Difference between revisions of "HFI detection chain"

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== Detection chain ==
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== Bolometers==
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<span style="color:red">(Francesco Piacentini)</span>
 
−
 
 
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This entire section has been moved to [[HFI_detection_chain | this page]].
 
−
 
 
−
=== Bolometers===
 
  
 
The heart of the HFI - the detectors - are bolometers, solid-state devices in which the
 
The heart of the HFI - the detectors - are bolometers, solid-state devices in which the
 
incoming radiation dissipates its energy as heat that increases the temperature of a
 
incoming radiation dissipates its energy as heat that increases the temperature of a
 
thermometer. The instrument Flight Model total number of bolometers is 52, split into 6
 
thermometer. The instrument Flight Model total number of bolometers is 52, split into 6
−
channels at central frequencies of 100, 143, 217, 353, 545, and 857GHz.  
+
channels at central frequencies of 100, 143, 217, 353, 545, and 857 GHz.  
 
Two extra bolometers not optically coupled to the telescope are added to the focal plane
 
Two extra bolometers not optically coupled to the telescope are added to the focal plane
−
to monitor thermal noise (Dark Bolometers).
+
to monitor thermal noise (dark bolometers).  
−
 
 
−
Thirty two of these bolometers are polarization sensitive allowing a map of the CMB polarisation to be built.
 
  
 +
The bolometers consist of
 +
* an absorber that transforms the in-coming radiation into heat,
 +
* a semi-conducting NTD thermistor that is thermally linked to the absorber and measures the temperature changes,
 +
* and a weak thermal link to a thermal sink, to which the bolometer is attached.
  
−
Bolometers consist of (i) an absorber that transforms the in-coming radiation into heat; (ii) a thermometer that is thermally linked to the absorber and measures the temperature changes; and (iii) a weak thermal link to a thermal sink, to which the bolometer is attached.
+
There are two kinds of detector modules: Polarization Sensitive Bolometers (PSB) and Spider Web Bolometers (SWB).
  
 +
'''Spider Web Bolometers'''{{BibCite|Bock1995}}{{BibCite|Mauskopf1997}}
  
−
The detectors are semi-conducting NTD thermistor bolometers. There are two kinds of detector modules:
+
In these bolometers, the absorber consists of a metallic grid deposited on a Si3 N4 substrate in the shape of a spider web.
−
 
 
−
* SWB, spider web bolometers, are mounted on an absorbing spider-web of metallised silicon nitride
 
−
* PSB, polarization sensitive bolometers, are mounted or on a parallel absorbing grid of metallised silicon nitride.
 
−
 
 
−
 
 
−
In the spider-web bolometers, or SWBs (Bock et al. 1995; Mauskopf et al. 1997), the absorbers consist of metallic grids
 
−
deposited on a Si3 N4 substrate in the shape of a spider web.
 
 
The mesh design and the impedance of the metallic layer are
 
The mesh design and the impedance of the metallic layer are
 
adjusted to match vacuum impedance and maximize the absorption of millimeter waves, while minimizing the cross section to
 
adjusted to match vacuum impedance and maximize the absorption of millimeter waves, while minimizing the cross section to
 
particles. The absorber is designed to offer equal impedance to
 
particles. The absorber is designed to offer equal impedance to
 
any linearly polarised radiation. Nevertheless, the thermometer
 
any linearly polarised radiation. Nevertheless, the thermometer
−
and its electrical leads define a privileged orientation (Fig. SWB) that
+
and its electrical leads define a privileged orientation that
 
makes the SWBs slightly sensitive to polarisation, as detailed in
 
makes the SWBs slightly sensitive to polarisation, as detailed in
−
(Rosset et al. 2010). The thermometers are
+
{{PlanckPapers|rosset2010}}. The thermometers are
−
made of neutron transmuted doped (NTD) germanium (Haller
+
made of neutron transmuted doped (NTD) germanium{{BibCite|Haller1996}} chosen to have an impedance of about 10 MΩ at
−
et al. 1996), chosen to have an impedance of about 10 MΩ at
 
 
their operating temperature.
 
their operating temperature.
  
 +
[[Image:HFI_2_4_1_FPiacentini_bolo1.png|thumb|500px|center|Picture of a Spider Web Bolometer. This a 143 GHz module, The temperature sensor is at the center of the absorbing grid.]]
  
−
[[Image:HFI_2_4_1_FPiacentini_bolo1.png|thumb|500px|Picture of a spider web bolometer. This a 143 GHz module, The temperature sensor is at the center of the absorbing grid]]
+
'''Polarization Sensitive Bolometers'''
  
−
 
+
The absorber of PSBs is a rectangular grid with metallization in one direction{{BibCite|Jones2003}}. Electrical fields parallel to this direction develop currents and then deposit some energy in the grid, while perpendicular electrical fields propagate through the grid without significant interaction. A second PSB perpendicular to the first one absorbs the other polarisation. Such a PSB pair measures two polarisations of radiation collected by the same horns and filtered by the same devices, which minimises the systematic effects: differences between polarised
−
The absorber of PSBs is a rectangular grid (Fig. PSB) with metallization in one direction (Jones et al.
 
−
2003). Electrical fields parallel to this direction develop currents and then deposit some power in the grid, while perpendicular electrical fields propagate through the grid without significant interaction. A second PSB perpendicular to the first one absorbs the other polarisation. Such a PSB pair measures two polarisations of radiation collected by the same horns and filtered by the same devices, which minimises the systematic effects: differences between polarised
 
 
beams collected by a given horn are typically less than −30 dB of
 
beams collected by a given horn are typically less than −30 dB of
 
the peak. The differences in the spectral responses of a PSB pair
 
the peak. The differences in the spectral responses of a PSB pair
Line 53: Line 42:
 
the U Stokes parameter.
 
the U Stokes parameter.
  
 +
[[Image:HFI_2_4_1_FPiacentini_bolo2.png|thumb|500px|center|Picture of a Polarization Sensitive Bolometer. This is a 217 GHz module, The temperature sensor is located at an edge of the absorbing grid.]]
  
−
[[Image:HFI_2_4_1_FPiacentini_bolo2.png|thumb|500px|Picture of a polarization sensitive bolometer. This a 217 GHz module, The temperature sensor is at the an edge  of the absorbing grid]]
+
The detectors operate at a temperature close to 100 mK, while the filters are distributed on the 100 mK, 1.6 K,
−
 
 
−
 
 
−
The detectors operate at a temperature close to 100 mK, while the filters are distributed on the 100mK, 1.6 K,
 
 
and 4 K stages in such a way that the heat load on the coldest stages is minimized to
 
and 4 K stages in such a way that the heat load on the coldest stages is minimized to
 
limit the heat load on the detectors and to decrease
 
limit the heat load on the detectors and to decrease
Line 65: Line 52:
  
  
−
[[Image:HFI_2_4_1_FPiacentini_table1.png|thumb|500px|to be change into a real table]]
+
[[Image:HFI_2_4_1_FPiacentini_table1.png|thumb|500px|center| ]]
  
−
===Focal plane layout===
+
==Focal plane layout==
  
−
The layout of the detectors in the focal plane is defined to cope with the
+
The layout of the detectors in the focal plane is defined in relation to the
 
scanning strategy. The HFI horns are positioned at the centre of the focal plane, where the optical
 
scanning strategy. The HFI horns are positioned at the centre of the focal plane, where the optical
 
quality is good enough for the high frequencies. The curvature of
 
quality is good enough for the high frequencies. The curvature of
 
rows compensates for the distortion of images by the telescope.
 
rows compensates for the distortion of images by the telescope.
 
A pair of identical SWB will scan the same circle on the sky to
 
A pair of identical SWB will scan the same circle on the sky to
−
provide additional redundancy. Similar horns feeding PSBs are
+
provide redundancy. Similar horns feeding PSBs are
−
also aligned so that two pairs of PSBs rotated by 45◦ with respect to each other scan the same line. This will provide the Q and U Stokes parameters with minimal correction for the pointing (Rosset et al. 2010). Residual systematics will come from the differences between the beam shapes of the two horns. In all
+
also aligned so that two PSBs rotated by 45◦ with respect to each other scan the same line. This will provide the Q and U Stokes parameters with minimal correction for the pointing {{PlanckPapers|rosset2010}}. Residual systematics will come from the differences between the beam shapes of the two horns. In all
 
cases except for the 100 GHz horns, a measurement is also done
 
cases except for the 100 GHz horns, a measurement is also done
 
by a pair of similar channels shifted by 1.25 arcminutes in the cross-scan direction, to ensure adequate sampling. In the figures focal plane layout is reported.  
 
by a pair of similar channels shifted by 1.25 arcminutes in the cross-scan direction, to ensure adequate sampling. In the figures focal plane layout is reported.  
  
−
[[Image:HFI_2_4_1_FPiacentini_FocalPlaneLayout.png|thumb|500px|Focal plane layout as seen from outside the celestial sphere. Each spot represents an horn in the focal plane. Coordinates are in pointing direction with respect to the telescope boresight. PSBs detectors are indicated with a cross oriented as the two polarimeters axes. Scan direction is from
+
[[Image:HFI_2_4_1_FPiacentini_FocalPlaneGeo.png|thumb|500px|center|Focal plane layout as seen from outside the celestial sphere. In this case PSB orientations are indicated. Red rod is for "a" elements of PSBs, blue rod is for "b" elements. The scan direction is from left to right.]]
−
left to right.]]
 
−
 
 
−
[[Image:HFI_2_4_1_FPiacentini_FocalPlaneGeo.png|thumb|500px|Focal plane layout as seen from outside the celestial sphere. In this case PSBs orientations are reported. Red rod is for a elements of PSBs, blue rod is for b elements.]]
 
−
 
 
−
===Readout===
 
−
 
 
−
The AC bias readout electronics of the HFI instrument (Gaertner et al. 1997) includes a number of original features proposed by several laboratories (CRTBT in Grenoble, CESR in Toulouse and IAS in Orsay), which were validated on the Diabolo experiment and on the balloon-borne Archeops experiment. It was developed for space by the CESR in Toulouse.
 
−
 
 
−
 
 
−
The particular features of the HFI AC bias readout are mainly
 
−
 
 
−
 
 
−
* i)that the cold load resistors were replaced by capacitors because they have no Johnson noise;
 
−
* ii)that the detectors are biased by applying a triangular voltage to the load capacitors
 
−
which produces a square current [Ibias ] in the capacitors, and a square voltage [T bias ] that compensates for the stray capacitance of the wiring (producing a nearly square bias current into the bolometer;
 
−
* iii)that a square offset com-pensation signal is subtracted to the bolometric signal to minimise the amplitude of the signal that has to be amplified and digitized;
 
−
* iv)that the electronic scheme is symmetrical and uses a differential amplification scheme to optimize the immunity to electromagnetic interferences;
 
−
* v)and finally that every parameter of the REU can be set by commands, which
 
−
is made possible by using digital-to-analog and analog-to-digital converters extensively.
 
  
 +
==Readout==
  
−
The readout electronics consist of 72 channels designed to perform low noise measurements of the impedance of 52 bolometers, two blind bolometers, 16 accurate low temperature thermometers, all in the 10 MΩ range, one resistor of 10 MΩ and one capacitor of 100 pF. The semiconductor bolometers and thermometers of Planck-HFI operate at cryogenic temperature around 100 mK on the focal plane, with impedance of about 10 MΩ when biased at the optimal current. The readout electronics on the contrary have to operate at “room” temperature (300 K). The distance between the two extremities of the readout chain is about 10 m and could represent a point of extreme susceptibility to electromagnetic interference. The readout electronic chain was split into three boxes. These are the JFET box, located on the 50 K stage of the satellite at 2.2 m from the focal plane, the pre-amplifier unit (PAU), located 1.8m further at 300 K, and the REU, located on the opposite side of the satellite, 5 m away. Each of the three boxes (JFET, PAU and
+
The AC bias readout electronics of the HFI instrument{{BibCite|Gaertner1997}} includes the following features
−
REU) consists of 12 belts of six channels. The first nine belts are dedicated to the bolometers, and the three last ones to the accurate thermometers, the resistor and the capacitor (see figure Organization of the HFI readout).  
+
* the cold load resistors were replaced by capacitors because they have no Johnson noise;
 +
* the detectors are biased by applying a triangular voltage to the load capacitors which produces a square current (Ibias) in the capacitors, and a square voltage (T bias) that compensates for the stray capacitance of the wiring (producing a nearly square bias current into the bolometer;
 +
* a square offset com-pensation signal is subtracted to the bolometric signal to minimise the amplitude of the signal that has to be amplified and digitized;
 +
* the electronic scheme is symmetrical and uses a differential amplification scheme to optimize the immunity to electromagnetic interferences;
 +
* and finally every parameter of the REU can be set by commands, which is made possible by using digital-to-analog and analog-to-digital converters extensively.
  
−
[[Image:HFI_2_4_1_FPiacentini_HFIreadout.png|thumb|500px|Principles of readout electronics. The three modules of the chain are shown: JFet Box, Pre-Amplifier Unit (PAU) and Readout Electronic Unit (REU)]]
+
The readout electronics consists of 72 channels designed to perform low noise measurements of the impedance of 52 bolometers, two blind bolometers, 16 accurate low-temperature thermometers, all in the 10 MΩ range, one resistor of 10 MΩ and one capacitor of 100 pF. The semiconductor bolometers and thermometers of Planck-HFI operate at cryogenic temperature around 100 mK on the focal plane, with impedance of about 10 MΩ when biased at the optimal current. The readout electronics on the contrary has to operate at “room” temperature (300 K). The distance between the two extremities of the readout chain is about 10 m and could bring about an extreme susceptibility to electromagnetic interference. The readout electronic chain was split into three boxes. These are the JFET box, located on the 50 K stage of the satellite at 2.2 m from the focal plane, the pre-amplifier unit (PAU), located 1.8 m further at 300 K, and the REU, located on the opposite side of the satellite, 5 m away. Each of the three boxes (JFET, PAU and REU) consists of 12 belts of six channels. The first nine belts are dedicated to the bolometers, and the three last ones to the accurate thermometers, the resistor and the capacitor.
  
−
[[Image:HFI_2_4_1_FPiacentini_table2.jpeg|thumb|500px|Organization of the HFI readout. Each row represents a belt. Each belt has 6 channels. (to be change into a real table ?)]]
+
[[Image:HFI_2_4_1_FPiacentini_HFIreadout.png|thumb|500px|center|Principles of readout electronics. The three modules of the chain are shown: JFET box, Pre-Amplifier Unit (PAU) and Readout Electronic Unit (REU)]]
  
−
===Principles of the readout electronics ===
+
[[Image:HFI_2_4_1_FPiacentini_table2.jpeg|thumb|500px|center|Organization of the HFI readout. Each row represents a belt. Each belt has six channels.]]
  
−
See figure [Principles of readout electronics]. The bolometer is biased by a square wave AC current obtained by the differentiation of a triangular voltage through a load capacitance, in a completely differential architecture. The presence of the stray capacitance due to losses of charge in the wiring requires a correction of the shape of the square bias current by a transient voltage. Thus the bias voltage generation is controlled by the two parameters I-bias and T-bias that express the amplitude of the triangular and transient voltage. The compensation voltage added to the bolometric signal to optimize the dynamic of the chain is controlled by the V-bal parameter.
+
==Principles of the readout electronics ==
  
−
Parameters of the Readout Unit can be set to optimize the detectors performance.
+
The bolometer is biased by a square wave AC current obtained by the differentiation of a triangular voltage through a load capacitance, in a completely differential architecture. The presence of the stray capacitance due to losses of charge in the wiring requires a correction of the shape of the square bias current by a transient voltage. Thus the bias voltage generation is controlled by the two parameters I-bias and T-bias that express the amplitude of the triangular and transient voltage. The compensation voltage added to the bolometric signal to optimize the dynamic of the chain is controlled by the V-bal parameter.
−
 
 
−
The modulation frequency of the AC bias system, fmod of the square bias current
 
−
can be tuned from 70 Hz to 112 Hz by the telecommand parameters:
 
−
Nsample, which defines the number of samples per half period of modulated signal,
 
−
fdiv which determines the sampling frequency of the ADC.
 
−
 
 
−
The optimal frequencies are around 90 Hz.
 
  
 +
The following parameters of the Readout Unit can be set to optimize the detector performance:
 +
* fmod, the modulation frequency of the square bias current, was set to 90.18685,
 +
* Nsample, which defines the number of samples per half period of modulated signal was set to 40.
  
 
Each channel has its own settings for the following parameters:
 
Each channel has its own settings for the following parameters:
−
I-bias, amplitude of the triangular bias voltage;
+
* I-bias, amplitude of the triangular bias voltage,
−
 
+
* T-bias, amplitude of the transient bias voltage,
−
T-bias, amplitude of the transient bias voltage;
+
* V-bal, amplitude of the square compensation voltage,
−
 
+
* G-amp, value of the programmable gain of the REU [1/3, 1, 3, 7.6],
−
V-bal, amplitude of the square compensation voltage;
+
* N-blank, number of blanked samples at the beginning of halfperiod not taken into account during integration of the signal,
−
 
+
* S-phase, phase shift when computing the integrated signal.
−
G-amp, value of the programmable gain of the REU [1/3, 1, 3, 7.6];
 
−
 
 
−
N-blank, number of blanked samples at the beginning of halfperiod not taken into account during integration of the signal;
 
−
 
 
−
S-phase, phase shift when computing the integrated signal.
 
  
 
All these parameters influence the effective response of the
 
All these parameters influence the effective response of the
 
detection chains, and were optimized during the calibration  
 
detection chains, and were optimized during the calibration  
 
campaigns and confirmed during the calibration and performance
 
campaigns and confirmed during the calibration and performance
−
verification (CPV) phase following the launch of
+
verification phase following the launch of
 
Planck. The scientific signal is provided by the integral of the
 
Planck. The scientific signal is provided by the integral of the
 
signal on each half-period, between limits fixed by the S-phase
 
signal on each half-period, between limits fixed by the S-phase
Line 146: Line 110:
 
The interaction of modulated readout electronics with semiconductor
 
The interaction of modulated readout electronics with semiconductor
 
bolometers is rather different from that of a classical
 
bolometers is rather different from that of a classical
−
DC bias readout (Jones 1953). The differences were seen during
+
DC bias readout{{BibCite|Jones1953}}. The differences were seen during
 
the calibration of the HFI, although the readout electronics
 
the calibration of the HFI, although the readout electronics
 
was designed to mimic the operation
 
was designed to mimic the operation
Line 159: Line 123:
 
response. Details of the effect of the HFI AC bias system into  
 
response. Details of the effect of the HFI AC bias system into  
 
the time response of the detectors are discussed in the  
 
the time response of the detectors are discussed in the  
−
[http://www.sciops.esa.int/wikiSI/planckpla/index.php?title=HFI_design,_qualification,_and_performance&instance=Planck_PLA_ES#Time_response| Time Response] Section.
+
[[HFI_detection_chain#Time_response| time response section]].
−
 
 
−
=== JFETs===
 
−
 
 
−
Given the high impedance of the bolometers and the length of the connecting cables, it it is  essential that the impedance of the signal is lowered as close as possible to the detectors. In our system this is accomplished by means of JFET source followers, located in boxes connected to the 50 K stage.
 
−
The JFET box has been designed, developed and tested in the Observational Cosmology group in the Physics Department of the University of Rome "La Sapienza" (Brienza D. et al 2006).
 
−
There are two JFETs per channel, since the readout is fully differential, and they provide a current amplification of the signal while keeping the voltage amplification very close to unity.
 
−
 
 
−
Inside the box, the JFETs are mounted on a thermally insulated plate with an active temperature control to keep them at the optimal temperature of 110 K. With a dissipated power lower than 240 mW, mainly produced by the JFETs and the source resistors, we obtained a noise power spectral density of less than 3 nV Hz1/2 for the frequency range of interest. This increases the total noise ofall bolometer channels by less than 5%.
 
−
 
 
−
 
 
−
===Data compression===
 
−
 
 
−
The output of the readout electronics unit (REU) consists of one
 
−
value for each of the 72 science channels for each half-period of
 
−
modulation. This number, <math>S_{REU}</math> , is the sum
 
−
of the 40 16-bit ADC signal values obtained within the given
 
−
half-period. The data processor unit (DPU) performs a lossy
 
−
quantization of <math>S_{REU}</math>.
 
−
 
 
−
We define a compression slice of 254 <math>S_{REU}</math> values, corresponding
 
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to about 1.4 s of observation for each detector and to a
 
−
strip of sky about 8 degrees long. The mean <math>\langle S_{REU} \rangle</math> of the data within
 
−
each compression slice is computed, and data are demodulated
 
−
using this mean:
 
−
 
 
−
<math>S_{demod,i} = (S_{REU,i} − \langle S_{REU} \rangle ) ∗ (−1)^{i}</math>
 
−
 
 
−
where <math>1 < i < 254</math> is the running index within the compression slice.
 
−
 
 
−
The mean <math>\langle S_{demod} \rangle</math> of the demodulated data <math>S_{demod,i}</math>
 
−
is computed and subtracted, and the resulting data slice is quantized
 
−
according to a step size Q that is fixed per detector:
 
−
 
 
−
<math> S_{DPU,i} = \mbox{round} \left[( S_{demod,i} − \langle S_{demod} \rangle) /Q \right ] </math>
 
−
 
 
−
This is the lossy part of the algorithm: the required compression
 
−
factor, obtained through the tuning of the quantization step Q,
 
−
adds a measure of noise to the data. Assuming Gaussian white
 
−
noise with standard deviation <math>\sigma</math>, a quantization setting of
 
−
<math>\sigma</math>/Q = 2 adds 1% to the noise (Pajot et al. 2010; Pratt 1978).
 
−
The value of <math>\sigma</math> was determined at the end of the CPV phase after
 
−
subtraction of the signal from the timeline.
 
−
 
 
−
The two means
 
−
<math>\langle S_{REU} \rangle</math>
 
−
and
 
−
<math>\langle S_{demod} \rangle</math>
 
−
are computed as
 
−
32-bit words and sent through the telemetry, together with the
 
−
<math>S_{DPU,i}</math> values.
 
−
Variable-length encoding of the <math>S_{DPU,i}</math> values is
 
−
performed on board, and the inverse decoding is applied on
 
−
ground.
 
−
 
 
−
 
 
−
Optimal use of the bandpass available for the downlink (75 kb/s 
 
−
average for HFI science) was obtained initially by using a value
 
−
of Q = <math>\sigma</math>/2.5 for all bolometer signals.
 
−
After 12 December 2009, only for the 857 GHz detectors, the
 
−
value was reset to Q = <math>\sigma</math>/2.0 to avoid data loss
 
−
due to exceeding the limit of downlink rate.
 
−
 
 
−
===Time response===
 
  
 +
== JFETs==
  
 +
Given the high impedance of the bolometers and the length of the connecting cables, it is  essential that the impedance of the signal is lowered as close as possible to the detectors. In our system this is accomplished by means of JFET source followers, located in boxes connected to the 50 K stage{{BibCite|Brienza2006}}. There are two JFETs per channel, since the readout is fully differential, and they provide a current amplification of the signal while keeping the voltage amplification very close to unity.
  
−
The HFI bolometers and readout electronics have a finite response time to changes in incident optical power.  The bolometers are thermal detectors of radiation whose response time is determined by the thermal circuit defined by the heat capacity of the detector and thermal conductivity.
+
Inside the box, the JFETs are mounted on a thermally insulated plate with an active temperature control to keep them at the optimal temperature of 110 K. With a dissipated power lower than 240 mW, mainly produced by the JFETs and the source resistors, we obtained a noise power spectral density of less than 3 nV Hz1/2 for the frequency range of interest. This increases the total noise of all bolometer channels by less than 5%.
  
−
Due to Planck's nearly constant scan rate, the time response is degenerate with the optical beam.  However, because of the long time scale effects present in the time response, the  time response is deconvolved from the data in the processing of the HFI data (see [[TOI processing|TOI processing]]).
+
== Time response ==
  
−
The time response of the HFI bolometers and readout electronics is modeled as a Fourier domain transfer function (called the LFER4 model) consisting of the product of an bolometer thermal response <math>F(\omega)</math> and an electronics response <math>H'(\omega)</math>.  
+
The HFI bolometers and readout electronics have a finite response-time to changes of the incident optical power modeled as a Fourier domain transfer function (called the LFER4 model). LFER4 has two factors. The first one represents the bolometer thermal response, driven by its heat capacity, the thermal link to the bolometer plate at 100 mK, and by the thermo-electrical feed-back{{BibCite|catalano2010}} resulting from the heat deposited in the bolometer by the readout electronics. This factor is empirically obtained from the observation of sources. The second factor is simply the time response of the part of the readout electronics that amplifies and digitizes the signal. It is obtained by modelling the electronics with only very few free parameters.
 +
 +
The time response of the HFI bolometers and readout electronics is modeled as a Fourier domain transfer function (called the LFER4 model) consisting of the product of a bolometer thermal response <math>F(\omega)</math> and an electronics response <math>H'(\omega)</math>.  
  
 
<math>\label{LFER4def}TF^{LFER4}(\omega) = F(\omega) H'(\omega)</math>
 
<math>\label{LFER4def}TF^{LFER4}(\omega) = F(\omega) H'(\omega)</math>
  
−
=== LFER4 model ===
+
Due to Planck's nearly constant scan rate, the time response is degenerate with the optical beam.  However, because of the long time scale effects present in the time response, the  time response is deconvolved from the data in the processing of the HFI data (see [[TOI processing|TOI processing]]).  <math>F(\omega)</math> is tuned to optimize the "compactness" of the beams reconstructed with the deconvolved signal from planets.
  
−
If we write the input signal (power) on a bolometer as <math>\label{bol_in}
+
Details about the time response model are to be found in [[HFI_time_response_model | this annex]].
−
s_0(t)=e^{i\omega t}
 
−
</math> the bolometer physical impedance can be written as: <math>\label{bol_out}
 
−
s(t)=e^{i\omega t}F(\omega)
 
−
</math> where <math>\omega</math> is the angular frequency of the signal and <math>F(\omega)</math> is the complex intrinsic bolometer transfer function. For HFI the bolometer transfer function is modelled as the sum of 4 single pole low pass filters: <math>\label{bol_tf}
 
−
F(\omega) = \sum_{i=0,4} \frac{a_i}{1 + i\omega\tau_i}
 
−
</math> The modulation of the signal is done with a square wave, written here as a composition of sine waves of decreasing amplitude: <math>\label{sigmod}
 
−
s'(t)=e^{i\omega t}F(\omega)\sum_{k=0}^{\infty} \frac{e^{i\omega_r(2k+1)t}-e^{-i\omega_r(2k+1)t}}{2i(2k+1)}
 
−
</math> where we have used the Euler relation <math>\sin x=(e^{ix}-e^{-ix})/2i</math> and <math>\omega_r</math> is the angular frequency of the square wave. The modulation frequency is <math>f_{mod} = \omega_r/2\pi</math> and was set to <math>f_{mod} = 90.18759 </math>Hz in flight. This signal is then filtered by the complex electronic transfer function <math>H(\omega)</math>. Setting: <math>\omega_k^+=\omega+(2k+1)\omega_r</math> <math>\omega_k^-=\omega-(2k+1)\omega_r</math> we have: <math>\label{sigele}
 
−
\Sigma(t)=\sum_{k=0}^\infty\frac{F(\omega)}{2i(2k+1)}\left[H(\omega_k^+)e^{i\omega_k^+t}-H(\omega_k^-)e^{i\omega_k^-t}\right]
 
−
</math> This signal is then sampled at high frequency (<math>2 f_{mod} NS</math>). <math>NS</math> is one of the parameters of the HFI electronics and corresponds to the number of high frequency samples in each modulation semi-period. In order to obtain an output signal sampled every <math>\pi/\omega_r</math> seconds, we must integrate on a semiperiod, as done in the HFI readout. To also include a time shift <math>\Delta t</math>, the integral is calculated between <math>n\pi/\omega_r+\Delta t</math> and <math>(n+1)\pi/\omega_r+\Delta t</math> (with <math>T=2 \pi/\omega_r</math> period of the modulation). The time shift <math>\Delta t</math> is encoded in the HFI electronics by the parameter <math>S_{phase}</math>, with the relation <math>\Delta t = S_{phase}/NS/f_{mod} </math>.
 
  
−
After integration, the <math>n</math>-sample of a bolometer can be written as <math>\label{eqn:output}
+
==Data compression==
−
Y(t_n) = (-1)^n F(\omega) H'(\omega) e^{i t_n \omega}
 
−
</math> where <math>\label{tfele}
 
−
H'(\omega) = \frac 12 \sum_{k=0}^\infty
 
−
e^{-i(\frac{\pi\omega}{2\omega_r}+\omega\Delta t)} \Bigg[
 
−
\frac{H(\omega_k^+)e^{i\omega_k^+ \Delta t}}{(2k+1)\omega_k^+}
 
−
\left(1-e^{\frac{i\omega_k^+\pi}{\omega_r}}\right)
 
−
\\ - \frac{H(\omega_k^-)e^{i\omega_k^- \Delta t}}{(2k+1)\omega_k^-}  \left(1-e^{\frac{i\omega_k^-\pi}{\omega_r}}\right)
 
−
\Bigg]
 
−
</math>
 
  
−
The output signal in equation eqn:output can be demodulated (thus removing the <math>(-1)^n</math>) and compared to the input signal in equation bol_in. The overall transfer function is composed of the bolometer transfer function and the effective electronics transfer function, <math>H'(\omega)</math>: <math>TF(\omega) = F(\omega) H'(\omega)
+
The output of the readout electronics unit (REU) consists of one
−
</math>
+
value for each of the 72 science channels (bolometers and thermometers) for each modulation half-period. This number, <math>S_{REU}</math>, is the sum
−
 
+
of the 40 16-bit ADC signal values measured within the given
−
The shape of <math>H(\omega)</math> is obtained combining low and high-pass filters with Sallen Key topologies (with their respective time constants) and accounting also for the stray capacitance low pass filter given by the bolometer impedance combined with the stray capacitance of the cables. The sequence of filters that define the electronic band-pass function <math>H(\omega) = h_0*h_1*h_2*h_3*h_4*h_{5}</math> are listed in table table:readout_electronics_filters.
+
half-period. The data processor unit (DPU) performs a lossy
−
 
+
quantization of <math>S_{REU}</math>.
−
=== Parameters of LFER4 model ===
 
−
 
 
−
The LFER4 model has are a total of 10 parameters(<math>A_1</math>,<math>A_2</math>,<math>A_3</math>,<math>A_4</math>,<math>\tau_1</math>,<math>\tau_2</math>,<math>\tau_3</math>,<math>\tau_4</math>,<math>S_{phase}</math>,<math>\tau_{stray}</math>) 9 of which are independent, for each bolometer. The free parameters of the LFER4 model are determined using in-flight data in the following ways:
 
−
 
 
−
* <math>S_{phase}</math> is fixed at the value of the REU setting.
 
−
* <math>\tau_{stray}</math> is measured during the QEC test during CPV.
 
−
* <math>A_1</math>, <math>\tau_1</math>, <math>A_2</math>, <math>\tau_2</math> are fit forcing the compactness of the scanning beam.
 
−
* <math>A_3</math>, <math>\tau_3</math>, <math>A_{4}</math> <math>\tau_4</math> are fit by forcing agreement of survey 2 and survey 1 maps.
 
−
* The overall normalization of the LFER4 model is forced to be 1.0 at the signal frequency of the dipole.
 
−
 
 
−
The details of determining the model parameters are given in (reference P03c paper) and the best-fit parameters listed here in table table:LFER4pars.
 
−
 
 
−
 
 
−
===HFI electronics filter sequence ===
 
  
−
{| class="wikitable" style="text-align: left; border-collapse: collapse; border-width: 1px; border-style: solid; border-color: #000"
+
Details about the data compression scheme, performance of the data compression during the mission, setting the quantization step in flight, impact of the data compression on science are given in [[HFI_data_compression | this annex]].
−
|+HFI electronics filter sequence. We define $s = i \omega$
 
−
|-
 
−
! style="border-style: solid; border-width: 1px"|Filter
 
−
! style="border-style: solid; border-width: 1px"|Parameters
 
−
! style="border-style: solid; border-width: 1px"|Function
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|0. Stray capacitance low pass filter
 
−
|style="border-style: solid; border-width: 1px"|<math>\tau_{stray}= R_{bolo} C_{stray}</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>h_0 = \frac{1}{1.0+\tau_{stray}*s}</math>
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|1. Low pass filter
 
−
|style="border-style: solid; border-width: 1px"|<math>R_1=1</math>k<math>\Omega</math> <br /> <math>C_1=100</math>nF
 
−
|style="border-style: solid; border-width: 1px"|<math>h_1 = \frac{2.0+R_1*C_1*s}{2.0*(1.0+R_1*C_1*s)}</math>
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|2. Sallen Key high pass filter
 
−
|style="border-style: solid; border-width: 1px"|<math>R_2=51</math>k<math>\Omega</math><br /> <math>C_2=1\mu</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>h_2= \frac{(R_2*C_2*s)^2}{(1.0+R_2*C_2*s)^2}</math>3
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|3. Sign reverse with gain
 
−
|style="border-style: solid; border-width: 1px"|
 
−
|style="border-style: solid; border-width: 1px"|<math>h_3=-5.1</math>
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|4. Single pole low pass filter with gain
 
−
|style="border-style: solid; border-width: 1px"|<math>R_4=10</math>k<math>\Omega</math><br /> <math>C_4=10</math>nF
 
−
|style="border-style: solid; border-width: 1px"|<math>h_4= \frac{1.5}{1.0+R_4*C_4*s}</math>
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|5. Single pole high pass filter coupled to a Sallen Key low pass filter
 
−
|style="border-style: solid; border-width: 1px"|<math>R_9=18.7</math>k<math>\Omega</math><br /><math>R_{12}=37.4</math>k<math>\Omega</math><br /> <math>C=10.0</math>nF<br /><math>R_{78}=510</math>k<math>\Omega</math><br /> <math>C_{18}=1.0\mu</math>F<br /><math>K_3 = R_9^2*R_{78}*R_{12}^2*C^2*C_{18}</math><br /> <math>K_2 = R_9*R_{12}^2*R_{78}*C^2+R_{9}^2*R_{12}^2*C^2+R_9*R_{12}^2*R_{78}*C_{18}*C</math><br /> <math>K_1 =R_9*R_{12}^2*C+R_{12}*R_{78}*R_9*C_{18}</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>h_{5} = \frac{2.0*R_{12}*R_9*R_{78}*C_{18}*s}{s^3*K_3 +
 
−
      s^2*K_2+
 
−
      s*K_1 + R_{12}*R_9 } </math>
 
  
−
|}
+
== References ==
 +
<References />
  
 +
  
  
−
{| class="wikitable" style="text-align: left; align: center; border-collapse: collapse; border-width: 1px; border-style: solid; border-color: #000"
+
[[Category:HFI design, qualification and performance|003]]
−
|+ Parameters for LFER4 model.
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|Bolometer
 
−
|style="border-style: solid; border-width: 1px"|<math>A_1</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>\tau_1</math> (s)
 
−
|style="border-style: solid; border-width: 1px"|<math>A_2</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>\tau_2</math> (s)
 
−
|style="border-style: solid; border-width: 1px"|<math>A_3</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>\tau_3</math> (s)
 
−
|style="border-style: solid; border-width: 1px"|<math>A_4</math>
 
−
|style="border-style: solid; border-width: 1px"|<math>\tau_4</math> (s)
 
−
|style="border-style: solid; border-width: 1px"|<math>\tau_{stray}</math> (s)
 
−
|style="border-style: solid; border-width: 1px"|<math>S_{phase}</math> (s)
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-1a
 
−
|style="border-style: solid; border-width: 1px"|0.392
 
−
|style="border-style: solid; border-width: 1px"|0.01
 
−
|style="border-style: solid; border-width: 1px"|0.534
 
−
|style="border-style: solid; border-width: 1px"|0.0209
 
−
|style="border-style: solid; border-width: 1px"|0.0656
 
−
|style="border-style: solid; border-width: 1px"|0.0513
 
−
|style="border-style: solid; border-width: 1px"|0.00833
 
−
|style="border-style: solid; border-width: 1px"|0.572
 
−
|style="border-style: solid; border-width: 1px"|0.00159
 
−
|style="border-style: solid; border-width: 1px"|0.00139
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-1b
 
−
|style="border-style: solid; border-width: 1px"|0.484
 
−
|style="border-style: solid; border-width: 1px"|0.0103
 
−
|style="border-style: solid; border-width: 1px"|0.463
 
−
|style="border-style: solid; border-width: 1px"|0.0192
 
−
|style="border-style: solid; border-width: 1px"|0.0451
 
−
|style="border-style: solid; border-width: 1px"|0.0714
 
−
|style="border-style: solid; border-width: 1px"|0.00808
 
−
|style="border-style: solid; border-width: 1px"|0.594
 
−
|style="border-style: solid; border-width: 1px"|0.00149
 
−
|style="border-style: solid; border-width: 1px"|0.00139
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-2a
 
−
|style="border-style: solid; border-width: 1px"|0.474
 
−
|style="border-style: solid; border-width: 1px"|0.00684
 
−
|style="border-style: solid; border-width: 1px"|0.421
 
−
|style="border-style: solid; border-width: 1px"|0.0136
 
−
|style="border-style: solid; border-width: 1px"|0.0942
 
−
|style="border-style: solid; border-width: 1px"|0.0376
 
−
|style="border-style: solid; border-width: 1px"|0.0106
 
−
|style="border-style: solid; border-width: 1px"|0.346
 
−
|style="border-style: solid; border-width: 1px"|0.00132
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-2b
 
−
|style="border-style: solid; border-width: 1px"|0.126
 
−
|style="border-style: solid; border-width: 1px"|0.00584
 
−
|style="border-style: solid; border-width: 1px"|0.717
 
−
|style="border-style: solid; border-width: 1px"|0.0151
 
−
|style="border-style: solid; border-width: 1px"|0.142
 
−
|style="border-style: solid; border-width: 1px"|0.0351
 
−
|style="border-style: solid; border-width: 1px"|0.0145
 
−
|style="border-style: solid; border-width: 1px"|0.293
 
−
|style="border-style: solid; border-width: 1px"|0.00138
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-3a
 
−
|style="border-style: solid; border-width: 1px"|0.744
 
−
|style="border-style: solid; border-width: 1px"|0.00539
 
−
|style="border-style: solid; border-width: 1px"|0.223
 
−
|style="border-style: solid; border-width: 1px"|0.0147
 
−
|style="border-style: solid; border-width: 1px"|0.0262
 
−
|style="border-style: solid; border-width: 1px"|0.0586
 
−
|style="border-style: solid; border-width: 1px"|0.00636
 
−
|style="border-style: solid; border-width: 1px"|0.907
 
−
|style="border-style: solid; border-width: 1px"|0.00142
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-3b
 
−
|style="border-style: solid; border-width: 1px"|0.608
 
−
|style="border-style: solid; border-width: 1px"|0.00548
 
−
|style="border-style: solid; border-width: 1px"|0.352
 
−
|style="border-style: solid; border-width: 1px"|0.0155
 
−
|style="border-style: solid; border-width: 1px"|0.0321
 
−
|style="border-style: solid; border-width: 1px"|0.0636
 
−
|style="border-style: solid; border-width: 1px"|0.00821
 
−
|style="border-style: solid; border-width: 1px"|0.504
 
−
|style="border-style: solid; border-width: 1px"|0.00166
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-4a
 
−
|style="border-style: solid; border-width: 1px"|0.411
 
−
|style="border-style: solid; border-width: 1px"|0.0082
 
−
|style="border-style: solid; border-width: 1px"|0.514
 
−
|style="border-style: solid; border-width: 1px"|0.0178
 
−
|style="border-style: solid; border-width: 1px"|0.0581
 
−
|style="border-style: solid; border-width: 1px"|0.0579
 
−
|style="border-style: solid; border-width: 1px"|0.0168
 
−
|style="border-style: solid; border-width: 1px"|0.37
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|100-4b
 
−
|style="border-style: solid; border-width: 1px"|0.687
 
−
|style="border-style: solid; border-width: 1px"|0.0113
 
−
|style="border-style: solid; border-width: 1px"|0.282
 
−
|style="border-style: solid; border-width: 1px"|0.0243
 
−
|style="border-style: solid; border-width: 1px"|0.0218
 
−
|style="border-style: solid; border-width: 1px"|0.062
 
−
|style="border-style: solid; border-width: 1px"|0.00875
 
−
|style="border-style: solid; border-width: 1px"|0.431
 
−
|style="border-style: solid; border-width: 1px"|0.00138
 
−
|style="border-style: solid; border-width: 1px"|0.00139
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-1a
 
−
|style="border-style: solid; border-width: 1px"|0.817
 
−
|style="border-style: solid; border-width: 1px"|0.00447
 
−
|style="border-style: solid; border-width: 1px"|0.144
 
−
|style="border-style: solid; border-width: 1px"|0.0121
 
−
|style="border-style: solid; border-width: 1px"|0.0293
 
−
|style="border-style: solid; border-width: 1px"|0.0387
 
−
|style="border-style: solid; border-width: 1px"|0.0101
 
−
|style="border-style: solid; border-width: 1px"|0.472
 
−
|style="border-style: solid; border-width: 1px"|0.00142
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-1b
 
−
|style="border-style: solid; border-width: 1px"|0.49
 
−
|style="border-style: solid; border-width: 1px"|0.00472
 
−
|style="border-style: solid; border-width: 1px"|0.333
 
−
|style="border-style: solid; border-width: 1px"|0.0156
 
−
|style="border-style: solid; border-width: 1px"|0.134
 
−
|style="border-style: solid; border-width: 1px"|0.0481
 
−
|style="border-style: solid; border-width: 1px"|0.0435
 
−
|style="border-style: solid; border-width: 1px"|0.27
 
−
|style="border-style: solid; border-width: 1px"|0.00149
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-2a
 
−
|style="border-style: solid; border-width: 1px"|0.909
 
−
|style="border-style: solid; border-width: 1px"|0.0047
 
−
|style="border-style: solid; border-width: 1px"|0.0763
 
−
|style="border-style: solid; border-width: 1px"|0.017
 
−
|style="border-style: solid; border-width: 1px"|0.00634
 
−
|style="border-style: solid; border-width: 1px"| 0.1
 
−
|style="border-style: solid; border-width: 1px"|0.00871
 
−
|style="border-style: solid; border-width: 1px"|0.363
 
−
|style="border-style: solid; border-width: 1px"|0.00148
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-2b
 
−
|style="border-style: solid; border-width: 1px"|0.912
 
−
|style="border-style: solid; border-width: 1px"|0.00524
 
−
|style="border-style: solid; border-width: 1px"|0.0509
 
−
|style="border-style: solid; border-width: 1px"|0.0167
 
−
|style="border-style: solid; border-width: 1px"|0.0244
 
−
|style="border-style: solid; border-width: 1px"|0.0265
 
−
|style="border-style: solid; border-width: 1px"|0.0123
 
−
|style="border-style: solid; border-width: 1px"|0.295
 
−
|style="border-style: solid; border-width: 1px"|0.00146
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-3a
 
−
|style="border-style: solid; border-width: 1px"|0.681
 
−
|style="border-style: solid; border-width: 1px"|0.00419
 
−
|style="border-style: solid; border-width: 1px"|0.273
 
−
|style="border-style: solid; border-width: 1px"|0.00956
 
−
|style="border-style: solid; border-width: 1px"|0.0345
 
−
|style="border-style: solid; border-width: 1px"|0.0348
 
−
|style="border-style: solid; border-width: 1px"|0.0115
 
−
|style="border-style: solid; border-width: 1px"|0.317
 
−
|style="border-style: solid; border-width: 1px"|0.00145
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-3b
 
−
|style="border-style: solid; border-width: 1px"|0.82
 
−
|style="border-style: solid; border-width: 1px"|0.00448
 
−
|style="border-style: solid; border-width: 1px"|0.131
 
−
|style="border-style: solid; border-width: 1px"|0.0132
 
−
|style="border-style: solid; border-width: 1px"|0.0354
 
−
|style="border-style: solid; border-width: 1px"|0.0351
 
−
|style="border-style: solid; border-width: 1px"|0.0133
 
−
|style="border-style: solid; border-width: 1px"|0.283
 
−
|style="border-style: solid; border-width: 1px"|0.00161
 
−
|style="border-style: solid; border-width: 1px"|0.000832
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-4a
 
−
|style="border-style: solid; border-width: 1px"|0.914
 
−
|style="border-style: solid; border-width: 1px"|0.00569
 
−
|style="border-style: solid; border-width: 1px"|0.072
 
−
|style="border-style: solid; border-width: 1px"|0.0189
 
−
|style="border-style: solid; border-width: 1px"|0.00602
 
−
|style="border-style: solid; border-width: 1px"|0.0482
 
−
|style="border-style: solid; border-width: 1px"|0.00756
 
−
|style="border-style: solid; border-width: 1px"|0.225
 
−
|style="border-style: solid; border-width: 1px"|0.00159
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-4b
 
−
|style="border-style: solid; border-width: 1px"|0.428
 
−
|style="border-style: solid; border-width: 1px"|0.00606
 
−
|style="border-style: solid; border-width: 1px"|0.508
 
−
|style="border-style: solid; border-width: 1px"|0.00606
 
−
|style="border-style: solid; border-width: 1px"|0.0554
 
−
|style="border-style: solid; border-width: 1px"|0.0227
 
−
|style="border-style: solid; border-width: 1px"|0.00882
 
−
|style="border-style: solid; border-width: 1px"|0.084
 
−
|style="border-style: solid; border-width: 1px"|0.00182
 
−
|style="border-style: solid; border-width: 1px"|0.00125
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-5
 
−
|style="border-style: solid; border-width: 1px"|0.491
 
−
|style="border-style: solid; border-width: 1px"|0.00664
 
−
|style="border-style: solid; border-width: 1px"|0.397
 
−
|style="border-style: solid; border-width: 1px"|0.00664
 
−
|style="border-style: solid; border-width: 1px"|0.0962
 
−
|style="border-style: solid; border-width: 1px"|0.0264
 
−
|style="border-style: solid; border-width: 1px"|0.0156
 
−
|style="border-style: solid; border-width: 1px"|0.336
 
−
|style="border-style: solid; border-width: 1px"|0.00202
 
−
|style="border-style: solid; border-width: 1px"|0.00139
 
−
|-
 
−
|style="border-style: solid; border-width: 1px"|143-6
 
−
|style="border-style: solid; border-width: 1px"|0.518
 
−
|style="border-style: solid; border-width: 1px"|0.00551
 
−
|style="border-style: solid; border-width: 1px"|0.409
 
−
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Latest revision as of 15:54, 22 July 2014

Bolometers[edit]

The heart of the HFI - the detectors - are bolometers, solid-state devices in which the incoming radiation dissipates its energy as heat that increases the temperature of a thermometer. The instrument Flight Model total number of bolometers is 52, split into 6 channels at central frequencies of 100, 143, 217, 353, 545, and 857 GHz. Two extra bolometers not optically coupled to the telescope are added to the focal plane to monitor thermal noise (dark bolometers).

The bolometers consist of

  • an absorber that transforms the in-coming radiation into heat,
  • a semi-conducting NTD thermistor that is thermally linked to the absorber and measures the temperature changes,
  • and a weak thermal link to a thermal sink, to which the bolometer is attached.

There are two kinds of detector modules: Polarization Sensitive Bolometers (PSB) and Spider Web Bolometers (SWB).

Spider Web Bolometers[1][2]

In these bolometers, the absorber consists of a metallic grid deposited on a Si3 N4 substrate in the shape of a spider web. The mesh design and the impedance of the metallic layer are adjusted to match vacuum impedance and maximize the absorption of millimeter waves, while minimizing the cross section to particles. The absorber is designed to offer equal impedance to any linearly polarised radiation. Nevertheless, the thermometer and its electrical leads define a privileged orientation that makes the SWBs slightly sensitive to polarisation, as detailed in Planck-PreLaunch-IX[3]. The thermometers are made of neutron transmuted doped (NTD) germanium[4] chosen to have an impedance of about 10 MΩ at their operating temperature.

Picture of a Spider Web Bolometer. This a 143 GHz module, The temperature sensor is at the center of the absorbing grid.

Polarization Sensitive Bolometers

The absorber of PSBs is a rectangular grid with metallization in one direction[5]. Electrical fields parallel to this direction develop currents and then deposit some energy in the grid, while perpendicular electrical fields propagate through the grid without significant interaction. A second PSB perpendicular to the first one absorbs the other polarisation. Such a PSB pair measures two polarisations of radiation collected by the same horns and filtered by the same devices, which minimises the systematic effects: differences between polarised beams collected by a given horn are typically less than −30 dB of the peak. The differences in the spectral responses of a PSB pair also proved to be a few percent in the worst case. Each pair of PSBs sharing the same horn is able to measure the intensity Stokes parameter and the Q parameter associated with its local frame. An associated pair of PSBs rotated by 45◦ scans exactly the same line (if the geometrical alignment is perfect), providing the U Stokes parameter.

Picture of a Polarization Sensitive Bolometer. This is a 217 GHz module, The temperature sensor is located at an edge of the absorbing grid.

The detectors operate at a temperature close to 100 mK, while the filters are distributed on the 100 mK, 1.6 K, and 4 K stages in such a way that the heat load on the coldest stages is minimized to limit the heat load on the detectors and to decrease the heat lift requirement and thus enhance the mission lifetime. The self-emission of the 4K stage is minimised to limit the photon noise contribution on the detectors from the instrument. The HFI Focal Plane Unit accommodates sub-millimiter absorbing material in order to decrease the scattering inside it.


HFI 2 4 1 FPiacentini table1.png

Focal plane layout[edit]

The layout of the detectors in the focal plane is defined in relation to the scanning strategy. The HFI horns are positioned at the centre of the focal plane, where the optical quality is good enough for the high frequencies. The curvature of rows compensates for the distortion of images by the telescope. A pair of identical SWB will scan the same circle on the sky to provide redundancy. Similar horns feeding PSBs are also aligned so that two PSBs rotated by 45◦ with respect to each other scan the same line. This will provide the Q and U Stokes parameters with minimal correction for the pointing Planck-PreLaunch-IX[3]. Residual systematics will come from the differences between the beam shapes of the two horns. In all cases except for the 100 GHz horns, a measurement is also done by a pair of similar channels shifted by 1.25 arcminutes in the cross-scan direction, to ensure adequate sampling. In the figures focal plane layout is reported.

Focal plane layout as seen from outside the celestial sphere. In this case PSB orientations are indicated. Red rod is for "a" elements of PSBs, blue rod is for "b" elements. The scan direction is from left to right.

Readout[edit]

The AC bias readout electronics of the HFI instrument[6] includes the following features

  • the cold load resistors were replaced by capacitors because they have no Johnson noise;
  • the detectors are biased by applying a triangular voltage to the load capacitors which produces a square current (Ibias) in the capacitors, and a square voltage (T bias) that compensates for the stray capacitance of the wiring (producing a nearly square bias current into the bolometer;
  • a square offset com-pensation signal is subtracted to the bolometric signal to minimise the amplitude of the signal that has to be amplified and digitized;
  • the electronic scheme is symmetrical and uses a differential amplification scheme to optimize the immunity to electromagnetic interferences;
  • and finally every parameter of the REU can be set by commands, which is made possible by using digital-to-analog and analog-to-digital converters extensively.

The readout electronics consists of 72 channels designed to perform low noise measurements of the impedance of 52 bolometers, two blind bolometers, 16 accurate low-temperature thermometers, all in the 10 MΩ range, one resistor of 10 MΩ and one capacitor of 100 pF. The semiconductor bolometers and thermometers of Planck-HFI operate at cryogenic temperature around 100 mK on the focal plane, with impedance of about 10 MΩ when biased at the optimal current. The readout electronics on the contrary has to operate at “room” temperature (300 K). The distance between the two extremities of the readout chain is about 10 m and could bring about an extreme susceptibility to electromagnetic interference. The readout electronic chain was split into three boxes. These are the JFET box, located on the 50 K stage of the satellite at 2.2 m from the focal plane, the pre-amplifier unit (PAU), located 1.8 m further at 300 K, and the REU, located on the opposite side of the satellite, 5 m away. Each of the three boxes (JFET, PAU and REU) consists of 12 belts of six channels. The first nine belts are dedicated to the bolometers, and the three last ones to the accurate thermometers, the resistor and the capacitor.

Principles of readout electronics. The three modules of the chain are shown: JFET box, Pre-Amplifier Unit (PAU) and Readout Electronic Unit (REU)
Organization of the HFI readout. Each row represents a belt. Each belt has six channels.

Principles of the readout electronics[edit]

The bolometer is biased by a square wave AC current obtained by the differentiation of a triangular voltage through a load capacitance, in a completely differential architecture. The presence of the stray capacitance due to losses of charge in the wiring requires a correction of the shape of the square bias current by a transient voltage. Thus the bias voltage generation is controlled by the two parameters I-bias and T-bias that express the amplitude of the triangular and transient voltage. The compensation voltage added to the bolometric signal to optimize the dynamic of the chain is controlled by the V-bal parameter.

The following parameters of the Readout Unit can be set to optimize the detector performance:

  • fmod, the modulation frequency of the square bias current, was set to 90.18685,
  • Nsample, which defines the number of samples per half period of modulated signal was set to 40.

Each channel has its own settings for the following parameters:

  • I-bias, amplitude of the triangular bias voltage,
  • T-bias, amplitude of the transient bias voltage,
  • V-bal, amplitude of the square compensation voltage,
  • G-amp, value of the programmable gain of the REU [1/3, 1, 3, 7.6],
  • N-blank, number of blanked samples at the beginning of halfperiod not taken into account during integration of the signal,
  • S-phase, phase shift when computing the integrated signal.

All these parameters influence the effective response of the detection chains, and were optimized during the calibration campaigns and confirmed during the calibration and performance verification phase following the launch of Planck. The scientific signal is provided by the integral of the signal on each half-period, between limits fixed by the S-phase and N-blank parameters.


The interaction of modulated readout electronics with semiconductor bolometers is rather different from that of a classical DC bias readout[7]. The differences were seen during the calibration of the HFI, although the readout electronics was designed to mimic the operation of a DC biased bolometric system as far as possible. With the AC readout the maximum of responsivity is lower and is obtained for higher bias current in the bolometer with respect to the DC model. This is caused by the stray capacitance in the wiring which has negligible effects for a DC bias and a major effect for an AC bias. In our case, a stray capacitance of 150 pF induces increases of NEP ranging from 4% (857 GHz bolometers) to 10% (100 GHz bolometers) and also affects the HFI time response. Details of the effect of the HFI AC bias system into the time response of the detectors are discussed in the time response section.

JFETs[edit]

Given the high impedance of the bolometers and the length of the connecting cables, it is essential that the impedance of the signal is lowered as close as possible to the detectors. In our system this is accomplished by means of JFET source followers, located in boxes connected to the 50 K stage[8]. There are two JFETs per channel, since the readout is fully differential, and they provide a current amplification of the signal while keeping the voltage amplification very close to unity.

Inside the box, the JFETs are mounted on a thermally insulated plate with an active temperature control to keep them at the optimal temperature of 110 K. With a dissipated power lower than 240 mW, mainly produced by the JFETs and the source resistors, we obtained a noise power spectral density of less than 3 nV Hz1/2 for the frequency range of interest. This increases the total noise of all bolometer channels by less than 5%.

Time response[edit]

The HFI bolometers and readout electronics have a finite response-time to changes of the incident optical power modeled as a Fourier domain transfer function (called the LFER4 model). LFER4 has two factors. The first one represents the bolometer thermal response, driven by its heat capacity, the thermal link to the bolometer plate at 100 mK, and by the thermo-electrical feed-back[9] resulting from the heat deposited in the bolometer by the readout electronics. This factor is empirically obtained from the observation of sources. The second factor is simply the time response of the part of the readout electronics that amplifies and digitizes the signal. It is obtained by modelling the electronics with only very few free parameters.

The time response of the HFI bolometers and readout electronics is modeled as a Fourier domain transfer function (called the LFER4 model) consisting of the product of a bolometer thermal response [math]F(\omega)[/math] and an electronics response [math]H'(\omega)[/math].

[math]\label{LFER4def}TF^{LFER4}(\omega) = F(\omega) H'(\omega)[/math]

Due to Planck's nearly constant scan rate, the time response is degenerate with the optical beam. However, because of the long time scale effects present in the time response, the time response is deconvolved from the data in the processing of the HFI data (see TOI processing). [math]F(\omega)[/math] is tuned to optimize the "compactness" of the beams reconstructed with the deconvolved signal from planets.

Details about the time response model are to be found in this annex.

Data compression[edit]

The output of the readout electronics unit (REU) consists of one value for each of the 72 science channels (bolometers and thermometers) for each modulation half-period. This number, [math]S_{REU}[/math], is the sum of the 40 16-bit ADC signal values measured within the given half-period. The data processor unit (DPU) performs a lossy quantization of [math]S_{REU}[/math].

Details about the data compression scheme, performance of the data compression during the mission, setting the quantization step in flight, impact of the data compression on science are given in this annex.

References[edit]

  1. ↑ A Novel Bolometer for Infrared and Millimeter-Wave Astrophysics, J. J. Bock, D. Chen, P. D. Mauskopf, A. E. Lange, Space Science Reviews, 74, 229-235, (1995).
  2. ↑ Composite infrared bolometers with Si 3 N 4 micromesh absorbers, P. D. Mauskopf, J. J. Bock, H. del Castillo, W. L. Holzapfel, A. E. Lange, Appl. Opt, 36, 765-771, (1997).
  3. ↑ 3.03.1 Planck pre-launch status: High Frequency Instrument polarization calibration, C. Rosset, M. Tristram, N. Ponthieu, P. Ade, J. Aumont, A. Catalano, L. Conversi, F. Couchot, B. P. Crill, F.-X. Désert, K. Ganga, M. Giard, Y. Giraud-Héraud, J. Haïssinski, S. Henrot-Versillé, W. Holmes, W. C. Jones, J.-M. Lamarre, A. Lange, C. Leroy, J. Macías-Pérez, B. Maffei, P. de Marcillac, M.-A. Miville-Deschênes, L. Montier, F. Noviello, F. Pajot, O. Perdereau, F. Piacentini, M. Piat, S. Plaszczynski, E. Pointecouteau, J.-L. Puget, I. Ristorcelli, G. Savini, R. Sudiwala, M. Veneziani, D. Yvon, A&A, 520, A13+, (2010).
  4. ↑ Neutron Transmutation Depot (NTD) Germanium Thermistors for Submillimetre Bolometer Applications, E. E. Haller, K. M. Itoh, J. W. Beeman, in Submillimetre and Far-Infrared Space Instrumentation E. J. Rolfe, G. Pilbratt (Ed.), ESA Special Publication, 388, 115-+, (1996).
  5. ↑ A Polarization Sensitive Bolometric Receiver for Observations of the Cosmic Microwave Background, W. C. Jones, R. Bhatia, J. J. Bock, A. E. Lange, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series T. G. Phillips, J. Zmuidzinas (Ed.), Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, 4855, 227-238, (2003).
  6. ↑ A new readout system for bolometers with improved low frequency stability, S. Gaertner, A. Benoît, J.-M. Lamarre, M. Giard, J.-L. Bret, J.-P. Chabaud, F.-X. Desert, J.-P. Faure, G. Jegoudez, J. Lande, J. Leblanc, J.-P. Lepeltier, J. Narbonne, M. Piat, R. Pons, G. Serra, G. Simiand, A&As, 126, 151-160, (1997).
  7. ↑ The general theory of bolometer performance, R. C. Jones, Journal of the Optical Society of America (1917-1983), 43, 1-+, (1953).
  8. ↑ Cryogenic pre-amplifiers for high resistance bolometers, D., de Angelis, L., de Bernardis, P., et al., Brienza, in Seventh International Workshop on Low Temperature Electronics WOLTE-7, ESA-WPP-264283, (2006).
  9. ↑ Analytical approach to optimizing alternating current biasing of bolometers, A. Catalano, A. Coulais, J.-M. Lamarre, Appl. Opt., 49, 5938--5946, (2010).

(Planck) High Frequency Instrument

Readout Electronic Unit

Junction Field Elect Transistor

Pre_Amplification Unit

Noise Equivalent Power

analog to digital converter

Data Processing Unit

European Space Agency

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