HFI spectral response data processing

HFI 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-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 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 #NaylorApod07 has been selected to be used for the final spectral transmission profile data set as it represents a good compromise between the desired ILS 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 detector relative spectral response.

Properties of HFI Detector Spectra

Band (GHz)	bc	# Ifgm.	# Spec.	MPD (cm)	ILS[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