Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...
Planck Pre-Launch Status Papers - APC - Université Paris Diderot ... Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...
of frequencies and shown to have polarization properties stableenough to be a calibrator for polarization experiments.Dedicated observations of this source were done by IRAM at89 GHz (Aumont et al. 2010). The impact of an approximateknowledge of the polarization sky calibrator leads to a uniformerror over the focal plane. In this case, the ω and ɛ parameters donot depend on the detector. From Eqs. (25)−(36), we found thatthe intensity does not leak into polarization with polarization efficiencyand orientation errors (∆ IQ =∆ IU = 0) and⎛ ⎞000∆ ρ s = ⎜⎝0 ɛ 000ɛ⎟⎠ s for polarization efficiency, (38)C. Rosset et al.: Planck-HFI: polarization calibration⎛⎞0 0 0∆ α s = ⎜⎝0 cos2ω sin 2ω ⎟⎠ s for orientation. (39)0 − sin 2ω cos 2ωIn terms of power spectra, an error in polarization efficienciesonly affects the amplitude of the E and B power spectra but doesnot result in leakage from E to B. Ontheotherhand,anerrorin orientations mixes Q and U maps resulting in both a leakagefrom E into B (as well as B into E) andamodificationofEand B amplitudes. However, as the E-mode signal is far abovethat of the B-mode in amplitude, ∆C l is dominated by E-modeto second order:∆C X l = 2ɛCX l + 4ω2 C E l , (40)for X either E or B-mode.Consequently, for E-mode, the polarization efficiency uncertaintymust be ɛ
A&A 520, A13 (2010)Fig. 7. ∆C l in rms due to polarization efficiency errors from 0.1% to 4%for E-mode (top) andB-mode (bottom) comparedtoinitialspectrum(solid black lines). Cosmic variance for E-mode is plotted in dashedblack line.Fig. 5. Distribution of ∆C EEl(top) and∆C BBl(bottom) forσ ω = 1 ◦ orientationerrors for multipoles l = 10, l = 100, l = 500, normalized totheir rms (red line).Fig. 8. ∆C l in rms due to various orientation errors from 0.25 to2degreesforE-mode (top) andB-mode (bottom) comparedtoinitialspectrum (solid black lines). Cosmic variance for E-mode is plotted indashed black line.Fig. 6. ∆C l in rms due to gain errors from 0.01% to 1% for E-mode(top) andB-mode (bottom) comparedtoinitialspectrum(solid blacklines). Cosmic variance for E-mode is plotted in dashed black line.we want to target, for a multipole range from l = 2to100.Withsuch an hypothesis, we find that the gain precision should bebetter than 0.05% and the orientations of the bolometers shouldbe known to better than 0. ◦ 75. The leakage due to polarizationefficiency into B-mode is very small (see bottom plot in Fig. 7),thus the constraint on the polarization efficiency determinationis not relevant in that case (we found 10%).7. Ground measurementsThe Planck-HFI polarization calibration on ground was dividedinto two parts: polarization efficiencies were measuredfor each detector separately, before focal plane assembly, at theUniversity of Wales in Cardiff in 2005, while orientations ofthe PSBs with respect to the focal plane were measured duringthe overall calibration of the Planck HFI in the Saturne cryostatat Orsay, France, in 2006.7.1. Polarization efficiency ground measurementsDetector-level polarization efficiency measurements were performedin a 2-stage adiabatic demagnetization refrigerator(ADR) at a base temperature of 200 mK. The ADR was configuredto take six detectors per cooldown (in most cases allof the same optical band per cooldown). Thermal blocking filterswere used at the 4 K, 77 K and 300 K stages of thetestbed. The anti-reflective coating on the cryostat window wasmatched to the optical band under test. The window, of 125 mmdiameter, and all the thermal blockers were sized such that theyfilled the beams. The polarization source was a rotating polarizergrid positioned over an extended temperature-controlledblack body source of 75 mm diameter running at 126 ◦ C. Thefinal source aperture was 70 mm indiameter.Themechanicalstructure of the source was fully clad with non-rotatingEccosorb (type AN-72). The source was positioned approximately690 mm from the cryostat window, tilted 4. ◦ 8off the opticalaxis, and mechanically chopped at 6 Hz. The experimentalsetup was fully surrounded with Eccosorb (type AN-72) whilethe data were recorded. Data wererecordedinastepandsamplefashion over five full rotations of the polarizer grid with a 4 ◦ stepsize and a 4 s integration time.Detailed results are given in the appendix in Tables B.1and B.2 for PSBs and SWBs, respectively. The polarization efficiencyof the SWBs is low, as expected, and range between 1.6%and 8.6%. The statistical error is typically 0.5%, and as muchas 1.8% for one SWB. The polarization efficiency of the PSBsis typically around 90%, ranging from 84% to 96%, with errorsbelow 0.3%.Page 8 of 12
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of frequencies and shown to have polarization properties stableenough to be a calibrator for polarization experiments.Dedicated observations of this source were done by IRAM at89 GHz (Aumont et al. 2010). The impact of an approximateknowledge of the polarization sky calibrator leads to a uniformerror over the focal plane. In this case, the ω and ɛ parameters donot depend on the detector. From Eqs. (25)−(36), we found thatthe intensity does not leak into polarization with polarization efficiencyand orientation errors (∆ IQ =∆ IU = 0) and⎛ ⎞000∆ ρ s = ⎜⎝0 ɛ 000ɛ⎟⎠ s for polarization efficiency, (38)C. Rosset et al.: <strong>Planck</strong>-HFI: polarization calibration⎛⎞0 0 0∆ α s = ⎜⎝0 cos2ω sin 2ω ⎟⎠ s for orientation. (39)0 − sin 2ω cos 2ωIn terms of power spectra, an error in polarization efficienciesonly affects the amplitude of the E and B power spectra but doesnot result in leakage from E to B. Ontheotherhand,anerrorin orientations mixes Q and U maps resulting in both a leakagefrom E into B (as well as B into E) andamodificationofEand B amplitudes. However, as the E-mode signal is far abovethat of the B-mode in amplitude, ∆C l is dominated by E-modeto second order:∆C X l = 2ɛCX l + 4ω2 C E l , (40)for X either E or B-mode.Consequently, for E-mode, the polarization efficiency uncertaintymust be ɛ
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