HFI spectral response data processing

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HFI(Planck) High Frequency Instrument spectral response pre-flight spectral characterization data processing and Fourier transformation

The bolometer signal is stored within the initial database in several formats: raw ADU, signal voltage, resistance, current, temperature, total power, electrical power, and radiant power, all of which may be exported as a function of sample time. A bolometer model was applied to the raw data to produce interferograms in units of absorbed optical power. This both reduced the in-band effects of detector nonlinearities, and allowed another comparison of optical efficiency to complement the EFF tests. The location of Zero Optical Path Difference (ZPD) is estimated for each interferogram, and the interferogram boundaries are determined as the mid-points between subsequent interferograms, less a small number of buffer points ([math]\sim[/math]10) to ensure that the extracted interferograms include regions associated with the FTS stage travel having constant velocity while excluding the acceleration regions. Visual verification of the extracted interferograms is performed prior to subsequent processing and averaging to ensure that each ZPD was identified correctly, and to remove any low-quality interferograms. The overlap of the extracted interferograms is also verified visually. Once interferograms have been extracted from each data set, the overall spectral resolution is evaluated and an evenly sampled Optical Path Difference (OPD) grid onto which each interferogram in the combined data is then interpolated is generated. This ensures that each individual interferogram is sampled at ZPD and that each spectrum has identical frequency sampling and can thus be averaged together. An example of a combined interferogram data set is illustrated in the figure below where the central portions of the recorded interferograms are shown.

Sample interferograms for HFI(Planck) High Frequency Instrument-bc00.

The Maximum Path Difference (MPD) value for each detector, and corresponding spectral resolution, is shown in the figure below

Maximum OPD and Spectral Resolution for each HFI(Planck) High Frequency Instrument detector.

In preparation for Fourier transformation, a low-order polynomial baseline removal is performed on the individual interferograms. Consequently, no information can be recovered from the spectrum below [math]\sim 0.1~\mbox{cm}^{-1}[/math], but this is of no concern as this region of the spectrum is replaced by a waveguide fit in the final data product (see HFI detector feedhorn model parameters section). An average interferogram is determined and used to identify glitches for removal from the interferogram data. Following glitch removal, individual interferograms undergo standard Fourier data processing. The modified Norton-Beer 1.5 apodization function[1] has been selected to be used for the final spectral transmission profile data set as it represents a good compromise between the desired ILSInstrument Line Shape sidelobe reduction and improved S/N with marginal reduction in spectral resolution. Data averaging is then performed in the spectral domain. The uncertainty for every spectral data point is determined statistically through the standard deviation at a given frequency. A check for poor quality spectra is performed by comparing the overall standard deviation including and excluding any given spectrum. An example of the individual spectra and uncertainty for bc00 is shown in the figure below, along with the corresponding S/N of the reference bolometer spectrum. An estimate of the spectral S/N for each detector is obtained using the average spectrum and its statistical uncertainty, averaged across the in-band region of the spectrum.

Spectrum and S/N for the bc=00 channel and S/N for the reference bolometer.

The averaged spectra are then normalized and divided by a (normalized) reference bolometer spectrum (see Reference bolometer spectra and HFI reference bolometer sections) to obtain the HFI(Planck) High Frequency Instrument detector relative spectral response.

Properties of HFI(Planck) High Frequency Instrument Detector Spectra

Band (GHz) bc # Ifgm. # Spec. MPD (cm) ILSInstrument Line Shape[math]_{\mbox{FWHM}}[/math] (cm[math]^{-1}[/math]) avg. S/N
100 00 96 93 29.648639 0.020355066 104.70555
100 01 96 95 29.648639 0.020355066 203.34226
100 20 96 96 29.649801 0.020354268 271.38262
100 21 95 94 29.650962 0.020353471 264.65385
100 40 96 94 29.652124 0.020352674 432.40921
100 41 96 96 29.652124 0.020352674 962.98064
100 80 95 95 29.650962 0.020353471 262.71036
100 81 96 96 29.650962 0.020353471 227.35782
143 02 96 95 29.652124 0.020352674 434.93136
143 03 96 96 29.652124 0.020352674 458.86741
143 10 95 95 29.652124 0.020352674 565.21311
143 30 92 92 29.653286 0.020351876 424.53824
143 31 92 92 29.652124 0.020352674 447.50343
143 42 92 92 29.652124 0.020352674 536.23423
143 50 96 96 29.652124 0.020352674 441.68983
143 51 96 96 29.652124 0.020352674 476.22684
143 60 96 96 29.652124 0.020352674 517.43269
143 70 95 94 29.652124 0.020352674 326.06542
143 82 96 96 29.652124 0.020352674 454.23293
143 83 96 96 29.652124 0.020352674 439.50612
217 04 96 96 29.652124 0.020352674 625.92713
217 11 96 96 29.652124 0.020352674 580.32904
217 12 67 67 29.663741 0.020344703 549.24264
217 22 96 96 29.652124 0.020352674 550.65242
217 43 95 95 29.652124 0.020352674 616.57750
217 44 96 96 29.652124 0.020352674 543.78288
217 52 95 94 29.652124 0.020352674 684.91039
217 61 92 92 29.652124 0.020352674 594.70296
217 62 95 95 29.652124 0.020352674 579.69385
217 71 96 96 29.652124 0.020352674 631.30065
217 72 96 96 29.652124 0.020352674 687.10844
217 84 92 92 29.652124 0.020352674 636.36790
353 05 55 55 29.651916 0.020352816 354.15815
353 13 57 57 29.651916 0.020352816 319.09858
353 23 55 55 29.651916 0.020352816 218.05772
353 24 64 64 29.651916 0.020352816 236.44464
353 32 56 56 29.651916 0.020352816 238.40018
353 33 55 55 29.651916 0.020352816 219.60443
353 45 64 64 29.653078 0.020352019 246.97889
353 53 57 57 29.651916 0.020352816 225.27621
353 54 57 57 29.651916 0.020352816 228.47058
353 63 57 56 29.651916 0.020352816 140.16991
353 64 55 55 29.651916 0.020352816 158.85037
353 85 57 57 29.653078 0.020352019 246.18460
545 14 63 63 29.654240 0.020351221 448.67624
545 34 64 64 29.654240 0.020351221 481.87111
545 55 57 57 29.654240 0.020351221 328.07835
545 73 57 57 29.654240 0.020351221 447.49901
857 25 64 64 29.653078 0.020352019 501.25106
857 35 64 64 29.654240 0.020351221 567.55125
857 65 42 42 29.653078 0.020352019 482.41906
857 74 64 64 29.654240 0.020351221 491.89133

References

  1. Apodizing functions for Fourier transform spectroscopy, D. A. Naylor, M. K. Tahic, J. Opt. Soc. Am. A, 24, 3644--3648, (2007).