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| − | The inversion of HFI data requires that one knows how the instrument selects photons, how these photons are transformed in data transmitted by telemetry and what spurious signals are added in this process.
| + | This section is intended to provide an overview of the instrument and of its different sub-systems. Two papers that include and detail this information are available: {{PlanckPapers|lamarre2010}} and {{PlanckPapers|planck2011-1-5}}. Additional detailed information potentially useful for the use of the HFI data is included into this section or annexed to it. |
| − | [[Category:Instruments]]
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| | | | |
| − | ==HFI high level description and Architecture==
| + | [[Image:HFI_2_4_1_JML_TheElectronicsAndServiceModule.png|thumb|500px|center|HFI electronics in the satellite]] |
| | | | |
| − | <span style="color:red">(Lamarre/Pajot)</span>
| + | The HFI instrument is designed around 52 bolometers. Twenty of the bolometers (spider-web bolometers or SWBs) are sensitive to total power, and the remaining 32 units are arranged in pairs of orthogonally-oriented polarisation-sensitive bolometers (PSBs). All bolometers are operated at a temperature of ~0.1 K by mean of a space qualified dilution cooler coupled with a high precision temperature control system. A 4He-JT provides an active cooling for 4 K stages using vibration controlled mechanical compressors to prevent excessive warming of the 100 mK stage and minimize microphonic effects in the bolometers. Bolometers and sensitive thermometers are read using AC-bias scheme through JFET amplifiers operated at ~130 K that provide high sensitivity and low frequency stability. The HFI covers six bands centered at 100, 143, 217, 353, 545 and 857 GHz, thanks to a thermo-optical design consisting of three corrugated horns and a set of compact reflective filters and lenses at cryogenic temperatures. |
| − | The HFI instrument is designed around | |
| − | 52 bolometers. Twenty | |
| − | of the bolometers (spider-web bolometers or SWBs) are sensitive | |
| − | to total power, and the remaining 32 units are arranged in | |
| − | pairs of orthogonally-oriented polarisation-sensitive bolometers | |
| − | (PSBs). All bolometers are operated at a temperature of ∼0.1 K by mean of a space qualified dilution cooler | |
| − | coupled with a high precision temperature control system. | |
| − | A 4He-JT provides an active cooling for 4 K stages using vibration controlled mechanical compressors | |
| − | to prevent excessive warming of the 100 mK stage | |
| − | and minimize microphonic effects in the bolometers. | |
| − | Bolometers and sensitive thermometers are read using AC-bias scheme through JFET amplifiers operated | |
| − | at ∼130 K that provide high sensitivity | |
| − | and low frequency stability. The HFI covers six bands centered at 100, 143, 217, 353, 545 and 857 GHz, thanks to a thermo-optical design consisting of three corrugated horns | |
| − | and a set of compact reflective filters and lenses at cryogenic temperatures. | |
| | | | |
| − | ==Cryogenics==
| + | [[Image:HFI_horns.jpg|thumb|500px|center|The HFI focal plane optics and 4K thermo-mechanical stage]] |
| − | <span style="color:red">(F .Pajot)</span>
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| − | ===Dilution===
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| | | | |
| − | The HFI 3He-4He dilution cooler produces temperatures of 0.1 K for the bolometers through | + | The whole satellite is organized to provide thermal transitions between its warm part exposed to the sun and earth radiation, and the focal plane instruments that include the cold receivers (Sections [[HFI_cold_optics|HFI cold optics]] and [[HFI_detection_chain|HFI cold optics]]). The various parts of the HFI are distributed among three different stages of the satellite in order to provide each sub-system an optimal operating temperature. The "warm" parts, including nearly all the electronics and the sources of fluids of the 4K and 0.1K coolers, are attached and thermally linked to the service module of the satellite. The first stage of the preamplifiers is attached to the back of the passively cooled telescope structure. The focal plane unit is attached to the 20K stage cooled by the sorption cooler. This is detailed in Section [[HFI_detection_chain|HFI detection chain]]. |
| − | the dilution of 3He into 4He and 1.4 K through JT expansion of the 3He and 4He mixture. The | |
| − | dilution cooler is described in detail in section 2.3.3 of {{PEarly|2|page=7}}.
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| − | The dilution was operated with flows set to the minimum available values, and provided a total
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| − | lifetime of 30.5 months, exceeding the nominal lifetime of 16 months by 14.5 months. The
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| − | dilution stage was stabilized by a PID control with a regulating power between 20 and 30 nW
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| − | providing a temperature close to 101 mK. The bolometer plate was stabilized at 102.8 mK with a
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| − | PID regulating power around 5 nW. The cooling power values were in very good agreement with those obtained during the ground tests and calibration.
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| − | However, the cosmic particles interactions with the 100 mK stages induced temperature fluctuations and glitches on the thermometers measurements.
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| − | The decorrelation of 100 mK bolometer stage temperatures fluctuations from the bolometers signals is described in section 4.4.2.
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| | | | |
| − | [[File:HFI_2_4_1_100mK_stability.png|500px|100 mK stages temperatures during the mission]]
| + | The telescope and horns select the geometrical origin of photons. They provide a high transmission efficiency to photons inside the main beam, while photons coming from the intermediate and far-side lobes have very low probability of being detected. This essential characteristics is known by a complex process mixing ground measurements of components (horns, reflectors), modeling the shape of the far side lobes, and measuring in-flight bright sources, especially planets. |
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| − | (here a few lines of 100 mK boloplate stability)
| + | The filters and bolometers define the spectral responses and absolute optical efficiency, that are known mostly from ground based measurements performed at component, sub-system and system levels reported in this document. The relations between spectral response and geometrical response are also addressed. |
| | | | |
| − | [[File:HFI_2_4_1_1_6K_stability.png|500px|1.6K stage temperatures during the mission]]
| + | Photons absorbed by a bolometer include the thermal radiation emitted by the various optical devices: telescope, horns and filters. They are transformed in heat that propagates to the bolometer thermometer and influence its temperature which is itself measured by the readout electronics. Temperatures of all these items must be stable enough not to contaminate the scientific signal delivered by the bolometers. How this stability is reached is described in Section [[HFI_cryogenics|HFI cryogenics]]. |
| | | | |
| − | Detailed analysis of the in-flight stability of the
| + | The bolometer temperature depends also on the temperature of the bolometer plate, on the intensity of the biasing current and on any spurious inputs, such as cosmic rays and mechanical vibrations. Such systematics are included in a list discussed in Section [[HFI-Validation|HFI Validation]]. |
| − | dilution cooler can be found in section
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| − | 5.4 of {{PEarly|2|page=23}}.
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| | | | |
| − | === 4K J-T cooler ===
| + | Since the bolometer thermometer is part of an active circuitry that also heats it, the response of this system is complex and has to be considered as a whole. In addition, due to the modulation of the bias current and to the sampling of the data, the response signal of the instrument when scanning a point source is still more complex. Item in Sub-Section [[HFI_detection_chain#Time_response|Time_response]] and Annex [[HFI_time_response_model|HFI time response model]] dedicated to the description of this time response. |
| | | | |
| − | The HFI 4K J-T cooler produces a temperature of
| + | [[Image:HFI_2_4_1_JML_SignalFormation.png|thumb|500px|center|HFI signal formation]] |
| − | 4K for the HFI 4K stage and optics and the
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| − | precooling of the dilution gases. Full
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| − | description of the 4K cooler can be found in
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| − | in section 2.3.2 of {{PEarly|2|page=7}}.
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| | | | |
| − | The 4K cooler was operated without interruption
| + | Logic of the formation of the signal in HFI. This is an idealized description of the physics that takes place in the instrument. The optical power that is absorbed by the bolometers comes from the observed sky and from the instrument itself. The bolometers and readout electronics, acting as a single and complex chain, transform this optical power in data that is compressed and transmitted for science data reduction. |
| − | during all the survey phase of the mission. It is
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| − | still in operation as it also provides the
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| − | cooling of the optical reference loads of the
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| − | LFI. The 4K PID stabilizing the temperature of
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| − | the HFI optics is regulated at 4.81 K using a | |
| − | power around 1.8 mW. | |
| | | | |
| − | [[File:HFI_2_4_1_4K_stability.png|500px|4K stage temperatures during the mission]]
| + | <div style="clear: both"></div> |
| − | | + | == References == |
| − | (here a few lines of 4K stability, including compressors operation)
| + | <references /> |
| − | | + | [[Category:HFI design, qualification and performance|000]] |
| − | Details on the in-flight performance of the
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| − | 4K J-T cooler can be found in in section
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| − | 5.3 of {{PEarly|2|page=21}}.
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| − | | |
| − | | |
| − | | |
| − | == Cold optics ==
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| − | <span style="color:red">(Lamarre)</span> | |
| − | === Horns,lenses=== | |
| − | links to Peter's paper
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| − | === filters, band===
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| − | Includes Locke's very detailed document.
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| − | | |
| − | == Detection chain ==
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| − | <span style="color:red">(Francesco Piacentini)</span> | |
| − | === Bolometers===
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| − | | |
| − | (notes by Alain: take from DOC file (50 Mo) from Francesco, email 15 Oct 2012 17:39:03)
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| − | | |
| − | The heart of the HFI - the detectors - are bolometers, solid-state devices in which the
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| − | incoming radiation dissipates its energy as heat that increases the temperature of a
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| − | thermometer. The instrument Flight Model total number of bolometers is 52, split into 6
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| − | channels at central frequencies of 100, 143, 217, 353, 545, and 857GHz.
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| − | | |
| − | Thirty two of these bolometers are polarization sensitive allowing a map of the CMB polarisation to be built.
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| − | | |
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| − | 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.
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| − | | |
| − | | |
| − | The detectors are semi-conducting NTD thermistor bolometers. There are two kinds of detector modules:
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| − | | |
| − | * SWB, spider web bolometers, are mounted on an absorbing spider-web of metallised silicon nitride
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| − | * PSB, polarization sensitive bolometers, are mounted or on a parallel absorbing grid of metallised silicon nitride.
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| − | | |
| − | | |
| − | In the spider-web bolometers, or SWBs (Bock et al. 1995; Mauskopf et al. 1997), the absorbers consist of metallic grids
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| − | deposited on a Si3 N4 substrate in the shape of a spider web.
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| − | The mesh design and the impedance of the metallic layer are
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| − | adjusted to match vacuum impedance and maximize the absorption of millimeter waves, while minimizing the cross section to
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| − | particles. The absorber is designed to offer equal impedance to
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| − | any linearly polarised radiation. Nevertheless, the thermometer
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| − | and its electrical leads define a privileged orientation (Fig. SWB) that
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| − | makes the SWBs slightly sensitive to polarisation, as detailed in
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| − | (Rosset et al. 2010). The thermometers are
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| − | made of neutron transmuted doped (NTD) germanium (Haller
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| − | et al. 1996), chosen to have an impedance of about 10 MΩ at
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| − | their operating temperature.
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| − | | |
| − | | |
| − | [[File:HFI_2_4_1_FPiacentini_bolo1.png|500px| | |
| − | ((Illustration 6)): Picture of a spider web bolometer. This a 143 GHz module, The temperature sensor is at the center of the absorbing grid]]
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| − | | |
| − | | |
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| − | The absorber of PSBs is a rectangular grid (Fig. PSB) with metallization in one direction (Jones et al.
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| − | 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
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| − | beams collected by a given horn are typically less than −30 dB of
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| − | the peak. The differences in the spectral responses of a PSB pair
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| − | also proved to be a few percent in the worst case. Each pair
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| − | of PSBs sharing the same horn is able to measure the intensity
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| − | Stokes parameter and the Q parameter associated with its local
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| − | frame. An associated pair of PSBs rotated by 45◦ scans exactly
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| − | the same line (if the geometrical alignment is perfect), providing
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| − | the U Stokes parameter.
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| − | | |
| − | | |
| − | [[File:HFI_2_4_1_FPiacentini_bolo2.png|500px|
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| − | Picture of a polarization sensitive bolometer. This a 217 GHz module, The temperature sensor is at the an edge of the absorbing grid]]
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| − | The detectors operate at a temperature close to 100 mK, while the filters are distributed on the 100mK, 1.6 K,
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| − | and 4 K stages in such a way that the heat load on the coldest stages is minimized to
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| − | limit the heat load on the detectors and to decrease
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| − | 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.
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| − | The HFI Focal Plane Unit accommodates sub-millimiter absorbing
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| − | material in order to decrease the scattering inside it.
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| − | Insert here table 1 from HFI-Early paper http://dx.doi.org/10.1051/0004-6361/201116487http://dx.doi.org/10.1051/0004-6361/201116487
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| − | I report the table as a figure for the moment
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| − | | |
| − | [[File:HFI_2_4_1_FPiacentini_table1.png|500px|to be change into a real table]]
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| − | | |
| − | ===Focal plane layout===
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| − | | |
| − | This section may also go somewhere else, like in optics
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| − | | |
| − | The layout of the detectors in the focal plane is defined to cope with the
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| − | scanning strategy. The HFI horns are positioned at the centre of the focal plane, where the optical
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| − | quality is good enough for the high frequencies. The curvature of
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| − | rows compensates for the distortion of images by the telescope.
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| − | A pair of identical SWB will scan the same circle on the sky to
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| − | provide additional redundancy. Similar horns feeding PSBs are
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| − | 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
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| − | cases except for the 100 GHz horns, a measurement is also done
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| − | 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.
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| − | | |
| − | [[File:HFI_2_4_1_FPiacentini_FocalPlaneLayout.png|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
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| − | left to right.]]
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| − | | |
| − | [[File:HFI_2_4_1_FPiacentini_FocalPlaneGeo.png|500px|Illustration 4: 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.]]
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| − | | |
| − | === Readout===
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| − | [From HFI pre flight paper]
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| − | 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.
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| − | The particular features of the HFI AC bias readout are mainly
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| − | * i)that the cold load resistors were replaced by capacitors because they have no Johnson noise;
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| − | * ii)that the detectors are biased by applying a triangular voltage to the load capacitors
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| − | 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;
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| − | * 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;
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| − | * iv)that the electronic scheme is symmetrical and uses a differential amplification scheme to optimize the immunity to electromagnetic interferences;
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| − | * v)and finally that every parameter of the REU can be set by commands, which
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| − | is made possible by using digital-to-analog and analog-to-digital converters extensively.
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| − | | |
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| − | 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
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| − | 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).
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| − | [[File:HFI_2_4_1_FPiacentini_HFIreadout.png|500px|
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| − | Illustration 6: Organization of the HFI readout. Each row represents a belt. Each belt has 6 channels.]]
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| − | | |
| − | [[File:HFI_2_4_1_FPiacentini_table2.jpeg|500px|Illustration 5: Organization of the HFI readout. Each row represents a belt. Each belt has 6 channels. (to be change into a real table ?)]]
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| − | | |
| − | ===Principles of the readout electronics. ===
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| − | From HFI pre-flight paper
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| − | 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.
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| − | Illustration 6: Principles of readout electronics. The three modules of the chain are shown: JFet Box, Pre-Amplifier
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| − | Unit (PAU) and Readout Electronic Unit (REU).
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| − | Parameters of the Readout Unit can be set to optimize the detectors performance.
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| − | The modulation frequency of the AC bias system, fmod of the square bias current
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| − | can be tuned from 70 Hz to 112 Hz by the telecommand parameters:
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| − | Nsample, which defines the number of samples per half period of modulated signal,
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| − | fdiv which determines the sampling frequency of the ADC.
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| − | The optimal frequencies are around 90 Hz.
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| − | Each channel has its own settings for the following parameters:
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| − | I-bias, amplitude of the triangular bias voltage;
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| − | T-bias, amplitude of the transient bias voltage;
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| − | V-bal, amplitude of the square compensation voltage;
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| − | G-amp, value of the programmable gain of the REU [1/3, 1, 3, 7.6];
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| − | | |
| − | N-blank, number of blanked samples at the beginning of halfperiod not taken into account during integration of the signal;
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| − | | |
| − | S-phase, phase shift when computing the integrated signal.
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| − | | |
| − | All these parameters influence the effective response of the
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| − | detection chains, and were optimized during the calibration
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| − | campaigns and confirmed during the calibration and performance
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| − | verification (CPV) phase following the launch of
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| − | Planck. The scientific signal is provided by the integral of the
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| − | signal on each half-period, between limits fixed by the S-phase
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| − | and N-blank parameters.
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| − | | |
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| − | The interaction of modulated readout electronics with semiconductor
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| − | bolometers is rather different from that of a classical
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| − | DC bias readout (Jones 1953). The differences were seen during
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| − | the calibration of the HFI, although the readout electronics
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| − | was designed to mimic the operation
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| − | of a DC biased bolometric system as far as possible. With the
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| − | AC readout the maximum of responsivity is lower and is obtained
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| − | for higher bias current in the bolometer with respect to the DC model.
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| − | This is caused by the stray capacitance in the
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| − | wiring which has negligible effects for a DC bias and a major
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| − | effect for an AC bias. In our case, a stray capacitance of 150 pF
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| − | induces increases of NEP ranging from 4% (857 GHz bolometers)
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| − | to 10% (100 GHz bolometers) and also affects the HFI time
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| − | response. Details of the effect of the HFI AC bias system into
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| − | the time response of the detectors are discussed in the Time Response Section [link].
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| − | | |
| − | [Here I suggest to copy the wiki post with in flight setting of parameters http://wiki.planck.fr/index.php/Proc/HFIstatehttp://wiki.planck.fr/index.php/Proc/HFIstate Or a table with the physical values. I have an excel file prepared by F-X Desert]
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| − | === JFETs===
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| − | Taken from pre-flight paper
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| − | 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. 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.
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| − | 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%.
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| − | === Data compression===
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| − | === Time response.===
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| − | 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.
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| − | | |
| − | 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]]).
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| − | 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>.
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| − | | |
| − | <math>\label{LFER4def}TF^{LFER4}(\omega) = F(\omega) H'(\omega)</math>
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| − | | |
| − | === LFER4 model ===
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| − | If we write the input signal (power) on a bolometer as <math>\label{bol_in}
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| − | s_0(t)=e^{i\omega t}
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| − | </math> the bolometer physical impedance can be written as: <math>\label{bol_out}
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| − | s(t)=e^{i\omega t}F(\omega)
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| − | </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}
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| − | F(\omega) = \sum_{i=0,4} \frac{a_i}{1 + i\omega\tau_i}
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| − | </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}
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| − | 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)}
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| − | </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}
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| − | \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]
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| − | </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>.
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| − | | |
| − | After integration, the <math>n</math>-sample of a bolometer can be written as <math>\label{eqn:output}
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| − | Y(t_n) = (-1)^n F(\omega) H'(\omega) e^{i t_n \omega}
| |
| − | </math> where <math>\label{tfele}
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| − | 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)
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| − | \Bigg]
| |
| − | </math>
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| − | | |
| − | 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)
| |
| − | </math>
| |
| − | | |
| − | 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.
| |
| − | | |
| − | === 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"
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| − | |+HFI electronics filter sequence. We define $s = i \omega$
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| − | |-
| |
| − | ! style="border-style: solid; border-width: 1px"|Filter
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| − | ! style="border-style: solid; border-width: 1px"|Parameters
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| − | ! style="border-style: solid; border-width: 1px"|Function
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| − | |-
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| − | |style="border-style: solid; border-width: 1px"|0. Stray capacitance low pass filter
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| − | |style="border-style: solid; border-width: 1px"|<math>\tau_{stray}= R_{bolo} C_{stray}</math>
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| − | |style="border-style: solid; border-width: 1px"|<math>h_0 = \frac{1}{1.0+\tau_{stray}*s}</math>
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|1. Low pass filter
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| − | |style="border-style: solid; border-width: 1px"|<math>R_1=1</math>k<math>\Omega</math> <br /> <math>C_1=100</math>nF
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| − | |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>
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|2. Sallen Key high pass filter
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| − | |style="border-style: solid; border-width: 1px"|<math>R_2=51</math>k<math>\Omega</math><br /> <math>C_2=1\mu</math>
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| − | |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
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|3. Sign reverse with gain
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| − | |style="border-style: solid; border-width: 1px"|
| |
| − | |style="border-style: solid; border-width: 1px"|<math>h_3=-5.1</math>
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| − | |-
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| − | |style="border-style: solid; border-width: 1px"|4. Single pole low pass filter with gain
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| − | |style="border-style: solid; border-width: 1px"|<math>R_4=10</math>k<math>\Omega</math><br /> <math>C_4=10</math>nF
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| − | |style="border-style: solid; border-width: 1px"|<math>h_4= \frac{1.5}{1.0+R_4*C_4*s}</math>
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|5. Single pole high pass filter coupled to a Sallen Key low pass filter
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| − | |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>
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| − | |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 +
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| − | s^2*K_2+
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| − | s*K_1 + R_{12}*R_9 } </math>
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| − | | |
| − | |}
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| − | | |
| − | | |
| − | | |
| − | {| class="wikitable" style="text-align: left; align: center; border-collapse: collapse; border-width: 1px; border-style: solid; border-color: #000"
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| − | |+ Parameters for LFER4 model.
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|Bolometer
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| − | |style="border-style: solid; border-width: 1px"|<math>A_1</math>
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| − | |style="border-style: solid; border-width: 1px"|<math>\tau_1</math> (s)
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| − | |style="border-style: solid; border-width: 1px"|<math>A_2</math>
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| − | |style="border-style: solid; border-width: 1px"|<math>\tau_2</math> (s)
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| − | |style="border-style: solid; border-width: 1px"|<math>A_3</math>
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| − | |style="border-style: solid; border-width: 1px"|<math>\tau_3</math> (s)
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| − | |style="border-style: solid; border-width: 1px"|<math>A_4</math>
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| − | |style="border-style: solid; border-width: 1px"|<math>\tau_4</math> (s)
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| − | |style="border-style: solid; border-width: 1px"|<math>\tau_{stray}</math> (s)
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| − | |style="border-style: solid; border-width: 1px"|<math>S_{phase}</math>
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| − | |-
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| − | |style="border-style: solid; border-width: 1px"|100-1a
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| − | |style="border-style: solid; border-width: 1px"|0.392
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| − | |style="border-style: solid; border-width: 1px"|0.01
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| − | |style="border-style: solid; border-width: 1px"|0.534
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| − | |style="border-style: solid; border-width: 1px"|0.0209
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| − | |style="border-style: solid; border-width: 1px"|0.0656
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| − | |style="border-style: solid; border-width: 1px"|0.0513
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| − | |style="border-style: solid; border-width: 1px"|0.00833
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| − | |style="border-style: solid; border-width: 1px"|0.572
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| − | |style="border-style: solid; border-width: 1px"|0.00159
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| − | |style="border-style: solid; border-width: 1px"|0.00139
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| − | |-
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| − | |style="border-style: solid; border-width: 1px"|100-1b
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| − | |style="border-style: solid; border-width: 1px"|0.484
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| − | |style="border-style: solid; border-width: 1px"|0.0103
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| − | |style="border-style: solid; border-width: 1px"|0.463
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| − | |style="border-style: solid; border-width: 1px"|0.0192
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| − | |style="border-style: solid; border-width: 1px"|0.0451
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| − | |style="border-style: solid; border-width: 1px"|0.0714
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| − | |style="border-style: solid; border-width: 1px"|0.00808
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| − | |style="border-style: solid; border-width: 1px"|0.594
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| − | |style="border-style: solid; border-width: 1px"|0.00149
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| − | |style="border-style: solid; border-width: 1px"|0.00139
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| − | |-
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| − | |style="border-style: solid; border-width: 1px"|100-2a
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| − | |style="border-style: solid; border-width: 1px"|0.474
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| − | |style="border-style: solid; border-width: 1px"|0.00684
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| − | |style="border-style: solid; border-width: 1px"|0.421
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| − | |style="border-style: solid; border-width: 1px"|0.0136
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| − | |style="border-style: solid; border-width: 1px"|0.0942
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| − | |style="border-style: solid; border-width: 1px"|0.0376
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| − | |style="border-style: solid; border-width: 1px"|0.0106
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| − | |style="border-style: solid; border-width: 1px"|0.346
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| − | |style="border-style: solid; border-width: 1px"|0.00132
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| − | |style="border-style: solid; border-width: 1px"|0.00125
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| − | |-
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| − | |style="border-style: solid; border-width: 1px"|100-2b
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| − | |style="border-style: solid; border-width: 1px"|0.126
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| − | |style="border-style: solid; border-width: 1px"|0.00584
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| − | |style="border-style: solid; border-width: 1px"|0.717
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| − | |style="border-style: solid; border-width: 1px"|0.0151
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| − | |style="border-style: solid; border-width: 1px"|0.142
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| − | |style="border-style: solid; border-width: 1px"|0.0351
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| − | |style="border-style: solid; border-width: 1px"|0.0145
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| − | |style="border-style: solid; border-width: 1px"|0.293
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| − | |style="border-style: solid; border-width: 1px"|0.00138
| |
| − | |style="border-style: solid; border-width: 1px"|0.00125
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|100-3a
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| − | |style="border-style: solid; border-width: 1px"|0.744
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| − | |style="border-style: solid; border-width: 1px"|0.00539
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| − | |style="border-style: solid; border-width: 1px"|0.223
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| − | |style="border-style: solid; border-width: 1px"|0.0147
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| − | |style="border-style: solid; border-width: 1px"|0.0262
| |
| − | |style="border-style: solid; border-width: 1px"|0.0586
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| − | |style="border-style: solid; border-width: 1px"|0.00636
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| − | |style="border-style: solid; border-width: 1px"|0.907
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| − | |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
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| − | |style="border-style: solid; border-width: 1px"|0.608
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| − | |style="border-style: solid; border-width: 1px"|0.00548
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| − | |style="border-style: solid; border-width: 1px"|0.352
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| − | |style="border-style: solid; border-width: 1px"|0.0155
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| − | |style="border-style: solid; border-width: 1px"|0.0321
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| − | |style="border-style: solid; border-width: 1px"|0.0636
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| − | |style="border-style: solid; border-width: 1px"|0.00821
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| − | |style="border-style: solid; border-width: 1px"|0.504
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| − | |style="border-style: solid; border-width: 1px"|0.00166
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| − | |style="border-style: solid; border-width: 1px"|0.00125
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|100-4a
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| − | |style="border-style: solid; border-width: 1px"|0.411
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| − | |style="border-style: solid; border-width: 1px"|0.0082
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| − | |style="border-style: solid; border-width: 1px"|0.514
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| − | |style="border-style: solid; border-width: 1px"|0.0178
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| − | |style="border-style: solid; border-width: 1px"|0.0581
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| − | |style="border-style: solid; border-width: 1px"|0.0579
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| − | |style="border-style: solid; border-width: 1px"|0.0168
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| − | |style="border-style: solid; border-width: 1px"|0.37
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| − | |style="border-style: solid; border-width: 1px"|0.00125
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| − | |style="border-style: solid; border-width: 1px"|0.00125
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|100-4b
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| − | |style="border-style: solid; border-width: 1px"|0.687
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| − | |style="border-style: solid; border-width: 1px"|0.0113
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| − | |style="border-style: solid; border-width: 1px"|0.282
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| − | |style="border-style: solid; border-width: 1px"|0.0243
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| − | |style="border-style: solid; border-width: 1px"|0.0218
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| − | |style="border-style: solid; border-width: 1px"|0.062
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| − | |style="border-style: solid; border-width: 1px"|0.00875
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| − | |style="border-style: solid; border-width: 1px"|0.431
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| − | |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
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| − | |style="border-style: solid; border-width: 1px"|0.00447
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| − | |style="border-style: solid; border-width: 1px"|0.144
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| − | |style="border-style: solid; border-width: 1px"|0.0121
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| − | |style="border-style: solid; border-width: 1px"|0.0293
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| − | |style="border-style: solid; border-width: 1px"|0.0387
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| − | |style="border-style: solid; border-width: 1px"|0.0101
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| − | |style="border-style: solid; border-width: 1px"|0.472
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| − | |style="border-style: solid; border-width: 1px"|0.00142
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| − | |style="border-style: solid; border-width: 1px"|0.00125
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| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|143-1b
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| − | |style="border-style: solid; border-width: 1px"|0.49
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| − | |style="border-style: solid; border-width: 1px"|0.00472
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| − | |style="border-style: solid; border-width: 1px"|0.333
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| − | |style="border-style: solid; border-width: 1px"|0.0156
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| − | |style="border-style: solid; border-width: 1px"|0.134
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| − | |style="border-style: solid; border-width: 1px"|0.0481
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| − | |style="border-style: solid; border-width: 1px"|0.0435
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| − | |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
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| − | |style="border-style: solid; border-width: 1px"|0.909
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| − | |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
| |
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| − | |style="border-style: solid; border-width: 1px"|353-2
| |
| − | |style="border-style: solid; border-width: 1px"|0.747
| |
| − | |style="border-style: solid; border-width: 1px"|0.00309
| |
| − | |style="border-style: solid; border-width: 1px"|0.225
| |
| − | |style="border-style: solid; border-width: 1px"|0.00726
| |
| − | |style="border-style: solid; border-width: 1px"|0.0252
| |
| − | |style="border-style: solid; border-width: 1px"|0.0447
| |
| − | |style="border-style: solid; border-width: 1px"|0.00267
| |
| − | |style="border-style: solid; border-width: 1px"|0.513
| |
| − | |style="border-style: solid; border-width: 1px"|0.00154
| |
| − | |style="border-style: solid; border-width: 1px"|0.00097
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|353-7
| |
| − | |style="border-style: solid; border-width: 1px"|0.448
| |
| − | |style="border-style: solid; border-width: 1px"|0.0009
| |
| − | |style="border-style: solid; border-width: 1px"|0.537
| |
| − | |style="border-style: solid; border-width: 1px"|0.0041
| |
| − | |style="border-style: solid; border-width: 1px"|0.0122
| |
| − | |style="border-style: solid; border-width: 1px"|0.0273
| |
| − | |style="border-style: solid; border-width: 1px"|0.00346
| |
| − | |style="border-style: solid; border-width: 1px"|0.433
| |
| − | |style="border-style: solid; border-width: 1px"|0.00178
| |
| − | |style="border-style: solid; border-width: 1px"|0.00125
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|353-8
| |
| − | |style="border-style: solid; border-width: 1px"|0.718
| |
| − | |style="border-style: solid; border-width: 1px"|0.00223
| |
| − | |style="border-style: solid; border-width: 1px"|0.261
| |
| − | |style="border-style: solid; border-width: 1px"|0.00608
| |
| − | |style="border-style: solid; border-width: 1px"|0.0165
| |
| − | |style="border-style: solid; border-width: 1px"|0.038
| |
| − | |style="border-style: solid; border-width: 1px"|0.00408
| |
| − | |style="border-style: solid; border-width: 1px"|0.268
| |
| − | |style="border-style: solid; border-width: 1px"|0.00177
| |
| − | |style="border-style: solid; border-width: 1px"|0.00111
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|545-1
| |
| − | |style="border-style: solid; border-width: 1px"|0.991
| |
| − | |style="border-style: solid; border-width: 1px"|0.00293
| |
| − | |style="border-style: solid; border-width: 1px"|0.00743
| |
| − | |style="border-style: solid; border-width: 1px"|0.026
| |
| − | |style="border-style: solid; border-width: 1px"|0.00139
| |
| − | |style="border-style: solid; border-width: 1px"| 2.6
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"|0.00216
| |
| − | |style="border-style: solid; border-width: 1px"|0.00111
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|545-2
| |
| − | |style="border-style: solid; border-width: 1px"|0.985
| |
| − | |style="border-style: solid; border-width: 1px"|0.00277
| |
| − | |style="border-style: solid; border-width: 1px"|0.0128
| |
| − | |style="border-style: solid; border-width: 1px"|0.024
| |
| − | |style="border-style: solid; border-width: 1px"|0.00246
| |
| − | |style="border-style: solid; border-width: 1px"| 2.8
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"|0.00187
| |
| − | |style="border-style: solid; border-width: 1px"|0.00097
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|545-4
| |
| − | |style="border-style: solid; border-width: 1px"|0.972
| |
| − | |style="border-style: solid; border-width: 1px"|0.003
| |
| − | |style="border-style: solid; border-width: 1px"|0.0277
| |
| − | |style="border-style: solid; border-width: 1px"|0.025
| |
| − | |style="border-style: solid; border-width: 1px"|0.000777
| |
| − | |style="border-style: solid; border-width: 1px"| 2.5
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"|0.00222
| |
| − | |style="border-style: solid; border-width: 1px"|0.00111
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|857-1
| |
| − | |style="border-style: solid; border-width: 1px"|0.974
| |
| − | |style="border-style: solid; border-width: 1px"|0.00338
| |
| − | |style="border-style: solid; border-width: 1px"|0.0229
| |
| − | |style="border-style: solid; border-width: 1px"|0.025
| |
| − | |style="border-style: solid; border-width: 1px"|0.00349
| |
| − | |style="border-style: solid; border-width: 1px"| 2.2
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"|0.00176
| |
| − | |style="border-style: solid; border-width: 1px"|0.00111
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|857-2
| |
| − | |style="border-style: solid; border-width: 1px"|0.84
| |
| − | |style="border-style: solid; border-width: 1px"|0.00148
| |
| − | |style="border-style: solid; border-width: 1px"|0.158
| |
| − | |style="border-style: solid; border-width: 1px"|0.00656
| |
| − | |style="border-style: solid; border-width: 1px"|0.00249
| |
| − | |style="border-style: solid; border-width: 1px"| 3.2
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"| 0
| |
| − | |style="border-style: solid; border-width: 1px"|0.0022
| |
| − | |style="border-style: solid; border-width: 1px"|0.00125
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|857-3
| |
| − | |style="border-style: solid; border-width: 1px"|0.36
| |
| − | |style="border-style: solid; border-width: 1px"|4.22e-05
| |
| − | |style="border-style: solid; border-width: 1px"|0.627
| |
| − | |style="border-style: solid; border-width: 1px"|0.0024
| |
| − | |style="border-style: solid; border-width: 1px"|0.0111
| |
| − | |style="border-style: solid; border-width: 1px"|0.017
| |
| − | |style="border-style: solid; border-width: 1px"|0.002
| |
| − | |style="border-style: solid; border-width: 1px"| 1.9
| |
| − | |style="border-style: solid; border-width: 1px"|0.00152
| |
| − | |style="border-style: solid; border-width: 1px"|0.00126
| |
| − | |-
| |
| − | |style="border-style: solid; border-width: 1px"|857-4
| |
| − | |style="border-style: solid; border-width: 1px"|0.278
| |
| − | |style="border-style: solid; border-width: 1px"|0.0004
| |
| − | |style="border-style: solid; border-width: 1px"|0.719
| |
| − | |style="border-style: solid; border-width: 1px"|0.00392
| |
| − | |style="border-style: solid; border-width: 1px"|0.00162
| |
| − | |style="border-style: solid; border-width: 1px"|0.09
| |
| − | |style="border-style: solid; border-width: 1px"|0.00152
| |
| − | |style="border-style: solid; border-width: 1px"| 0.8
| |
| − | |style="border-style: solid; border-width: 1px"|0.00149
| |
| − | |style="border-style: solid; border-width: 1px"|0.000558
| |
| − | |}
| |
| − | | |
| − | | |
| − | | |
| − | | |
| − | == System (Ken) ==
| |
| − | ===List of systematics===
| |
| − | | |
| − | {{:HFI-bottom_up}}
| |
| − | | |
| − | ==Summary==
| |
| − | <span style="color:red">(Lamarre)</span>
| |
| − | here remind worse sytematics and point to DPC
| |
| − | Summary of sucess and limitations. JML. Link to early HFI in flight perf.
| |
