flux density estimations are based on aperture photometry, PSF fitting and Gaussian fitting (see {{PlanckPapers|planck2013-p05}} for a detailed description of these additional photometries). The native flux density estimation is the only one that is obtained directly from the projected filtered maps while for the others the flux density estimates have a local background subtracted. The flux density estimations have not been colour corrected because that would limit the usability of the catalogue. Colour corrections are available in Section 7.4 of the LFI DPC paper '''REF''' and Section ?.? of the HFI DPC paper '''Ref''', and can be applied by the user.<br />
<br />
=== Validation process ===<br />
The PCCS, its sources and the four different estimates of the flux density, have undergone an extensive internal and external validation process to ensure the quality of the catalogues. The validation of the non-thermal radio sources can be done with a large number of existing catalogues, whereas the validation of thermal sources is mostly done with simulations. These two approaches will be discussed below. Detections identified with known sources have been appropriately flagged in the catalogues.<br />
<br />
==== Internal validation ====<br />
The catalogues have been validated through an internal Monte-Carlo quality assessment process that uses large numbers of source injection and detection loops to characterize their properties, both in total intensity and polarization. For each channel, we calculate statistical quantities describing the quality of detection, photometry and astrometry of the detection code. The detection in total intensity is described by the completeness and reliability of the catalogue: completeness is a function of intrinsic flux, the selection threshold applied to detection (S/N) and location, while reliability is a function only of the detection S/N. The quality of photometry and astrometry is assessed through direct comparison of detected position and flux density parameters with the known inputs of matched sources. An input source is considered to be detected if a detection is made within one beam FWHM of the injected position. In polarization, we have also made Monte-Carlo quality assesments injecting polarized sources into the maps and attempting to detect and characterize their properties. In the three lowest frequencies, the sources have been injected in the real Q and U maps, while at 100 Ghz and above, maps from the Full Focal Plane 8 simulations have been used.<br />
<br />
==== External validation ====<br />
At the three lowest frequencies of Planck, it is possible to validate the PCCS source identifications, completeness, reliability, positional accuracy and flux density accuracy using external data sets, particularly large-area radio surveys (NEWPS, AT20G, CRATES). Moreover, the external validation offers the opportunity for an absolute validation of the different photometries, directly related with the calibration and the knowledge of the beams. We have used several external catalogues to validate the data, but one additional excercise has been done. Simulatenous observations of a sample of 92 sources has been carried out in the Very Large Array, the Australia Compact Array and Planck at 30 and 44 GHz. Special Planck maps have been made covering just the observation period to avoid having more than one observation of the same source in the maps, minimizing the variability effects. As a result of this exercise, we have been able to validate our flux densities at the few percent level. <br />
<br />
At higher frequencies, surveys as the South-Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT) and H-ATLAS or HERMES from Herschel are very important, although only for limited regions of the sky. In particular, the Herschel synergy is crucial to study the possible contamination of the catalogues caused by the Galactic cirrus at high frequencies.<br />
<br />
=== Cautionary notes ===<br />
We list here some cautionary notes for users of the PCCS.<br />
<br />
* Variability: At radio frequencies, many of the extragalactic sources are highly variable. A small fraction of them vary even on time scales of a few hours based on the brightness of the same source as it passes through the different Planck horns {{PlanckPapers|planck2013-p02}}{{PlanckPapers|planck2013-p03}}. Follow-up observations of these sources might show significant differences in flux density compared to the values in the data products. Although the maps used for the PCCS are based on 2.6 sky coverages, the PCCS provides only a single average flux density estimate over all Planck data samples that were included in the maps and does not contain any measure of the variability of the sources from survey to survey.<br />
<br />
* Contamination from CO: At infrared/submillimetre frequencies (100 GHz and above), the Planck bandpasses straddle energetically significant CO lines (see {{PlanckPapers|planck2013-p03a}}). The effect is the most significant at 100 GHz, where the line might contribute more than 50% of the measured flux density of some sources. Follow-up observations of these sources, especially those associated with Galactic star-forming regions, at a similar frequency but different bandpass, should correct for the potential contribution of line emission to the measured continuum flux density of the source.<br />
<br />
* Bandpass corrections: For many sources in the three lowest Planck frequency channels, the bandpass correction of the Q and U flux densities is not negligible. Even though we have attempted to correct for this effect on a source by source basis and have propagated this uncertainty into the error bars on the polarized flux densities and polarization angles, there is still room for improvement. This can be seen in the residual leakage present at the position of Taurus A in the Stokes U maps. It is anticipated that there will be future updates to the LFI PCCS2 catalogues once the bandpass corrections and errors have been improved.<br />
<br />
* Photometry: Each source has multiple estimates of flux density, DETFLUX, APERFLUX, GAUFLUX and PSFFLUX, as defined above. The evaluation of APERFLUX makes the smallest number of assumptions about the data and hence is the most robust, especially in regions of high non-Gaussian background emission, but it may have larger uncertainties than the other methods. For bright resolved sources, GAUFLUX is recommended, with the caveat that it may not be robust for sources close to the Galactic plane due to the strong backgrounds.<br />
<br />
* Colour correction: The flux density estimates have not been colour corrected. Colour corrections are described in {{PlanckPapers|planck2013-p02}} and {{PlanckPapers|planck2013-p03}}.<br />
<br />
* Cirrus/ISM: The upper bands of HFI could be contaminated with sources associated with Galactic interstellar medium features (ISM) or cirrus. The values of the parameters, CIRRUS N and SKY BRIGHTNESS in the catalogues may be used as indicators of contamination. CIRRUS N may be used to flag sources that might be clustered together and thereby associated with ISM structure. In order to provide some indications of the range of values of these parameters which could indicate contamination, we compared the properties of the IRAS-identified and non-IRAS-identified sources for both the PCCS2 and the PCCS2E, since outside the Galactic plane at Galactic latitudes |b| > 20◦, we can use the RIIFSCz {{BibCite|wang2014}} to provide a guide to the likely nature of sources. We cross match the PCCS2 857 GHz catalogue and the PCCS2E 857 GHz catalogue to the IRAS sources in the RIIFSCz using a 3 arcmin matching radius. Of the 4891 sources in the PCCS2 857 GHz catalogue 3094 have plausible IRAS counterparts while 1797 do not. Examination of histograms of the CIRRUS N and SKY BRIGHTNESS parameters in the PCCS2 show that these two classes of objects behave rather differently. The IRAS-identified sources have a peak sky brightness at about 1 MJy.sr−1. The non-IRAS-identified sources have a bimodal distribution with a slight peak at 1 MJy.sr−1 and a second peak at about 2.6 MJy.sr−1 . Both distributions have a long tail, but the non-IRAS-Identified tail is much longer. On this basis sources with SKY BRIGHTNESS > 4 MJy.sr−1 should be treated with caution. In contrast non-IRAS-identified sources with SKY BRIGHTNESS < 1.4 MJy.sr−1 are likely reliable. Examination of their sky distribution, for example, shows that many such sources lie in the IRAS coverage gaps. The CIRRUS N flag tells a rather similar story. Both IRAS-matched and IRAS non-matched sources have a peak CIRRUS N value of 2, but the non-matched sources have a far longer tail. Very few IRAS-matched sources have a value > 8 but many non- matched sources do. These should be treated with caution. The PCCS2E 857 GHz catalogue contains 10470 sources with |b| > 20◦ of which 1235 are matched to IRAS sources in the RIIFSCz and 9235 are not. As with the PCCS2 catalogue the distributions of CIRRUS N and SKY BRIGHTNESS are different, with the differences even more pronounced for these PCCS2E sources. Once again, few IRAS-matched sources have SKY BRIGHTNESS > 4 MJy.sr−1 , but the non-matched sources have brightnesses extending to >55MJy.sr−1. Similarly hardly any of the IRAS-matched sources have CIRRUS N > 8 but nearly half the unmatched sources do. The WHICH ZONE flag in the PCCS2E encodes the region in which the source sits, be it inside the filament mask (WHICH ZONE=1), the Galactic region (WHICH ZONE=2), or both (WHICH ZONE=3). Of the 9235 PCCS2E 857GHz sources that do not match an IRAS source and that lie in the region, |b| > 20◦, 1850 (20%) have WHICH ZONE=1, 2637 (29 %) have WHICH ZONE=2 and 4748 (51 %) have WHICH ZONE=3. The PCCS2E covers 30.36 % of the region |b| > 20◦ , where 2.47 % is in the filament mask, 23.15 % in the Galactic region and 4.74 % in both. If the 9235 unmatched detections were distributed uniformly over the region, |b| > 20◦, we can predict the number of non-matched sources in each zone and compare this to the values we have. We find that there are 2.5 and 3.3 times more sources than expected in zones 1 and 3, showing that the filament mask is indeed a useful criterion for regarding sources detected within it as suspicious. It should be noted that the EXTENDED flag could also be used to identify ISM features, but nearby Galactic and extra-galactic sources that are extended at Planck spatial resolution will also meet this criterion.<br />
<br />
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<br />
==Planck Sunyaev-Zeldovich catalogue==<br />
<br />
The Planck SZ catalogue is a nearly full-sky list of SZ detections obtained from the Planck data. It is fully described in {{PlanckPapers|planck2013-p05a}}. The catalogue is derived from the HFI frequency channel maps after masking and filling the bright point sources (SNR >= 10) from the PCCS catalogues in those channels. Three detection pipelines were used to construct the catalogue, two implementations of the matched multi-filter (MMF) algorithm and PowellSnakes (PwS), a Bayesian algorithm. All three pipelines use a circularly symmetric pressure profile, the non-standard universal profile from {{BibCite|arnaud2010}}, in the detection.<br />
<br />
* MMF1 and MMF3 are full-sky implementations of the MMF algorithm. The matched filter optimizes the cluster detection using a linear combination of maps, which requires an estimate of the statistics of the contamination. It uses spatial filtering to suppress both foregrounds and noise, making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum.<br />
<br />
* PwS differs from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects in a diffuse background. The detection process is based on a statistical model comparison test. Detections may be accepted or rejected based on a generalized likelihood ratio test or in full Bayesian mode. These two modes allow quantities measured by PwS to be consistently compared with those of the MMF algorithms.<br />
<br />
A union catalogue is constructed from the detections by all three pipelines. A mask to remove Galactic dust, nearby galaxies and point sources (leaving 83.7% of the sky) is applied a posteriori to avoid detections in areas where foregrounds are likely to cause spurious detections.<br />
<br />
<br />
== Catalogue of ''Planck'' Galactic Cold Clumps ==<br />
<br />
The catalogue of ''Planck'' Galactic Cold Clumps (PGCC) is a list of 13188 Galactic sources and 54 sources located in the Small and Large Magellanic Clouds, identified as cold sources in Planck data, as described in {{PlanckPapers|planck2014-a37}}. The sources are extracted with the CoCoCoDeT algorithm {{BibCite|Montier2010}}, using Planck-HFI 857, 545, and 353 GHz maps and the 3 THz IRIS map <br />
{{BibCite|Miville2005}}, an upgraded version of the IRAS data at 5 arcmin resolution. This is the first all-sky catalogue of Galactic cold sources obtained with homogeneous methods and data.<br />
<br />
The CoCoCoDeT detection algorithm uses the 3 THz map as a spatial template of a warm background component. Local estimates of the average colour of the background are derived at 30 arcmin resolution around each pixel of the maps at 857, 545, and 353 GHz. Together these describe a local warm component that is subtracted, leaving 857, 545, and 353 GHz maps of the cold residual component map over the full sky. A point source detection algorithm is applied to these three maps. A detection requires S/N > 4 in pixels in all Planck bands and a minimum angular distance of 5 arcmin to other detections.<br />
<br />
A 2D Gaussian fit provides an estimate of the position angle and FWHM size along the major and minor axes. The ellipse defined by the FWHM values is used in aperture photometry to derive the flux density estimates in all four bands. Based on the quality of the flux density estimates in all four bands, PGCC sources are divided into three categories of FLUX_QUALITY:<br />
* FLUX_QUALITY=1 : sources with flux density estimates at S/N > 1 in all bands ;<br />
* FLUX_QUALITY=2 : sources with flux density estimates at S/N > 1 only in 857, 545, and 353 GHz Planck bands, considered as very cold source candidates ;<br />
* FLUX_QUALITY=3 : sources without any reliable flux density estimates, listed as poor candidates.<br />
We also raise a flag on the blending between sources which can be used to quantify the reliability of the aperture photometry processing.<br />
<br />
To estimate possible contamination by extragalactic sources we (1) cross-correlated the positions with catalogues of extragalactic sources, (2) rejected detections with SED [in colour-colour plots] consistent with radio sources, and (3) rejected detections with clear association to extragalactic sources visible in DSS images. Compared to the original number of sources, these only resulted in a small number of rejections.<br />
<br />
Distance estimates, combining seven different methods, have been obtained for 5574 sources with estimates ranging from hundreds of pc in local molecular clouds up to 10.5 kpc along the Galactic plane. The methods include cross-correlation with kinematic distances previously listed for infrared dark clouds (IRDCs), optical and near-infrared extinction using SDSS and 2MASS data, respectively, association with molecular clouds with known distances, and finally referencing parallel work done on a small sample of sources followed up with Herschel. Most PGCC sources appear to be located in the solar neighbourhood.<br />
<br />
The derived physical properties of the PGCC sources are: temperature, column density, physical size, mass, density and luminosity.<br />
PGCC sources exhibit an average temperature of about 14K, and ranging from 5.8 to 20K. They span a large range of physical properties (such as column density, mass and density) covering a large varety of objects, from dense cold cores to large molecular clouds.<br />
<br />
The validation of this catalogue has been performed with a Monte Carlo Quality Assessment analysis wich allowed us to quantify the statistical reliability of the flux densities and of the source position and geometry estimates. The position accuracy is better than 0.2' and 0.8' for 68% and 95% of the sources, respectively, while the ellipticity of the sources is recovered with an accuracy better than 10% at 1<math>\sigma</math>. This kind of analysis is also very powerful to characterize the selection function of the CoCoCoDeT algorithm applied to Planck data. The completeness of the detection has been studied as a function of the temperature of the injected sources. It has been shown that sources with FLUX_QUALITY=2 are effectively sources with low temperatures and have a high completeness level for temperatures below 10K.<br />
<br />
We computed the cross-correlation between the PGCC catalogue and the other internal ''Planck'' catalogues: PCCS2, PCCS2E, PSZ and PH''z''. The PGCC catalogue contains about 45% new sources, not simultaneously detected in the 857, 545, and 353 GHz bands of the PCCS2 and PCCS2E. A few sources (65) are also detected in the PSZ2 and PGCC catalogues, suggesting a dusty nature of these candidates. Finally there are only 15 sources in common between the PGCC and PHz (which is focused on extragalactic sources at high redshift), that require further analysis to elucidate.<br />
<br />
The PGCC catalogue contains also 54 sources located in the Small and Large Magellanic Clouds (SMC and LMC), two nearby galaxies which are so close that we can identify individual clumps in them.<br />
<br />
<br />
<!--- ---------------------------------------><br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|002]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Detector_pointing&diff=11256Detector pointing2015-02-04T17:35:47Z<p>Agregori: /* A model for Planck LFI Pointing */</p>
<hr />
<div>== Introduction and Summary ==<br />
<br />
The overall geometry of the Planck focal plane is shown here:<br />
<br />
[[Image:FocalPlane.png| thumb|500px|center| The Planck Focal Plane]]<br />
<br />
In order to take full advantage of the Planck beams, we must know the individual detector pointing positions to a precision of better than several arcseconds, over the course of the entire mission. <br />
<br />
Spacecraft pointing comes from the on-board star tracker sampled at 8 Hz between repointings (Attitude History File, AHF). This is translated via a series of three-dimensional rotations to a pointing for the centre of the focal plane and resampled to the HFI or LFI TOI data rate for convenience after correcting for the wobble angle (see below). We must then further rotate this focal-plane boresight pointing to the individual detector locations. Because neither the rotations from the star tracker to the boresight nor those from the boresight to the individual detectors are known exactly a priori, we must calibrate them using flight data.<br />
<br />
Specifically, measurements of HFI and LFI detector pointing are based largely on observations of the brighter planets, with information from the much more frequent observations of lower-flux Galactic and extragalactic high-frequency sources used to monitor and build a model of overall pointing drift. This long-term drift of the spacecraft attitude is due to changes in the moment of inertia of the spacecraft, and also includes specific events which may induce sudden changes, essentially random as far as our ability to predict their effects is concerned. In this delivery HFI used a model (described below) to follow the pointing drift continuously, while LFI uses two different focal plane descriptions for the two time periods separated by operations perfomed on the instrument that modified the thermal behaviour. The two approach are consistent to better than a few arcsec. <br />
<br />
Note that for HFI the resulting pointing model cannot easily be directly compared to a physical/optical model: in particular, it includes a phase shift in the scan direction from the convolution and deconvolution of the detector transfer function, which is complex in the Fourier domain (see {{PlanckPapers|planck2013-p03c}}). This phase shift was not measured during normal operations, but a short campaign during which the spacecraft was spun at a higher rate will be used to determine these offsets in future date releases. Comparison with the initial optical model indicates that the in-scan change due to this phase shift is of the order of 1 arcminute. Note also that aberration is corrected in all observations.<br />
<br />
The final pointing model is measured to be better than 2 arcsecond rms in the co-scan and cross-scan directions averaged over ten-day periods, as shown below. Note that there are larger hourly drifts of up to 10 arcseconds due to interference from the radiometer electronics box assembly (REBA) as discussed more fully in {{PlanckPapers|planck2013-p03}}.<br />
<br />
==Wobble Angle ==<br />
<br />
The wobble angle is the angle between the Principal Axis Reference Frame and the Body Reference Frame of Planck, both of which have their origin in the Planck Baricenter (ACMS, AHF-ICD). It is normally decomposed into its three components <math> \psi_1, \psi_2, \psi_3 </math>.<br />
<br />
Pointings are determined by a set of rotations converting coordinates in the STR (Star Tracker) reference frame to ECL (Ecliptic) reference frame, i.e. defining the rotation matrix <math> R_{ecl,str} </math>. The matrix can be decomposend in a sequence of matrix mutiplications:<br />
<br />
:<math> R_{ecl,str} = R_{ecl,A} R_{A,B} R_{B,str} </math><br />
<br />
here we used <math> R_{rfb,rfa} </math> to denote transformation from Rerference Frame RFA to Reference Frame RFB, and <math> R_{rfa,rfb} = R_{rfb,rfa}^{-1} </math>. <br />
<br />
The <math> R_{B,str} </math> converts from STR coordinates to Body Reference Frame coordinates, it is a constant matrix.<br />
<br />
:<math> \begin{bmatrix} \cos \beta & 0 & -\sin \beta \\ 0 & 1 & 0 \\ \sin \beta & 0 & \cos \beta \end{bmatrix} </math><br />
<br />
where <math> \beta = 85 \deg </math> is the STR boresight angle assumed to be constant and aligned with the telescope LOS, but this is not the case. The STR is located on the SVM, at about 1.5 m from the origin of the Body reference frame, a change in its position of 0.15 mm will result in a change of its orientation of about <math> 10^{-4} </math> radiants about 20 arcsec.<br />
<br />
There is no way to measure directly those changes. So the effect is that to have an apparent change in the <math> \psi_1 </math>, <math> \psi_2 </math> (tilt angles as defined in the AHF) and <math> \psi_3 </math> (azimuth angle as defined in the AHF) angles: the reason is apparent immediately when looking at the way a perturbation in STR reference frame orientation propagates.<br />
<br />
AHF provides wobble angle measures at 1 minute (<math> \psi_1 </math>, <math> \psi_2 </math>) and one OD (<math> \psi_3 </math>) rate. Indeed <math> \psi_3 </math> is provided at each pointing period but measures within each given OD are constant.<br />
<br />
Assuming to have quaternions represented by rotation matrix <math> R_{ecl,B}(t) </math> at a time <math> t </math>, and assuming to have representative values of true wobble angles <math> \psi_{1,0} </math>, <math> \psi_{2,0} </math>, <math> \psi_{3,0} </math> and a way to estimate the apparent <math> \delta\psi_1(t) </math>, <math> \delta\psi_2(t) </math>, <math> \delta\psi_3(t) </math> it is possible to remove the apparent effect.<br />
<br />
With the available information it can be done for <math> \psi_1 </math> and <math> \psi_2 </math>. <br />
<br />
The correction algorithm initializes two rotation matrices as references using <math> \psi_1 </math> and <math> \psi_2 </math> from the first pointing period of the nominal mission:<br />
<br />
:<math> R_{psi1} = \begin{bmatrix} \cos \psi_{1,ref} & \sin \psi_{1,ref} & 0 \\ -\sin \psi_{1,ref} & \cos \psi_{1,ref} & 0 \\ 0 & 0 & 1 \end{bmatrix} </math><br />
<br />
:<math> R_{psi2} = \begin{bmatrix} \cos \psi_{2,ref} & 0 & -\sin \psi_{2,ref} \\ 0 & 1 & 0 \\ \sin \psi_{2,ref} & 0 & \cos \psi_{2,ref} \end{bmatrix} </math><br />
<br />
Then, for each pointing period, builds two correction matrices using <math> \psi_1 </math> and <math> \psi_2 </math> as provided by the AHF in the Observation section:<br />
<br />
:<math> R_{psi1}^T = \begin{bmatrix} \cos \psi_{1} & -\sin \psi_{1} & 0 \\ \sin \psi_{1} & \cos \psi_{1} & 0 \\ 0 & 0 & 1 \end{bmatrix} </math><br />
<br />
:<math> R_{psi2}^T = \begin{bmatrix} \cos \psi_{2} & 0 & \sin \psi_{2} \\ 0 & 1 & 0 \\ -\sin \psi_{2} & 0 & \cos \psi_{2} \end{bmatrix} </math><br />
<br />
From these matrices the correction matrix is build:<br />
<br />
:<math> R = R_{psi1}^T R_{psi2}^T R_{psi2} R_{psi1} </math><br />
<br />
Each quaternion of the AHF is finally corrected using <math> R </math>.<br />
<br />
==Stellar Aberration==<br />
<br />
The corrected quaternions are interpolated using Spherical Linear Interpolation algorithm and transformed in cartesian vector, which we call <math> DPT </math>. For each sample the stellar aberration correction is applied:<br />
<br />
:<math> DPT = DPT - {v_{sat} \over c } </math><br />
<br />
where <math> v_{sat} </math> is the satellite velocity and <math> c </math> is the speed of light. After this operation the vector is normalized.<br />
<br />
Finally the cartesian vetor is converted in Ecliptic Coordinates, the detector pointing.<br />
<br />
==Beam Rotation==<br />
<br />
The rotation of the beam with respect to North is the <math> \psi </math> angle and is computed rotating the corrected quaternions <math> Q </math> using:<br />
<br />
:<math> R = R_{\theta} R_{\phi} Q ax2det </math><br />
<br />
The resulting rotation matrix represents the rotation of the beam, the <math> \psi </math> angle is then:<br />
<br />
:<math> \psi = -\arctan (R[0][1],R[0][0]) </math><br />
<br />
== Initial measurements: Mars 1 and other planets ==<br />
<br />
The first observation of Mars, which occured around 180 days from launch, is the baseline against which other objects are compared. Here, we show the relative pointing of Mars 1 to the pre-launch RFFM.<br />
<br />
[[Image:Mars1.png|thumb|500px|center| Individual detector pointing measured from the first Mars crossing, relative to the pre-launch RFFM model.]]<br />
<br />
== Focal plane drift: map-based measurement of detector positions ==<br />
<br />
Prior to modeling of systematic changes in the Planck pointing, we find secular drifts of order one arcminute over the course of the nominal mission. We monitor this by making point-source catalogs based on single Planck surveys, only counting those objects which are observed over the course of less than seven days (this limits us to observations away from the ecliptic poles where Planck's observing strategy is highly cross-linked). We cross-match these catalog positions to the known IRAS point-source catalog {{BibCite|Lingyu2009}} and average the deviations in ten-day blocks (the individual measurements are shown as lighter points; error bars assume equal weighting for all points, but the results are not sensitive to any imposed S/N cutoff):<br />
<br />
[[Image:mapbased1.png | thumb|500px|center | Planck pointing before correction, measured by comparing point sources seen at 857 GHz to known IRAS positions. Light-colored points show individual source deviations, points with error bars give ten-day errors. Different colors correspond to the four individual Planck sky surveys. ]]<br />
<br />
An analysis performed directly in the timestream gives similar results, below (evaluated until the end of HFI operations in January 2012).<br />
<br />
[[Image:Pointing_offset_100--217GHz_CPP_better_coords.png | thumb|500px|center | The points give positions of individual objects (planets and bright radio sources) and the green dotted line labeled "PTCOR6" gives the corrected mean pointing, discussed below. (In this plot, "OD" refers to the number of days since launch.)]]<br />
<br />
== A model for Planck HFI Pointing ==<br />
<br />
These analyses allow us to build a model for the pointing drift. The following describes the procedures used for the HFI detectors.<br />
<br />
The correction is based on the measurement of pointing offset directly from the timeline, on a small sample of known and bright radio sources and planets. First the beam shape of each detector is measured by stacking individual timeline observation of bright planets. This process is of course contaminated by pointing error, but this is reduced by allowing each pass on the planet to be slightly displaced in order to correct for the observed location of the planet. This process yields a very clean estimate of the beam of each detector.<br />
<br />
Those beams are then used to determine the offset of the observed location of the planets (Mars, Saturn, and Jupiter) and of a few (~10) bright radio sources. These offsets are estimated using detectors at all frequencies for the planets, and only at 100GHz, 143GHz and 217GHz for the radio sources. <br />
<br />
From the planet observations, one can recover the alignment of each detector in the focal plane, as well as a first pointing correction measured at the times of individual planet crossings. This pointing correction is obtained by fitting splines on the planet observation from each detector. We further allow this correction to have a sharp jump between the second and third survey (the time of the [[LFI_design,_qualification,_and_performance#The_Sorption_Cooler|SCS switchover on OD 455]]).<br />
<br />
This first pointing correction is further refined (at the lower HFI frequencies only) using the point sources observations in order to fill the period between planet observations. The radio source offsets require further treatment than the planet based offsets. First, the brightness of the sources being much smaller than planets, the offset on individual detector observation are very noisy, and we filter out the noise by building median offsets for each point source observation. Second, since the sources can be slightly extended we still observe systematic offset above and below the planet based pointing correction in a regular alternating pattern. This is due to the fact that we are observing those extended objects scanning in alternating directions, and our fit of those extended sources to our beam translate into this systematic alternating pattern. We thus allow for a small, arcsec correction of those offsets: i.e., each object is allowed a single offset displacement of order arc seconds in order to minimize the offset between different observations of the same object at different time. <br />
<br />
The resulting list of point source offsets is then merged with the planet offsets. Again a spline based correction is built fitting all of this data, and allowing rupture of continuity at the time of the SCS switchover and other major onboard event (typically between each surveys).<br />
<br />
Once we assume the full Planck pointing model and re-measure the position of Mars for this observation, we see sub-arcsecond deviations (as expected); this gives an indication of the purely numerical limitations of the method. Further planet observations show the small remaining uncorrected drift present in the pointing model (note that cross-scan positions are measured with considerably less data than in-scan positions due to the scan strategy):<br />
<br />
[[Image:S1vM1_v53.png | thumb|500px|center| Saturn 1 vs Mars 1 ]] [[Image:S2vM1_v53.png| thumb|500px|center| Saturn 2 vs Mars 1]]<br />
<br />
Redoing the single-survey map- and catalog-based computation with the corrected pointing shows that Planck has achieved the arcsecond-scale rms uncertainty of pointing:<br />
<br />
[[Image:mapbased_ptcor6.png | thumb|500px|center| As above, after correction by the "ptcor6" model. This plot shows both 545 GHz and 857 GHz sources.]]<br />
<br />
== A model for Planck LFI Pointing ==<br />
The profiles and locations of the beams are determined from the four observations of Jupiter listed in Table 1. Details are given in {{PlanckPapers|planck2013-p02d}}.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Table 1: Approximate dates of the Jupiter observations. The periods include the scan by the entire LFI field of view'''<br />
| Jupiter transit || Date || OD <br />
|- <br />
| Scan 1(J1) || 21/10/09 - 05/11/09 || 161-176 <br />
|- <br />
| Scan 2(J2) || 27/06/10 - 12/07/10 || 410-425 <br />
|-<br />
| Scan 3(J3) || 03/12/10 - 18/12/10 || 569-584 <br />
|-<br />
| Scan 4(J4) || 30/07/11 - 08/08/11 || 808-817 <br />
|-<br />
|}<br />
<br />
The origin of the focal plane is the optical line of sight defined in {{PlanckPapers|tauber2010b}}. In the LFI RIMO, the beam centres are given by four numbers, <math>\theta_{\mathrm uv}</math>, <math>\phi_{\mathrm uv}</math>, <math>\psi_{\mathrm uv}</math>, and <math>\psi_{\mathrm pol}</math>. Only <math>\theta_{\mathrm uv}</math> and <math>\phi_{\mathrm uv}</math>, which are the beam pointing in spherical coordinates referred to the line of sight, can be determined with Jupiter observations. The polarization orientation of the beams, defined by <math>\psi_{\mathrm uv} + \psi_{\mathrm pol}</math>, is not estimated from flight data but is derived from main beam simulations based on ground measurements.<br />
<br />
For each beam, the pointing is determined by the location of the maximum of an<br />
elliptical Gaussian fit to that beam. This was done for each beam in each<br />
single scan. Results are reported, with errors, in {{PlanckPapers|planck2013-p02d}}. In addition, the beams are stacked in pairs (J1+J2 and J3+J4) and all together (J1J2J3J4) in order to improve the signal-to-noise ratio of the measurements. Before the stacking, each beam is artificially repointed along the direction given by the arithmetic average of the centre of each beam to be stacked. Then a fit is performed again on the stacked beams and the resulting parameters recorded. For single scans it has been found that there is an agreement within 2 arcsec in the pointing direction between J1 and J2. The same agreement occurs between J3 and J4. In contrast, a 15 arcsec systematic deviation of the beam centre was detected when comparing J1+J2 to J3+J4. The figure below shows the reconstructed beam positions and<br />
errors in the line-of-sight frame magnified by a factor of 100. The shift is evident for the 70 GHz beams, as well as in all<br />
the J1+J2 and J3+J4 stacked beam centres. The change in the pointing has been found mainly in the scan direction (i.e., <math>v</math>-coordinate). To account for this pointing shift, we apply two pointing solutions for LFI. The first focal plane calibration is valid from OD91 to OD540 and is based on the J1+J2 beam pointing determination. The second calibration is valid from OD541 to OD563 and is based on the J3+J4 beam<br />
pointing calibration. <br />
<br />
[[Image:uv-M_cropped.jpg | thumb|500px|center| Main beam pointing directions measured with the first<br />
four Jupiter crossings. Single scans are yellow, light red, green, and<br />
light blue. First and second stacked scans are red, third and<br />
fourth stacked scans are blue, and four stacked scans are grey. The colored boxes refer to the measured uncertainties<br />
magnified by a factor of 100. The differences in pointing were<br />
normalized to the J1 measurements, and were magnified by the same factor of 100 ]]<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|001]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Detector_pointing&diff=11255Detector pointing2015-02-04T17:33:25Z<p>Agregori: /* Introduction and Summary */</p>
<hr />
<div>== Introduction and Summary ==<br />
<br />
The overall geometry of the Planck focal plane is shown here:<br />
<br />
[[Image:FocalPlane.png| thumb|500px|center| The Planck Focal Plane]]<br />
<br />
In order to take full advantage of the Planck beams, we must know the individual detector pointing positions to a precision of better than several arcseconds, over the course of the entire mission. <br />
<br />
Spacecraft pointing comes from the on-board star tracker sampled at 8 Hz between repointings (Attitude History File, AHF). This is translated via a series of three-dimensional rotations to a pointing for the centre of the focal plane and resampled to the HFI or LFI TOI data rate for convenience after correcting for the wobble angle (see below). We must then further rotate this focal-plane boresight pointing to the individual detector locations. Because neither the rotations from the star tracker to the boresight nor those from the boresight to the individual detectors are known exactly a priori, we must calibrate them using flight data.<br />
<br />
Specifically, measurements of HFI and LFI detector pointing are based largely on observations of the brighter planets, with information from the much more frequent observations of lower-flux Galactic and extragalactic high-frequency sources used to monitor and build a model of overall pointing drift. This long-term drift of the spacecraft attitude is due to changes in the moment of inertia of the spacecraft, and also includes specific events which may induce sudden changes, essentially random as far as our ability to predict their effects is concerned. In this delivery HFI used a model (described below) to follow the pointing drift continuously, while LFI uses two different focal plane descriptions for the two time periods separated by operations perfomed on the instrument that modified the thermal behaviour. The two approach are consistent to better than a few arcsec. <br />
<br />
Note that for HFI the resulting pointing model cannot easily be directly compared to a physical/optical model: in particular, it includes a phase shift in the scan direction from the convolution and deconvolution of the detector transfer function, which is complex in the Fourier domain (see {{PlanckPapers|planck2013-p03c}}). This phase shift was not measured during normal operations, but a short campaign during which the spacecraft was spun at a higher rate will be used to determine these offsets in future date releases. Comparison with the initial optical model indicates that the in-scan change due to this phase shift is of the order of 1 arcminute. Note also that aberration is corrected in all observations.<br />
<br />
The final pointing model is measured to be better than 2 arcsecond rms in the co-scan and cross-scan directions averaged over ten-day periods, as shown below. Note that there are larger hourly drifts of up to 10 arcseconds due to interference from the radiometer electronics box assembly (REBA) as discussed more fully in {{PlanckPapers|planck2013-p03}}.<br />
<br />
==Wobble Angle ==<br />
<br />
The wobble angle is the angle between the Principal Axis Reference Frame and the Body Reference Frame of Planck, both of which have their origin in the Planck Baricenter (ACMS, AHF-ICD). It is normally decomposed into its three components <math> \psi_1, \psi_2, \psi_3 </math>.<br />
<br />
Pointings are determined by a set of rotations converting coordinates in the STR (Star Tracker) reference frame to ECL (Ecliptic) reference frame, i.e. defining the rotation matrix <math> R_{ecl,str} </math>. The matrix can be decomposend in a sequence of matrix mutiplications:<br />
<br />
:<math> R_{ecl,str} = R_{ecl,A} R_{A,B} R_{B,str} </math><br />
<br />
here we used <math> R_{rfb,rfa} </math> to denote transformation from Rerference Frame RFA to Reference Frame RFB, and <math> R_{rfa,rfb} = R_{rfb,rfa}^{-1} </math>. <br />
<br />
The <math> R_{B,str} </math> converts from STR coordinates to Body Reference Frame coordinates, it is a constant matrix.<br />
<br />
:<math> \begin{bmatrix} \cos \beta & 0 & -\sin \beta \\ 0 & 1 & 0 \\ \sin \beta & 0 & \cos \beta \end{bmatrix} </math><br />
<br />
where <math> \beta = 85 \deg </math> is the STR boresight angle assumed to be constant and aligned with the telescope LOS, but this is not the case. The STR is located on the SVM, at about 1.5 m from the origin of the Body reference frame, a change in its position of 0.15 mm will result in a change of its orientation of about <math> 10^{-4} </math> radiants about 20 arcsec.<br />
<br />
There is no way to measure directly those changes. So the effect is that to have an apparent change in the <math> \psi_1 </math>, <math> \psi_2 </math> (tilt angles as defined in the AHF) and <math> \psi_3 </math> (azimuth angle as defined in the AHF) angles: the reason is apparent immediately when looking at the way a perturbation in STR reference frame orientation propagates.<br />
<br />
AHF provides wobble angle measures at 1 minute (<math> \psi_1 </math>, <math> \psi_2 </math>) and one OD (<math> \psi_3 </math>) rate. Indeed <math> \psi_3 </math> is provided at each pointing period but measures within each given OD are constant.<br />
<br />
Assuming to have quaternions represented by rotation matrix <math> R_{ecl,B}(t) </math> at a time <math> t </math>, and assuming to have representative values of true wobble angles <math> \psi_{1,0} </math>, <math> \psi_{2,0} </math>, <math> \psi_{3,0} </math> and a way to estimate the apparent <math> \delta\psi_1(t) </math>, <math> \delta\psi_2(t) </math>, <math> \delta\psi_3(t) </math> it is possible to remove the apparent effect.<br />
<br />
With the available information it can be done for <math> \psi_1 </math> and <math> \psi_2 </math>. <br />
<br />
The correction algorithm initializes two rotation matrices as references using <math> \psi_1 </math> and <math> \psi_2 </math> from the first pointing period of the nominal mission:<br />
<br />
:<math> R_{psi1} = \begin{bmatrix} \cos \psi_{1,ref} & \sin \psi_{1,ref} & 0 \\ -\sin \psi_{1,ref} & \cos \psi_{1,ref} & 0 \\ 0 & 0 & 1 \end{bmatrix} </math><br />
<br />
:<math> R_{psi2} = \begin{bmatrix} \cos \psi_{2,ref} & 0 & -\sin \psi_{2,ref} \\ 0 & 1 & 0 \\ \sin \psi_{2,ref} & 0 & \cos \psi_{2,ref} \end{bmatrix} </math><br />
<br />
Then, for each pointing period, builds two correction matrices using <math> \psi_1 </math> and <math> \psi_2 </math> as provided by the AHF in the Observation section:<br />
<br />
:<math> R_{psi1}^T = \begin{bmatrix} \cos \psi_{1} & -\sin \psi_{1} & 0 \\ \sin \psi_{1} & \cos \psi_{1} & 0 \\ 0 & 0 & 1 \end{bmatrix} </math><br />
<br />
:<math> R_{psi2}^T = \begin{bmatrix} \cos \psi_{2} & 0 & \sin \psi_{2} \\ 0 & 1 & 0 \\ -\sin \psi_{2} & 0 & \cos \psi_{2} \end{bmatrix} </math><br />
<br />
From these matrices the correction matrix is build:<br />
<br />
:<math> R = R_{psi1}^T R_{psi2}^T R_{psi2} R_{psi1} </math><br />
<br />
Each quaternion of the AHF is finally corrected using <math> R </math>.<br />
<br />
==Stellar Aberration==<br />
<br />
The corrected quaternions are interpolated using Spherical Linear Interpolation algorithm and transformed in cartesian vector, which we call <math> DPT </math>. For each sample the stellar aberration correction is applied:<br />
<br />
:<math> DPT = DPT - {v_{sat} \over c } </math><br />
<br />
where <math> v_{sat} </math> is the satellite velocity and <math> c </math> is the speed of light. After this operation the vector is normalized.<br />
<br />
Finally the cartesian vetor is converted in Ecliptic Coordinates, the detector pointing.<br />
<br />
==Beam Rotation==<br />
<br />
The rotation of the beam with respect to North is the <math> \psi </math> angle and is computed rotating the corrected quaternions <math> Q </math> using:<br />
<br />
:<math> R = R_{\theta} R_{\phi} Q ax2det </math><br />
<br />
The resulting rotation matrix represents the rotation of the beam, the <math> \psi </math> angle is then:<br />
<br />
:<math> \psi = -\arctan (R[0][1],R[0][0]) </math><br />
<br />
== Initial measurements: Mars 1 and other planets ==<br />
<br />
The first observation of Mars, which occured around 180 days from launch, is the baseline against which other objects are compared. Here, we show the relative pointing of Mars 1 to the pre-launch RFFM.<br />
<br />
[[Image:Mars1.png|thumb|500px|center| Individual detector pointing measured from the first Mars crossing, relative to the pre-launch RFFM model.]]<br />
<br />
== Focal plane drift: map-based measurement of detector positions ==<br />
<br />
Prior to modeling of systematic changes in the Planck pointing, we find secular drifts of order one arcminute over the course of the nominal mission. We monitor this by making point-source catalogs based on single Planck surveys, only counting those objects which are observed over the course of less than seven days (this limits us to observations away from the ecliptic poles where Planck's observing strategy is highly cross-linked). We cross-match these catalog positions to the known IRAS point-source catalog {{BibCite|Lingyu2009}} and average the deviations in ten-day blocks (the individual measurements are shown as lighter points; error bars assume equal weighting for all points, but the results are not sensitive to any imposed S/N cutoff):<br />
<br />
[[Image:mapbased1.png | thumb|500px|center | Planck pointing before correction, measured by comparing point sources seen at 857 GHz to known IRAS positions. Light-colored points show individual source deviations, points with error bars give ten-day errors. Different colors correspond to the four individual Planck sky surveys. ]]<br />
<br />
An analysis performed directly in the timestream gives similar results, below (evaluated until the end of HFI operations in January 2012).<br />
<br />
[[Image:Pointing_offset_100--217GHz_CPP_better_coords.png | thumb|500px|center | The points give positions of individual objects (planets and bright radio sources) and the green dotted line labeled "PTCOR6" gives the corrected mean pointing, discussed below. (In this plot, "OD" refers to the number of days since launch.)]]<br />
<br />
== A model for Planck HFI Pointing ==<br />
<br />
These analyses allow us to build a model for the pointing drift. The following describes the procedures used for the HFI detectors.<br />
<br />
The correction is based on the measurement of pointing offset directly from the timeline, on a small sample of known and bright radio sources and planets. First the beam shape of each detector is measured by stacking individual timeline observation of bright planets. This process is of course contaminated by pointing error, but this is reduced by allowing each pass on the planet to be slightly displaced in order to correct for the observed location of the planet. This process yields a very clean estimate of the beam of each detector.<br />
<br />
Those beams are then used to determine the offset of the observed location of the planets (Mars, Saturn, and Jupiter) and of a few (~10) bright radio sources. These offsets are estimated using detectors at all frequencies for the planets, and only at 100GHz, 143GHz and 217GHz for the radio sources. <br />
<br />
From the planet observations, one can recover the alignment of each detector in the focal plane, as well as a first pointing correction measured at the times of individual planet crossings. This pointing correction is obtained by fitting splines on the planet observation from each detector. We further allow this correction to have a sharp jump between the second and third survey (the time of the [[LFI_design,_qualification,_and_performance#The_Sorption_Cooler|SCS switchover on OD 455]]).<br />
<br />
This first pointing correction is further refined (at the lower HFI frequencies only) using the point sources observations in order to fill the period between planet observations. The radio source offsets require further treatment than the planet based offsets. First, the brightness of the sources being much smaller than planets, the offset on individual detector observation are very noisy, and we filter out the noise by building median offsets for each point source observation. Second, since the sources can be slightly extended we still observe systematic offset above and below the planet based pointing correction in a regular alternating pattern. This is due to the fact that we are observing those extended objects scanning in alternating directions, and our fit of those extended sources to our beam translate into this systematic alternating pattern. We thus allow for a small, arcsec correction of those offsets: i.e., each object is allowed a single offset displacement of order arc seconds in order to minimize the offset between different observations of the same object at different time. <br />
<br />
The resulting list of point source offsets is then merged with the planet offsets. Again a spline based correction is built fitting all of this data, and allowing rupture of continuity at the time of the SCS switchover and other major onboard event (typically between each surveys).<br />
<br />
Once we assume the full Planck pointing model and re-measure the position of Mars for this observation, we see sub-arcsecond deviations (as expected); this gives an indication of the purely numerical limitations of the method. Further planet observations show the small remaining uncorrected drift present in the pointing model (note that cross-scan positions are measured with considerably less data than in-scan positions due to the scan strategy):<br />
<br />
[[Image:S1vM1_v53.png | thumb|500px|center| Saturn 1 vs Mars 1 ]] [[Image:S2vM1_v53.png| thumb|500px|center| Saturn 2 vs Mars 1]]<br />
<br />
Redoing the single-survey map- and catalog-based computation with the corrected pointing shows that Planck has achieved the arcsecond-scale rms uncertainty of pointing:<br />
<br />
[[Image:mapbased_ptcor6.png | thumb|500px|center| As above, after correction by the "ptcor6" model. This plot shows both 545 GHz and 857 GHz sources.]]<br />
<br />
== A model for Planck LFI Pointing ==<br />
The profiles and locations of the beams are determined from the four observations of Jupiter listed in Table 1. Details are given in {{PlanckPapers|planck2013-p02d}}.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Table 1: Approximate dates of the Jupiter observations. The periods include the scan by the entire LFI field of view'''<br />
| Jupiter transit || Date || OD <br />
|- <br />
| Scan 1(J1) || 21/10/09 - 05/11/09 || 161-176 <br />
|- <br />
| Scan 2(J2) || 27/06/10 - 12/07/10 || 410-425 <br />
|-<br />
| Scan 3(J3) || 03/12/10 - 18/12/10 || 569-584 <br />
|-<br />
| Scan 4(J4) || 30/07/11 - 08/08/11 || 808-817 <br />
|-<br />
|}<br />
<br />
The origin of the focal plane is the optical line of sight defined in {{PlanckPapers|tauber2010b}}. In the LFI RIMO, the beam centres are given by four numbers, $\theta_{\mathrm uv}$, $\phi_{\mathrm uv}$, $\psi_{\mathrm uv}$, and $\psi_{\mathrm pol}$. Only $\theta_{\mathrm uv}$ and $\phi_{\mathrm uv}$, which are the beam pointing in spherical coordinates referred to the line of sight, can be determined with Jupiter observations. The polarization orientation of the beams, defined by $\psi_{\mathrm uv} + \psi_{\mathrm pol}$, is not estimated from flight data but is derived from main beam simulations based on ground measurements.<br />
<br />
For each beam, the pointing is determined by the location of the maximum of an<br />
elliptical Gaussian fit to that beam. This was done for each beam in each<br />
single scan. Results are reported, with errors, in {{PlanckPapers|planck2013-p02d}}. In addition, the beams are stacked in pairs (J1+J2 and J3+J4) and all together (J1J2J3J4) in order to improve the signal-to-noise ratio of the measurements. Before the stacking, each beam is artificially repointed along the direction given by the arithmetic average of the centre of each beam to be stacked. Then a fit is performed again on the stacked beams and the resulting parameters recorded. For single scans it has been found that there is an agreement within 2 arcsec in the pointing direction between J1 and J2. The same agreement occurs between J3 and J4. In contrast, a 15 arcsec systematic deviation of the beam centre was detected when comparing J1+J2 to J3+J4. The figure below shows the reconstructed beam positions and<br />
errors in the line-of-sight frame magnified by a factor of 100. The shift is evident for the 70 GHz beams, as well as in all<br />
the J1+J2 and J3+J4 stacked beam centres. The change in the pointing has been found mainly in the scan direction (i.e., $v$-coordinate). To account for this pointing shift, we apply two pointing solutions for LFI. The first focal plane calibration is valid from OD91 to OD540 and is based on the J1+J2 beam pointing determination. The second calibration is valid from OD541 to OD563 and is based on the J3+J4 beam<br />
pointing calibration. <br />
<br />
[[Image:uv-M_cropped.jpg | thumb|500px|center| Main beam pointing directions measured with the first<br />
four Jupiter crossings. Single scans are yellow, light red, green, and<br />
light blue. First and second stacked scans are red, third and<br />
fourth stacked scans are blue, and four stacked scans are grey. The colored boxes refer to the measured uncertainties<br />
magnified by a factor of 100. The differences in pointing were<br />
normalized to the J1 measurements, and were magnified by the same factor of 100 ]]<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:HFI/LFI joint data processing|001]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=L3_LFI&diff=11236L3 LFI2015-02-04T17:06:54Z<p>Agregori: </p>
<hr />
<div>{{DISPLAYTITLE:Power spectra}}<br />
== Power Spectra ==<br />
<br />
The TT, TE, and EE power spectra are described in [[CMB_spectrum_%26_Likelihood_Code | CMB spectrum]] section of the Products chapter.<br />
<br />
<!--<br />
LFI temperature power spectra are computed from frequency maps using cROMAster, an implementation of the pseudo-<math> C_\ell</math> method described in{{BibCite|master}}, extended to derive both auto- and cross-power spectra{{BibCite|polenta_CrossSpectra}} for a comparison between the two estimators. Noise bias and covariance matrices have been computed through the Full Focal Plane Simulations version 7 ''FFP7'', which includes 1000 realization of both signal and noise maps consistent with Planck data. The angular response of the instrument is accounted for by using the beam window functions presented in {{PlanckPapers|planck2013-p02d}} {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Coupling kernels to correct for incomplete sky coverage are computed as described in Annex B of {{PlanckPapers|planck2013-p08}} {{PlanckPapers|planck2014-a13||Planck-2015-A13}}. We have masked the Galactic plane and point sources using masks described in Sec. 3 of {{PlanckPapers|planck2013-p06}} {{PlanckPapers|planck2014-a12||Planck-2015-A12}}. In particular, we have used the 70% Galactic mask for 44 and 70 GHz, and the 60% Galactic mask for 30 GHz.<br />
We report in Fig. 1 the 30, 44, and 70 GHz temperature power spectra. These have been produced from frequency maps without performing component separation. Nevertheless, there is a clear agreement between the observed spectra and the Planck Likelihood Code bestfit {{PlanckPapers|planck2013-p08}} {{PlanckPapers|planck2014-a13||Planck-2015-A13}}when adding a simple foreground component to account for unresolved point source residuals at small angular scales.<br />
<br />
The details can be found in {{PlanckPapers|planck2013-p02}} {{PlanckPapers|planck2014-a03||Planck-2015-A03}}. <br />
<br />
[[File:LFI_TTspectra_styleguide_final.jpg|thumb|center|500px|'''Figure 1. Temperature power spectra at 30, 44 and 70 GHz. Dashed lines correspond to the Planck Likelihood Code best-fit plus a foreground component to account for unresolved point sources.''']]<br />
--><br />
<br />
<!--<br />
<br />
== LFI specific L3 activities: masks, MCQA, etc ==<br />
<br />
=== Masks ===<br />
<br />
=== MCQA ===<br />
<br />
--><br />
<br />
== References ==<br />
<br />
<References /><br />
<br />
<br />
<br />
<br />
[[Category:LFI data processing|007]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11231Beams LFI2015-02-04T16:57:13Z<p>Agregori: </p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Please note that many figures below refer to the previous Planck release {{PlanckPapers|planck2013-p02d}} since they have not changed significantly. <br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Beam Normalization ==<br />
<br />
With respect to the previous release, the beam normalization convention adopted in the LFI pipeline has changed. In previous work, the main beam used in the calculation of the effective beams (and effective beam window functions) was a full-power main beam (i.e unrealistically set to 100% efficiency). The resulting beam window function was normalized to unity because the calibration was performed assuming a pencil beam. This assumption provides that all the power entering the feed horn comes from the beam line of sight. We know that this assumption is not realistic, since up to 1% of the solid angle of the LFI beams falls into the sidelobes, unevenly distributed and concentrated mainly in two areas: the main and sub spillover. <br />
<br />
Important to note is that the roughly 1% of the signal found in the sidelobes is missing from the vicinity of the main beam, so the main beam efficiency η ≈ 99%; and this must be accounted for in any analysis of the maps. In particular, the window function used to correct the power spectra extracted from the maps (which is based on the main beam only) allows for this efficiency.<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}.<br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>. In the current release we deliver both TT and EE window functions defined as:<br />
<br />
<math><br />
B_\ell^{TT,EE}= \widetilde{C}_\ell^{TT,EE} / C_\ell^{TT,EE}<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11227Beams LFI2015-02-04T16:51:04Z<p>Agregori: /* Overview */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Please note that many figures below refer to the previous Planck release {{PlanckPapers|planck2013-p02d}} since they have not changed significantly. <br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>. In the current release we deliver both TT and EE window functions defined as:<br />
<br />
<math><br />
B_\ell^{TT,EE}= \widetilde{C}_\ell^{TT,EE} / C_\ell^{TT,EE}<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11220Beams LFI2015-02-04T16:33:07Z<p>Agregori: /* Overview */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Most of the figures below refer to the previous Planck release {{PlanckPapers|planck2013-p02d}} since they have not changed significantly. <br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>. In the current release we deliver both TT and EE window functions defined as:<br />
<br />
<math><br />
B_\ell^{TT,EE}= \widetilde{C}_\ell^{TT,EE} / C_\ell^{TT,EE}<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11219Beams LFI2015-02-04T16:29:36Z<p>Agregori: /* Overview */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Most of the figures below refer to the previous Planck release {{PlanckPapers|planck2013-p04}} since they have not changed significantly. <br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>. In the current release we deliver both TT and EE window functions defined as:<br />
<br />
<math><br />
B_\ell^{TT,EE}= \widetilde{C}_\ell^{TT,EE} / C_\ell^{TT,EE}<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11215Beams LFI2015-02-04T16:23:10Z<p>Agregori: /* Window Functions */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Most of the figures below refer to the previous Planck release since they have not changed significantly. <br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>. In the current release we deliver both TT and EE window functions defined as:<br />
<br />
<math><br />
B_\ell^{TT,EE}= \widetilde{C}_\ell^{TT,EE} / C_\ell^{TT,EE}<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11213Beams LFI2015-02-04T16:21:07Z<p>Agregori: /* Overview */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}. Most of the figures below refer to the previous Planck release since they have not changed significantly. <br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>:<br />
<br />
<math><br />
B_\ell= \widetilde{C}_\ell / C_\ell<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11211Beams LFI2015-02-04T16:16:55Z<p>Agregori: /* Beam Window functions, W_\ell , for LFI channels */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}.<br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>:<br />
<br />
<math><br />
B_\ell= \widetilde{C}_\ell / C_\ell<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>B_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11210Beams LFI2015-02-04T16:16:32Z<p>Agregori: /* Window Functions */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}.<br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
<br />
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
<br />
<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
<br />
(see the instrument [[The RIMO|RIMOs]])<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====Beam cutoff radii====<br />
<br />
* N times the geometric mean of FWHM of all detectors in a channel, where N=2.5 for all LFI frequency channels.<br />
<!--<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' ||<br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|}<br />
--><br />
<br />
====Map resolution for the derived beam data object====<br />
<br />
* <math>N_{side} = 1024 </math> for all LFI frequency channels.<br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for 30GHz frequency channel, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<br />
[[File:30.png| 600px| thumb | center| '''30GHz''']]<br />
<br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''4pi* sum(effbeam)/max(effbeam)'''<br />
ie <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 600px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
<br />
<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
[[File:e_030_GB.png| 600px| thumb | center| '''ellipticity - 30GHz''']]<br />
[[File:solidarc_030_GB.png| 600px| thumb | center| '''beam solid angle (relative variations wrt scanning beam - 30GHz''']]<br />
<br />
<br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 768 directions on the sky for LFI data. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|}<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: <math> 4 \pi*sum(effective_{beam})/max(effective_{beam})</math> , i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|}<br />
<br />
===Related products===<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for Nominal Mission data<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, <math>C_\ell^{out}</math>, and 1 sigma errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations.<br />
<!--, FFP#,<br />
for example [[HL-sims#FFP6 data set|FFP6]].<br />
--><br />
<br />
== Window Functions ==<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> B_\ell </math> relates the true angular power spectra <math>C_\ell </math> with the observed angular power spectra <math>\widetilde{C}_\ell </math>:<br />
<br />
<math><br />
B_\ell= \widetilde{C}_\ell / C_\ell<br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_\ell </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_\ell </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_\ell </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
B^{est}_\ell = < C^{conv}_\ell / C^{in}_\ell ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing <math> C^{conv}_\ell</math> with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, <math>W_\ell </math>, for LFI channels====<br />
<br />
[[File:Plot_channels_T_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: temperature, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
:[[File:Plot_channels_E_LFI_log.jpg| 500px | thumb | center |'''FEBeCoP beam window functions for Planck 30, 44, and 70 GHz frequency maps: polarisation, computed from GRASP beams (GB) and hybrid beams (HB)''']]<br />
<!--<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, <math>W_\ell </math>, for LFI channels''']]--><br />
<br />
== Sidelobes ==<br />
<br />
There is no direct measurements of sidelobes for LFI. The sidelobe pattern for LFI was been simulated using GRASP9 Multi-reflector GTD.<br />
We used the RFTM electromagnetic model. Seven beams for each radiometer have been computed in spherical polar cuts with a step of 0.5 degrees both in theta and phi.<br />
The beams have been computed in the same frames used for the main beams.<br />
The intermediate beam region (theta < 5 degrees) has been replaced with null values.<br />
<br />
*In the computation we considered:<br />
**the direct field from the feed<br />
**the 1st order contributions: Bd, Br, Pd, Pr, Sd, Sr, Fr<br />
**the 2nd order contributions SrPd and SdPd <br />
<br />
where B=buffle', P=primary reflector, S=secondary reflector, F=Focal Plane Unit Box. <br />
and where d=diffraction, r=reflection.<br />
For example Br, means that we considered in the calculation the reflection on the telescope baffle system. <br />
<br />
A refinement of the sidelobes model will be considered in a future release, taking into account more contributions together with Physical Optics models.<br />
<br />
[[File:slb_lfi_30_27_y_tricromia.png|500px|thumb|centre|'''The image of the LFI27-M sidelobes is created as RGB picture where the red channel is the 27 GHz (f0), the green channel is the 30 GHz (f3), and the blue channel is the 33 GHz (f6). Because of the combined map does not show any wide white region, the sidelobe pattern change with frequency, as expected.''']]<br />
<br />
== References ==<br />
<br />
<References /> <br />
<br />
<br />
[[Category:LFI data processing|003]]</div>Agregorihttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams_LFI&diff=11205Beams LFI2015-02-04T16:06:32Z<p>Agregori: /* Beam Window functions, W_\ell , for LFI channels */</p>
<hr />
<div>{{DISPLAYTITLE:Beams}}<br />
<br />
== Overview ==<br />
<br />
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers.<br />
Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers {{BibCite|darcangelo2009b}} (see also [[LFI design, qualification, and performance#Naming Convention|LFI naming convention]]). <br />
<br />
[[File:fieldofview.png|500px|thumb|centre|'''Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completeness and they are not representative of flight beams.''']]<br />
<br />
Details are given in {{PlanckPapers|planck2014-a05||Planck-2015-A05}}.<br />
<br />
<!--<br />
<br />
For the beam we consider these three regions:<br />
<br />
<br />
; main beam: is the portion of the pattern that extends up to 1.9, 1.3, and 0.9 degrees from the beam center at 30, 44, and 70 GHz, respectively.<br />
; near sidelobes: is the pattern contained between the main beam angular limit and 5 degrees from the beam center (this is often called <b>intermediate beam</b>).<br />
; far sidelobes: is the pattern at angular regions more than 5 degrees from the beam center.<br />
--><br />
<br />
== Polarized Scanning Beams and Focal Plane calibration ==<br />
<br />
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurements using Jupiter transits. The parameters that characterise the beam pointing are the following:<br />
<br />
* THETA_UV (<math>\theta_{uv}</math>)<br />
* PHI_UV (<math>\phi_{uv}</math>)<br />
<br />
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as <br />
<br />
<math>\theta_{uv} = \arcsin(u^2+v^2)</math><br />
<br />
<math>\phi_{uv} = \arctan(v/u)</math><br />
<br />
Two additional angles are used to characterize the beams in the RIMO: <br />
<br />
* PSI_UV (<math>\psi_{uv}</math>)<br />
* PSI_POL (<math>\psi_{pol}</math>)<br />
<br />
<math>\psi_{uv}</math> and <math>\psi_{pol}</math> are '''not''' derived from measurements but they are estimated from '''optical simulations'''. They are the quantities that represent the polarization direction of each beam, in the following approximation: '''the M- and S- beams of the same RCA point at the same direction on the sky'''.<br />
<br />
The polarized scanning beams have been evaluated from optical simulations using GRASP Physical Optics code, by appropriately tuning the Radio Frequency Flight Model (RFFM) {{PlanckPapers|tauber2010b}}. <br />
<br />
The Radio Frequency Tuned Model, called RFTM, was implemented to fit the in-flight beam measurements with the electromagnetic model. The LFI main beams can be considered linearly polarized, but the non-null cross-polarization has an impact on the polarization measurements. Since we are not able to measure the cross polar beam in flight, we have relied on simulations validated by accurate beam measurements.<br />
<br />
The model beams were monochromatic and were computed throughout a 6 GHz band around the Optical Center Frequency (OCF) with non-regular step (denser sampling where the band-pass was higher). For the RFTM model the OCF were at <math>28.0, \, 44.0, \, 70.0</math> GHz. <br />
<br />
For each simulated beam we created a map of the Stokes polarization parameters. On those maps we performed a weighted in-band average to recover our best estimation of the polarized beam shape. The weighting function was the [[The_RIMO#LFI_2|RIMO]] transmission function.<br />
<br />
The delivered [[Scanning_Beams|products]] include the in-band averaged Stokes scanning maps of Main Beams, Intermediate Beams and Sidelobes.<br />
<br />
== Effective beams ==<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in {{BibCite|mitra2010}}. Here we summarise the main results. The observed temperature sky <math>\widetilde{\mathbf{T}} </math> is a convolution of the true sky <math>\mathbf{T} </math> and the effective beam <math>\mathbf{B}</math>:<br />
<br />
<math><br />
\widetilde{\mathbf{T}} \ = \ \Delta\Omega \, \mathbf{B} \cdot \mathbf{T},<br />
\label{eq:a0}<br />
</math><br />
<br />
where<br />
<br />
<math><br />
B_{ij} \ = \ \left( \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \right) / \left({\sum_t A_{ti}} \right) \, ,<br />
\label{eq:EBT2}<br />
</math><br />
<br />
<math>t</math> is time samples, <math>A_{ti}</math> is <math>1</math> if the pointing direction falls in pixel number <math>i</math>, else it is <math>0</math>, <math>\mathbf{p}_t</math> represents the exact pointing direction (not approximated by the pixel centre location), and <math>\hat{\mathbf{r}}_j</math> is the centre of the pixel number <math>j</math>, where the scanbeam <math>b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t)</math> is being evaluated (if the pointing direction falls within the cut-off radius of <math>\sim 2.5 \times</math> FWHM.<br />
<br />
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel <math>i</math>, <math>(\widetilde{I}, \widetilde{Q}, \widetilde{U})_i</math>, are related to the true stokes parameters <math>(I, Q, U)_i</math>, by the following relation:<br />
<br />
<math><br />
( \widetilde{I} \quad \widetilde{Q} \quad \widetilde{U})_i^T \ = \ \Delta\Omega \sum_j \mathbf{B}_{ij} \cdot (I \quad Q \quad U)_j^T,<br />
\label{eq:a1}<br />
</math><br />
<br />
where the polarised effective beam matrix<br />
<br />
<math><br />
\mathbf{B}_{ij} \ = \ \left[ \sum_t A_{tp} \mathbf{w}_t \mathbf{w}^T_t \right]^{-1} \sum_t A_{ti} \, b(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) \, \mathbf{w}_t \mathbf{W}^T(\hat{\mathbf{n}}_j,\hat{\mathbf{p}}_t) \, ,<br />
\label{eq:a2}<br />
</math><br />
<br />
and <math>\mathbf{w}_t </math>and <math>\mathbf{W}(\hat{\mathbf{r}}_j, \hat{\mathbf{p}}_t) </math> are the the polarisation weight vectors, as defined in \cite{mitra2010}.<br />
<br />
The task is to compute <math>B_{ij}</math> for temperature only beams and the <math>3 \times 3</math> matrices <math>\mathbf{B}_{ij}</math> for each pixel <math>i</math>, at every neighbouring pixel <math>j</math> that fall within the cut-off radius around the the center of the <math>i^\text{th}</math> pixel.<br />
<br />
<br />
<br />
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky. <br />
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FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.<br />
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<br />
===Production process===<br />
<br />
<br />
The methodology for computing effective beams for a scanning CMB experiment like Planck<br />
was presented in {{BibCite|mitra2010}}.<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
====Pixel Ordered Detector Angles (PODA)====<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
====effBeam====<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
====Computational Cost====<br />
<br />
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ Computational cost for PODA, Effective Beam and single map convolution.The cost in Human time is computed using an arbitrary number of nodes/core on Carver or Hopper NERSC Supercomputers<br />
|-<br />
|Channel ||030 || 044 || 070 <br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 <br />
|-<br />
|PODA/Detector Computation time (Human minutes) || 7 || 10 || 20 <br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 <br />
|-<br />
|Beam/Channel Computation time (Human hrs) || 0.5 || 0.8 || 1 <br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 <br />
|-<br />
|Convolution Computation time (Human sec) || 1 || 1 || 1 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 <br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
===Inputs===<br />
<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 600px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
====The Focal Plane DataBase (FPDB)====<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
* {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
====The scanning strategy====<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
====The scanbeam====<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole miss