Spectral response

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HFI(Planck) High Frequency Instrument Spectral Response

This section outlines the unit conversion and colour correction protocol for Planck/HFI(Planck) High Frequency Instrument. 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(Planck) High Frequency Instrument/LFI(Planck) Low Frequency Instrument section). There will be links to the UcCC subsection of the PLAPlanck Legacy Archive section, but the numbers and details belong here. The PLAPlanck Legacy Archive UcCC subsection is primarily to introduce the software tools.

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

Band-average HFI(Planck) High Frequency Instrument 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.

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).

Variation of individual detector contribution to band-average frequency maps across the sky, for various HFI(Planck) High Frequency Instrument surveys.


The following table presents basic characteristics of the HFI(Planck) High Frequency Instrument detector spectral response, including optical efficiency, effective frequency, etc. Further details on the definition of these parameters are available in Planck-2013-IX[1].

Properties of HFI(Planck) High Frequency Instrument 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

  1. Planck 2013 results: HFI spectral response, Planck Collaboration 2013 IX, A&A, in press, (2014).