Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...

M. Sandri et al.: Planck pre-launch status: Low Frequency Instrument opticsTable 2. Main beam frames.BEAM ν 0 θ MB φ MB ψ MB U MB V MB(GHz) ( ◦ ) ( ◦ ) ( ◦ )18 70 3.2975 –131.8147 22.3 –0.03835 –0.0428719 70 3.1750 –150.8570 22.4 –0.04837 –0.0269720 70 3.1649 –168.4438 22.4 –0.05409 –0.0110621 70 3.1649 168.4438 –22.4 –0.05409 0.0110622 70 3.1747 150.8570 –22.4 –0.04837 0.0269723 70 3.2975 131.8147 –22.3 –0.03835 0.0428724 44 4.0536 180.0000 0.0 –0.07069 0.0000025 44 5.0186 61.1350 –113.5 0.04223 0.0766126 44 5.0186 –61.1350 113.5 0.04223 –0.0766127 30 4.3466 153.6074 –22.5 –0.06789 0.0336928 30 4.3466 –153.6074 22.5 –0.06789 –0.03369Notes. θ MB , φ MB ,andψ MB angles defining the coordinate systems, with respect to the LOS frame, in which each main beams was computed. θ MBand φ MB indicate the main beam locations on the sky (U MB = sin θ MB × cos φ MB and V MB = sin θ MB × sin φ MB reported in the last two columns) andψ MB is the polarization angle.Table 3. Main beam characteristics at the central frequency.HW at −3dB HW at −10dB HW at −20dBBeam (deg) (deg) (deg) FWHM e τ D XPD d Smin max min max min max (arcmin) ( ◦ ) (dBi) (dB) (%) (%)18 and 23 X 0.0969 0.1235 0.1702 0.2212 0.2247 0.3147 13.22 1.27 –0.1 58.80 28.01 0.38 0.55Y 0.0989 0.1219 0.1725 0.2176 0.2273 0.3096 13.25 1.23 –89.8 58.83 28.54 0.40 0.5019 and 22 X 0.0969 0.1219 0.1667 0.2167 0.2229 0.3013 13.13 1.26 0.0 59.02 29.73 0.26 0.64Y 0.0969 0.1203 0.1690 0.2131 0.2247 0.2967 13.03 1.24 –90.0 59.06 30.21 0.28 0.5820 and 21 X 0.0949 0.1203 0.1643 0.2140 0.2264 0.2981 12.91 1.27 0.0 59.17 31.20 0.21 0.73Y 0.0949 0.1187 0.1655 0.2112 0.2256 0.2941 12.82 1.25 89.9 59.22 30.99 0.23 0.6924 X 0.1655 0.2176 0.2880 0.3927 0.3815 0.5539 22.99 1.31 0.0 54.14 29.98 0.31 0.14Y 0.1619 0.2229 0.2839 0.4025 0.3779 0.5654 23.09 1.38 90.0 54.09 29.97 0.29 0.1625 and 26 X 0.2229 0.2727 0.4001 0.5260 0.5370 0.7923 29.74 1.22 0.5 51.71 24.90 0.99 0.16Y 0.2112 0.2639 0.3790 0.5170 0.5211 0.7948 28.51 1.25 89.7 51.97 25.32 0.96 0.1627 and 28 X 0.2349 0.3208 0.4093 0.5706 0.5392 0.7808 33.34 1.37 0.2 50.97 28.21 0.44 0.58Y 0.2299 0.3239 0.4015 0.5757 0.5301 0.7891 33.23 1.41 89.9 51.00 28.31 0.41 0.58Notes. The half width (HW, minimumandmaximum)at−3, −10, −20 dB, the full width half maximum (FWHM), the ellipticity (e), the rotationangle of the polarization ellipse (τ), the main beam directivity (D), the cross polar discrimination factor (XPD), the main beam depolarizationparameter (d), and the spillover (S)arereported.beam simulations are performed by considering the feed as asource, and by computing the pattern scattered by both reflectorsonto the far field with GRASP8 using physical optics (PO)and physical theory of diffraction (PTD) for both reflectors. Weassumed an ideal telescope and computed main beam and sidelobeproperties for each channel, taking into account the effectsof the surrounding structures.7.1. LFI main beam characterisationFar field radiation patterns were computed on the co- andcross-polar basis according to Ludwig’s third definition in UVsphericalgrids. We computed the main beam angular resolutionof each feed model analysed, as well as all major electromagneticcharacteristics reported in Tables 2 and 3. U (sin θ × cos φ)and V (sin θ × sin φ) rangefrom–0.026to0.026(θ ≤ 1.5 ◦ )for the 30 and 44 GHz channels, and from –0.015 to 0.015(θ ≤ 0.9 ◦ )forthe70GHzchannel.Eachgridhasbeensampledwith 301 × 301 points, therefore ∆U =∆V ≃ 1.7 × 10 −4 forthe 30 and 44 GHz channels and 10 −4 for the 70 GHz channel.In Table 2,thecoordinatesystemsinwhicheachmainbeamwascomputed are reported: U MB and V MB correspond to the centreof the UV-grids shown in this section. In Table 3, relevantmainbeam characteristics computed at the central frequency are summarized,such as the full width half maximum, the cross polardiscrimination factor, and the main beam depolarization parameter.In Fig. 9, thecontourplotintheUV-planeoftheco-andcross-polar components is shown for the main beam #27 and #28(Y-polarized). The lines in the contour plots, normalized with respectto the power peak (the directivity reported in Table 3 for theco-polar plot and the directivity minus the XPD for the cross- polarplot), are at –3, –10, –20, –30, –40, –50, and –60. The colourscales goes from –90 to 0 dB. Figure 10 shows the differencesbetween the two polarization X- and Y- for the main beam #27,which are imperceptible below –40 dB. In Figs. 11 and 12, thecontour plot in the UV-plane of the co- and cross-polar componentsis shown for the main beam #24, #26, #21, #22, and #23(Y-polarized), respectively.The cross-polar response of the OMT affects the beam patternin a significant way below the –40 dB contour since theco-polar component is a linear combination of the co- and crosspolarpattern with coefficients of about 1 and 10 −4 .Adetailedstudy of the LFI polarization capability is reported in Leahy et al.(2010).Page 7 of 12