Spectral response

HFI Spectral Response

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This section outlines the unit conversion and colour correction protocol for Planck/HFI. Tables of unit conversion and colour correction coefficients will be included (there is not room for these in the P03d Co-Paper). Some of the checks on the unit conversion and colour correction coefficients will be described here also. Planet colour correction coefficients will be provided here (or perhaps in the joint HFI/LFI section). There will be links to the UcCC subsection of the PLA section, but the numbers and details belong here. The PLA UcCC subsection is primarily to introduce the software tools.

The band-average HFI spectral response data are shown in the figure below, and provided in the RIMO file (here).

Band-average HFI transmission spectra. Vertical bars illustrate the CO rotational transition frequencies.

The integration ranges used in determining the unit conversion and colour correction coefficients are verified through an iterative approach starting at one extreme and reducing to the band-centre for both the low and high frequency edges. The figure below demonstrates the stability in the integral once a sufficient data range has been employed. The range used in the official coefficients is thus sufficient to ensure that it falls within the flat region of the demonstration figure below.

• 

  100 GHz

• 

  143 GHz

• 

  217 GHz

• 

  353 GHz

• 

  545 GHz

• 

  857 GHz

Colour Correction (alpha = -1 to +2) stability with integration cut-off variation. The horizontal bars illustrate the nominal colour correction values. Similar results are found for the integration cut-on.

The band-average spectrum for a given frequency band is derived using a hit-map normalized inverse-square noise weighted detector spectrum average. Thus, the effective band-average spectrum changes depending on the region of sky in question, really the Planck coverage of any sky region. The histograms below demonstrate the variation across the sky of the detector weight coefficients, and thus the validity of using a single band-average spectrum for the entire sky map. Future analysis with the full Planck dataset may require incorporating the variation of the relative detector weights across the sky into understanding the differential spectral transmission between complementary maps (e.g. detset -1 cf. detset-2 maps).

• 

  100 GHz

• 

  143 GHz

• 

  217 GHz

• 

  353 GHz

• 

  545 GHz

• 

  857 GHz

Colour Correction (alpha = -1 to +2) stability with integration cut-off variation. The horizontal bars illustrate the nominal colour correction values. Similar results are found for the integration cut-on.

The following table presents basic characteristics of the HFI detector spectral response, including optical efficiency, effective frequency, etc. Further details on the definition of these parameters are available in #planck2013-p03d.

Properties of HFI detector spectra

Band (GHz)	[math]\nu[/math]cut-on [GHz]	[math]\nu[/math]cut-off [GHz]	BW [GHz]	[math]\nu[/math]cen. [GHz]	[math]\nu[/math]eff. [GHz]	[math]\varepsilon[/math]	[math]\epsilon[/math]Int.	[math]\nu[/math] -1 [GHz]	[math]\nu[/math] +2 [GHz]	[math]\nu[/math] +4 [GHz]
100-1a	84.8 ± 0.5	113.96 ± 0.16	29.1 ± 0.6	99.4 ± 0.3	100.28 ± 0.11	0.419 ± 0.008	0.310 ± 0.008	99.45 ± 0.12	101.93 ± 0.11	103.59 ± 0.10
100-1b	86.5 ± 1.0	115.32 ± 0.08	28.8 ± 1.0	100.9 ± 0.5	100.87 ± 0.11	0.563 ± 0.011	0.324 ± 0.011	100.06 ± 0.11	102.51 ± 0.10	104.18 ± 0.09
100-2a	86.0 ± 0.6	116.4 ± 0.4	30.4 ± 0.9	101.2 ± 0.3	101.34 ± 0.12	0.550 ± 0.012	0.372 ± 0.012	100.38 ± 0.12	103.34 ± 0.11	105.47 ± 0.10
100-2b	84.3 ± 0.5	115.5 ± 0.4	31.3 ± 0.7	99.9 ± 0.3	101.19 ± 0.11	0.634 ± 0.009	0.334 ± 0.009	100.23 ± 0.11	103.14 ± 0.10	105.16 ± 0.09
100-3a	84.21 ± 0.17	117.36 ± 0.06	33.14 ± 0.18	100.78 ± 0.09	101.64 ± 0.12	0.493 ± 0.005	0.331 ± 0.005	100.68 ± 0.12	103.60 ± 0.10	105.60 ± 0.09
100-3b	84.19 ± 0.19	116.81 ± 0.16	32.6 ± 0.2	100.50 ± 0.13	100.63 ± 0.12	0.426 ± 0.004	0.281 ± 0.004	99.74 ± 0.12	102.45 ± 0.11	104.35 ± 0.10
100-4a	84.74 ± 0.07	118.09 ± 0.09	33.34 ± 0.12	101.42 ± 0.05	101.77 ± 0.12	0.461 ± 0.003	0.255 ± 0.003	100.77 ± 0.13	103.82 ± 0.11	105.96 ± 0.10
100-4b	84.9 ± 0.3	118.30 ± 0.05	33.4 ± 0.3	101.58 ± 0.14	101.91 ± 0.13	0.396 ± 0.003	0.258 ± 0.003	100.92 ± 0.13	103.92 ± 0.12	105.98 ± 0.10
100-avg	84.4 ± 0.3	117.36 ± 0.05	32.9 ± 0.3	100.89 ± 0.13	101.31 ± 0.05	0.479 ± 0.003	0.304 ± 0.003	100.36 ± 0.05	103.24 ± 0.05	105.25 ± 0.04
100-detset1	84.77 ± 0.05	117.81 ± 0.06	33.03 ± 0.08	101.29 ± 0.04	101.43 ± 0.07	0.4199 ± 0.0020	0.2645 ± 0.0020	100.49 ± 0.07	103.35 ± 0.06	105.34 ± 0.06
100-detset2	84.3 ± 0.3	117.14 ± 0.05	32.8 ± 0.3	100.72 ± 0.13	101.25 ± 0.06	0.505 ± 0.003	0.321 ± 0.003	100.31 ± 0.06	103.19 ± 0.06	105.21 ± 0.05
143-1a	121.2 ± 0.4	162 ± 2	41 ± 2	141.5 ± 1.1	141.71 ± 0.04	0.66 ± 0.02	0.43 ± 0.02	140.37 ± 0.04	144.48 ± 0.04	147.35 ± 0.03
143-1b	119.99 ± 0.03	162.8 ± 0.7	42.8 ± 0.8	141.4 ± 0.4	142.29 ± 0.04	0.608 ± 0.007	0.347 ± 0.007	140.97 ± 0.04	145.02 ± 0.04	147.79 ± 0.04
143-2a	119.7 ± 0.2	162.76 ± 0.05	43.1 ± 0.2	141.21 ± 0.11	141.79 ± 0.04	0.626 ± 0.003	0.449 ± 0.003	140.42 ± 0.04	144.61 ± 0.04	147.51 ± 0.04
143-2b	119.2 ± 0.4	163.3 ± 0.5	44.1 ± 0.6	141.3 ± 0.3	142.50 ± 0.04	0.619 ± 0.007	0.443 ± 0.007	141.17 ± 0.05	145.21 ± 0.04	148.00 ± 0.04
143-3a	120.2 ± 0.3	158.8 ± 0.4	38.6 ± 0.5	139.5 ± 0.2	140.51 ± 0.05	0.970 ± 0.008	0.539 ± 0.008	139.17 ± 0.05	143.28 ± 0.05	146.09 ± 0.05
143-3b	119.88 ± 0.04	161.3 ± 1.0	41.4 ± 1.0	140.6 ± 0.5	141.63 ± 0.05	0.718 ± 0.012	0.457 ± 0.012	140.28 ± 0.05	144.41 ± 0.04	147.22 ± 0.04
143-4a	118.7 ± 0.2	168.21 ± 0.03	49.5 ± 0.2	143.47 ± 0.12	142.71 ± 0.04	0.532 ± 0.002	0.324 ± 0.002	141.29 ± 0.05	145.61 ± 0.04	148.56 ± 0.04
143-4b	119.0 ± 0.3	161.58 ± 0.04	42.6 ± 0.3	140.27 ± 0.14	142.19 ± 0.05	0.538 ± 0.003	0.339 ± 0.003	140.87 ± 0.05	144.87 ± 0.04	147.59 ± 0.04
143-5	119.9 ± 0.3	166.608 ± 0.016	46.7 ± 0.3	143.28 ± 0.16	144.24 ± 0.04	0.386 ± 0.002	0.305 ± 0.002	142.93 ± 0.04	146.86 ± 0.04	149.48 ± 0.03
143-6	119.97 ± 0.20	166.14 ± 0.04	46.2 ± 0.2	143.06 ± 0.10	143.00 ± 0.04	0.4531 ± 0.0016	0.3128 ± 0.0016	141.66 ± 0.05	145.72 ± 0.04	148.49 ± 0.04
143-7	120.39 ± 0.07	167.5 ± 0.3	47.1 ± 0.3	143.95 ± 0.15	144.46 ± 0.04	0.427 ± 0.002	0.308 ± 0.002	143.14 ± 0.05	147.09 ± 0.04	149.69 ± 0.04
143-8	120.7 ± 0.4	165.59 ± 0.06	44.8 ± 0.4	143.16 ± 0.18	143.55 ± 0.04	0.393 ± 0.002	0.277 ± 0.002	142.18 ± 0.05	146.30 ± 0.04	149.02 ± 0.04
143-avg	119.994 ± 0.018	165.76 ± 0.04	45.76 ± 0.05	142.876 ± 0.018	142.710 ± 0.012	0.5069 ± 0.0007	0.3669 ± 0.0007	141.363 ± 0.012	145.458 ± 0.011	148.235 ± 0.011
143-detset1	120.05 ± 0.03	160.18 ± 0.09	40.13 ± 0.10	140.12 ± 0.05	141.45 ± 0.02	0.7049 ± 0.0017	0.4614 ± 0.0017	140.11 ± 0.02	144.22 ± 0.02	147.05 ± 0.02
143-detset2	118.95 ± 0.08	164.9 ± 0.8	45.9 ± 0.8	141.9 ± 0.4	142.27 ± 0.02	0.507 ± 0.007	0.379 ± 0.007	140.91 ± 0.02	145.05 ± 0.02	147.902 ± 0.019
143-SWBs	120.17 ± 0.03	166.308 ± 0.018	46.14 ± 0.04	143.238 ± 0.017	143.96 ± 0.02	0.3967 ± 0.0006	0.3123 ± 0.0006	142.64 ± 0.02	146.63 ± 0.02	149.282 ± 0.020
217-1	189.0 ± 0.4	251.24 ± 0.05	62.2 ± 0.4	220.14 ± 0.20	222.817 ± 0.016	0.414 ± 0.002	0.322 ± 0.002	221.099 ± 0.016	226.274 ± 0.017	229.76 ± 0.02
217-2	188.66 ± 0.02	253.68 ± 0.02	65.03 ± 0.04	221.169 ± 0.017	223.231 ± 0.018	0.4575 ± 0.0004	0.3624 ± 0.0004	221.430 ± 0.018	226.814 ± 0.018	230.35 ± 0.02
217-3	190.49 ± 0.05	253.174 ± 0.018	62.68 ± 0.06	221.83 ± 0.03	223.116 ± 0.016	0.4125 ± 0.0004	0.3257 ± 0.0004	221.440 ± 0.017	226.458 ± 0.016	229.774 ± 0.019
217-4	190.8 ± 0.4	253.219 ± 0.017	62.4 ± 0.4	222.03 ± 0.18	222.717 ± 0.018	0.4043 ± 0.0018	0.3132 ± 0.0018	221.033 ± 0.018	226.116 ± 0.017	229.55 ± 0.02
217-5a	182.69 ± 0.07	253.2 ± 0.6	70.5 ± 0.6	217.9 ± 0.3	220.421 ± 0.017	0.548 ± 0.003	0.387 ± 0.003	218.489 ± 0.018	224.293 ± 0.017	228.15 ± 0.02
217-5b	182.75 ± 0.06	250.1 ± 0.4	67.3 ± 0.4	216.41 ± 0.19	220.655 ± 0.018	0.621 ± 0.002	0.377 ± 0.002	218.746 ± 0.018	224.465 ± 0.018	228.234 ± 0.020
217-6a	182.284 ± 0.020	253.70 ± 0.02	71.41 ± 0.03	217.991 ± 0.014	220.619 ± 0.018	0.4497 ± 0.0003	0.3019 ± 0.0003	218.705 ± 0.018	224.441 ± 0.018	228.24 ± 0.02
217-6b	182.85 ± 0.04	253.373 ± 0.015	70.52 ± 0.04	218.113 ± 0.019	220.619 ± 0.017	0.5274 ± 0.0004	0.3349 ± 0.0004	218.707 ± 0.017	224.408 ± 0.016	228.109 ± 0.017
217-7a	188.217 ± 0.019	253.88 ± 0.02	65.66 ± 0.03	221.049 ± 0.012	220.766 ± 0.016	0.4299 ± 0.0003	0.3065 ± 0.0003	218.925 ± 0.016	224.458 ± 0.016	228.122 ± 0.018
217-7b	189.22 ± 0.03	250.88 ± 0.02	61.66 ± 0.04	220.054 ± 0.018	220.332 ± 0.018	0.4371 ± 0.0003	0.2776 ± 0.0003	218.468 ± 0.018	224.055 ± 0.018	227.718 ± 0.019
217-8a	181.98 ± 0.02	253.722 ± 0.018	71.74 ± 0.03	217.852 ± 0.013	220.510 ± 0.018	0.5282 ± 0.0003	0.3768 ± 0.0003	218.544 ± 0.019	224.432 ± 0.018	228.32 ± 0.02
217-8b	181.875 ± 0.013	252.99 ± 0.04	71.12 ± 0.04	217.433 ± 0.018	220.712 ± 0.017	0.6265 ± 0.0004	0.3872 ± 0.0004	218.837 ± 0.018	224.440 ± 0.017	228.127 ± 0.020
217-avg	188.892 ± 0.012	253.419 ± 0.007	64.527 ± 0.014	221.156 ± 0.006	221.915 ± 0.005	0.39900 ± 0.00013	0.33846 ± 0.00013	220.113 ± 0.005	225.517 ± 0.005	229.097 ± 0.006
217-detset1	183.32 ± 0.15	253.61 ± 0.02	70.29 ± 0.15	218.46 ± 0.07	220.548 ± 0.009	0.4577 ± 0.0007	0.3053 ± 0.0007	218.666 ± 0.010	224.312 ± 0.009	228.038 ± 0.010
217-detset2	182.159 ± 0.012	253.592 ± 0.008	71.433 ± 0.015	217.875 ± 0.007	220.614 ± 0.009	0.47458 ± 0.00016	0.34838 ± 0.00016	218.697 ± 0.009	224.429 ± 0.009	228.200 ± 0.010
217-SWBs	189.02 ± 0.06	253.247 ± 0.014	64.22 ± 0.06	221.14 ± 0.03	222.957 ± 0.008	0.4072 ± 0.0003	0.3226 ± 0.0003	221.241 ± 0.008	226.395 ± 0.008	229.834 ± 0.010
353-1	306.3 ± 0.5	406.8 ± 0.4	100.5 ± 0.7	356.5 ± 0.3	360.289 ± 0.018	0.540 ± 0.003	0.390 ± 0.003	357.546 ± 0.018	365.762 ± 0.019	371.15 ± 0.02
353-2	305.82 ± 0.16	409.697 ± 0.020	103.88 ± 0.16	357.76 ± 0.08	360.866 ± 0.019	0.5947 ± 0.0008	0.4515 ± 0.0008	358.005 ± 0.019	366.615 ± 0.020	372.29 ± 0.02
353-3a	308.5 ± 0.3	404.77 ± 0.03	96.3 ± 0.3	356.63 ± 0.13	359.59 ± 0.02	0.4106 ± 0.0008	0.2862 ± 0.0008	357.16 ± 0.02	364.49 ± 0.02	369.37 ± 0.02
353-3b	308.3 ± 0.4	406.230 ± 0.015	98.0 ± 0.4	357.24 ± 0.19	359.65 ± 0.02	0.4689 ± 0.0014	0.3546 ± 0.0014	357.02 ± 0.02	365.01 ± 0.02	370.41 ± 0.02
353-4a	321.275 ± 0.018	407.94 ± 0.11	86.66 ± 0.11	364.61 ± 0.06	362.224 ± 0.018	0.4334 ± 0.0004	0.3119 ± 0.0004	359.944 ± 0.017	366.853 ± 0.019	371.52 ± 0.02
353-4b	311.71 ± 0.05	407.71 ± 0.03	96.00 ± 0.06	359.71 ± 0.02	362.212 ± 0.019	0.4152 ± 0.0003	0.3123 ± 0.0003	359.739 ± 0.019	367.22 ± 0.02	372.23 ± 0.02
353-5a	302.25 ± 0.04	406.41 ± 0.15	104.17 ± 0.16	354.33 ± 0.08	358.73 ± 0.02	0.3991 ± 0.0005	0.2965 ± 0.0005	355.88 ± 0.02	364.42 ± 0.02	370.01 ± 0.02
353-5b	301.37 ± 0.05	416.77 ± 0.05	115.40 ± 0.07	359.07 ± 0.03	358.84 ± 0.02	0.3626 ± 0.0002	0.2542 ± 0.0002	355.80 ± 0.02	364.98 ± 0.02	371.11 ± 0.03
353-6a	302.4 ± 0.4	407.99 ± 0.03	105.6 ± 0.4	355.19 ± 0.19	359.91 ± 0.03	0.3036 ± 0.0007	0.1946 ± 0.0007	357.09 ± 0.03	365.58 ± 0.03	371.18 ± 0.03
353-6b	314.08 ± 0.03	398.19 ± 0.04	84.11 ± 0.05	356.13 ± 0.02	356.06 ± 0.02	0.2990 ± 0.0002	0.2193 ± 0.0002	353.67 ± 0.02	360.93 ± 0.02	365.83 ± 0.03
353-7	323.2 ± 1.6	406.0 ± 0.9	83 ± 2	364.6 ± 0.7	363.35 ± 0.03	0.313 ± 0.006	0.272 ± 0.006	360.84 ± 0.03	368.40 ± 0.02	373.41 ± 0.03
353-8	309 ± 3	408.20 ± 0.08	99 ± 3	358.5 ± 1.7	365.10 ± 0.02	0.374 ± 0.011	0.294 ± 0.011	362.25 ± 0.02	370.82 ± 0.02	376.53 ± 0.04
353-avg	306.8 ± 0.6	408.22 ± 0.02	101.4 ± 0.6	357.5 ± 0.3	361.290 ± 0.008	0.4057 ± 0.0019	0.3353 ± 0.0019	358.564 ± 0.008	366.764 ± 0.009	372.193 ± 0.010
353-detset1	303.582 ± 0.016	406.333 ± 0.018	102.75 ± 0.03	354.957 ± 0.011	359.156 ± 0.011	0.39123 ± 0.00015	0.29902 ± 0.00015	356.386 ± 0.011	364.744 ± 0.011	370.302 ± 0.012
353-detset2	318.885 ± 0.015	407.86 ± 0.02	88.97 ± 0.03	363.372 ± 0.013	360.870 ± 0.013	0.35915 ± 0.00014	0.28730 ± 0.00014	358.409 ± 0.013	365.850 ± 0.013	370.837 ± 0.013
353-SWBs	306.3 ± 0.4	408.81 ± 0.03	102.5 ± 0.4	357.56 ± 0.18	361.921 ± 0.013	0.4381 ± 0.0013	0.3575 ± 0.0013	359.158 ± 0.013	367.455 ± 0.013	372.930 ± 0.015
545-1	466.41 ± 0.03	642.58 ± 0.05	176.17 ± 0.06	554.50 ± 0.03	559.83 ± 0.05	0.37600 ± 0.00018	0.29576 ± 0.00018	554.44 ± 0.07	570.00 ± 0.03	579.24 ± 0.02
545-2	466.78 ± 0.03	641.44 ± 0.07	174.66 ± 0.08	554.11 ± 0.04	556.05 ± 0.05	0.31937 ± 0.00019	0.26874 ± 0.00019	550.61 ± 0.07	566.37 ± 0.03	575.78 ± 0.03
545-3	470.6 ± 0.9	637.44 ± 0.05	166.9 ± 0.9	554.0 ± 0.4	557.40 ± 0.08	0.2536 ± 0.0011	0.2127 ± 0.0011	552.26 ± 0.13	567.14 ± 0.04	576.05 ± 0.03
545-4	470.9 ± 0.3	638.52 ± 0.10	167.6 ± 0.3	554.73 ± 0.16	556.85 ± 0.05	0.2630 ± 0.0004	0.2143 ± 0.0004	551.76 ± 0.08	566.48 ± 0.03	575.32 ± 0.02
545-avg	469.5 ± 0.6	640.81 ± 0.03	171.3 ± 0.6	555.2 ± 0.3	557.53 ± 0.03	0.3036 ± 0.0008	0.2612 ± 0.0008	552.22 ± 0.04	567.596 ± 0.016	576.778 ± 0.014
545-detset1	466.44 ± 0.02	642.36 ± 0.04	175.91 ± 0.05	554.40 ± 0.02	557.86 ± 0.03	0.32548 ± 0.00013	0.28031 ± 0.00013	552.43 ± 0.05	568.118 ± 0.020	577.458 ± 0.018
545-detset2	470.9 ± 0.3	638.52 ± 0.09	167.6 ± 0.3	554.73 ± 0.18	556.85 ± 0.05	0.2631 ± 0.0004	0.2143 ± 0.0004	551.76 ± 0.08	566.48 ± 0.03	575.32 ± 0.02
857-1	748.7 ± 0.9	992.5 ± 0.3	243.8 ± 1.0	870.6 ± 0.5	866.05 ± 0.10	0.2595 ± 0.0010	0.2283 ± 0.0010	858.1 ± 0.3	880.89 ± 0.03	894.38 ± 0.03
857-2	726.3 ± 0.4	989.09 ± 0.13	262.8 ± 0.4	857.7 ± 0.2	860.55 ± 0.08	0.2435 ± 0.0003	0.1973 ± 0.0003	852.28 ± 0.19	876.22 ± 0.03	890.59 ± 0.03
857-3	742.0 ± 0.5	991.7 ± 1.4	249.7 ± 1.5	866.8 ± 0.7	864.92 ± 0.09	0.2888 ± 0.0015	0.2573 ± 0.0015	857.0 ± 0.2	879.90 ± 0.03	893.53 ± 0.03
857-4	731.4 ± 0.4	979.9 ± 0.2	248.4 ± 0.4	855.7 ± 0.2	854.75 ± 0.09	0.1414 ± 0.0002	0.1189 ± 0.0002	847.2 ± 0.2	868.94 ± 0.03	881.94 ± 0.03
857-avg	743.9 ± 0.5	989.78 ± 0.08	245.9 ± 0.5	866.8 ± 0.3	862.68 ± 0.05	0.2412 ± 0.0005	0.2165 ± 0.0005	854.69 ± 0.11	877.724 ± 0.017	891.462 ± 0.014
857-detset1	736.9 ± 0.3	990.38 ± 0.06	253.4 ± 0.3	863.65 ± 0.13	863.42 ± 0.07	0.2446 ± 0.0002	0.2121 ± 0.0002	855.33 ± 0.16	878.67 ± 0.02	892.59 ± 0.02
857-detset2	741.79 ± 0.14	987.01 ± 0.09	245.22 ± 0.18	864.40 ± 0.08	861.74 ± 0.08	0.23780 ± 0.00017	0.21419 ± 0.00017	853.89 ± 0.18	876.53 ± 0.03	890.03 ± 0.03

References

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1. References

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