Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...
Planck Pre-Launch Status Papers - APC - Université Paris Diderot ... Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...
A&A 520, A7 (2010)Table 4. Galactic straylight contamination.BEAM POL GI IB GSC (µK) FB GSC (µK)(10 −5 ) % RMS p–p % RMS p–p18 and 23 X 1.652150 0.0634 0.027 0.87 0.330 0.14 0.86Y 1.639975 0.0583 0.025 0.80 0.267 0.11 0.7019 and 22 X 1.569425 0.0662 0.028 0.91 0.400 0.16 1.1Y 1.553854 0.0616 0.026 0.85 0.339 0.14 0.8920 and 21 X 1.513895 0.0761 0.032 1.1 0.448 0.18 1.2Y 1.499650 0.0726 0.031 1.0 0.401 0.16 1.124 X 4.841957 0.0261 0.051 1.3 0.0789 0.088 0.56Y 4.887753 0.0271 0.053 1.3 0.1040 0.12 0.7325 and 26 X 8.468192 0.0472 0.091 2.3 0.0536 0.060 0.38Y 7.977703 0.0734 0.14 3.5 0.0826 0.092 0.5827 and 28 X 10.023255 0.0444 0.30 6.0 0.432 1.1 6.7Y 9.969366 0.0520 0.35 7.0 0.426 1.1 6.6Fig. 14. Co- (top panel) andcross-(bottom panel) polarcomponentsof the 4π beam at 44 GHz (feed horn #24 Y polarized) computed withMrGTD. The maximum level of the main spillover is about –5.4 dBiat φ = 0 ◦ and θ ≃ 85 ◦ for the co-polar component, and the cross-polarcomponent is down to –15 dBi everywhere.Fig. 15. Co- (top panel) andcross-(bottom panel) polarcomponentsofthe 4π beam at 70 GHz (feed horn #23 FM, Y polarized) computed withMrGTD. The maximum level of the main spillover is about –1.8 dBi atφ ≃ 10 ◦ and θ ≃ 85 ◦ for the co-polar component, and the cross-polarcomponent is, in the main spillover region, at about –4.8 dBi.(Gruppuso et al. 2007), provided that the relative uncertainty inthe modelling of the far sidelobes is < ∼ 20%.9. ConclusionsFrom the beginning of the Phase A study to the currentflight configuration, we have reported reported the historyof the optimization of the LFI optical interface. The definition,optimization, and characterization of the LFI feed hornscoupled the Planck telescope have been derived by means ofelectromagnetic simulations devoted to maximizing the angularresolution and at the same time minimizing systematic effectsproduced by the sidelobes of the radiation pattern. The positionand orientation of each horn was set taking into accountthe mechanical constraints imposed by the LFI interfaces andthe 4 K reference loads. The feeds and corresponding OMTshave been adjusted in the focal surface in such a way that themain beam polarization directions of the two symmetrically locatedfeed horns in the FPU are at an angle of 45 degrees whenthey observe the same direction in the sky, in order to measurethe Q and U Stokes parameters and thus the linear polarizationof the CMB. Finally, the LFI optical performance computedwith the ideal telescope has been presented. The requirementshave been met and in some cases exceeded. Typical LFI mainbeams have angular resolutions of about 33 ′ ,24 ′ ,and13 ′ ,respectively,at 30 GHz, 44 GHz, and 70 GHz, slightly exceedingthe requirements for the cosmological 70 GHz channel. Thebeams have been delivered to the LFI data processing center andthey are the current baseline data used in the testing of the datareduction pipeline. Of course, the performance in-flight will bePage 10 of 12
M. Sandri et al.: Planck pre-launch status: Low Frequency Instrument opticsdifferent owing to the true telescope and focal surface alignment,the surface roughness, and the distortion of the reflectors causedby the cooldown. However, simulations on the Planck radio frequencyflight model (Tauber et al. 2010) have shown that the LFIperformance is quite similar to the ideal case, so values reportedin the tables of this paper (beam characteristics and straylightcontamination) are presumably not far from the true values.Acknowledgements. Planck is a project of the European Space Agency withinstruments funded by ESA member states, and with special contributionsfrom Denmark and NASA (USA). The Planck-LFI project is developed by anInternational Consortium lead by Italy and involving Canada, Finland, Germany,Norway, Spain, Switzerland, UK, USA. The Italian contribution to Planck issupported by the Italian Space Agency (ASI). We wish to thank people of theHerschel/Planck Project of ESA, ASI, THALES Alenia Space Industries, andthe LFI Consortium that are involved in activities related to optical simulations.Some of the results in this paper have been derived using the HEALPix (Górski,Hivon, and Wandelt 1999). Special thanks to Denis Dubruel (THALES AleniaSpace), for his professional collaboration in all these years. We warmly thankDavid Pearson for constructive comments and suggestions, and for the carefulreading of the first version of this work.Appendix A: Main beam descriptive parametersOwing to the telescope configuration and the feed horn off-axislocation on the focal surface, the main beams are strongly distortedand their shape differs from a Gaussian. In other words,the main beams cannot be mathematically represented by a singleparameter (for instance, the fullwidthhalfmaximum)andby a simple formula (Gaussian function, polynomial function)because aberrations prevail at power levels lower than –10 dB.However, it is indispensable to characterize the main beams asprecisely as possible, and several descriptive parameters havebeen evaluated: the angular resolution (FWHM), the ellipticity(e), the main beam directivity (D), the cross polar discriminationfactor (XPD), the depolarization parameter (d), the rotationangle of the polarization ellipse (τ), and the main spillover (S).A.1. Angular resolutionFor CMB anisotropy measurements, an effective angular resolutioncan be defined as the FWHM of a perfect (symmetricGaussian) beam, which produces the same signal as the distortedbeam when the CMB field is observed (Burigana et al. 1998).Nevertheless, this definition involves astrophysical simulationstaking into account the scanning strategy and the CMB expectedanisotropy map (or the WMAP results). Owing to the large computationtime, this approach is not practical for the optimizationactivity of the LFI feed horns.Main beam aberrations degrade its angular resolution.Instead of the effective FWHM, theangularresolutioncanbeevaluated by taking the average FWHM of the distorted beam.The average FWHM has been computed in three different ways,using the minimum and maximum values:– arithmetic average: by taking the average value betweenthe maximum and minimum of the FWHM of the distortedbeam:FWHM A = FWHM min + FWHM max2– quadratic average: by taking the quadratic mean betweenthe maximum and minimum of the FWHM of the distortedbeam:√FWHM 2 minFWHM Q =+ FWHM2 max2– equal area average 5 :thedistortedbeamexhibitsthesamebeam area of a symmetric beam with a FWHM defined as:FWHM E = √ FWHM min · FWHM max .The differences between the three average values are about 2.8%at 30 GHz, 2.5% at 44 GHz, and less than 1.3% at 70 GHz.It is noticed that the arithmetical average value is in-betweenthe other two values, and small differences exist between theFWHM A and the arithmetic mean of FWHM Q and FWHM E .Theaverage can be written as a function of the ellipticity (e, computedas the ratio of the maximum to minumum values of thebeam width at –3 dB) in the following way:FWHM Q + FWHM E= FWHM A2⎡− ⎢⎣ 1 ⎛2 · FWHM min · ⎜⎝1 + e − √ √ ⎞⎤2 √e − 1 + e2⎟⎠⎥⎦2or alternatively:FWHM Q + FWHM E= FWHM A2⎡− ⎢⎣ 1 ⎛2 · FWHM max · ⎜⎝ 1 + e√ √ √1 2−e e − 1 + 1 ⎤2 e⎞⎟⎠ 2 ⎥⎦ ·(A.1)(A.2)The term between the inner brackets is small (≃10 −4 –10 −5 ),and it is zero in the case of perfect symmetric beam (e = 1).Although it is important to include in the data analysis the detailedinformation of the beam shape, these small differences arenot a concern for the angular resolution requirements, and theadopted angular resolution is the FWHM computed arithmetically(FWHM A ).A.2. Directivity and gainDirectivity is the ability of an antenna to focus energy in a particulardirection when transmitting, or when receiving to receiveenergy preferentially from a particular direction. In a realistic,but lossless antenna (i.e., of efficiency η ∼ 1), the directivityD(θ, φ)isessentiallyequaltothegainG(θ, φ):G(θ, φ) = η · D(θ, φ) ∼4πP(θ, φ)∫∫P(θ, φ)dΩ·(A.3)Thus, gain or directivity is also a normalized power pattern similarto P n in Eq. (3)withthedifference that the normalizing factoris ∫ P(θ, φ)dΩ/4π.SubstitutingEq.(3) intoEq.(A.3), it is easyto see that the maximum directive gain G max ,improperlycalleddirectivity D, canbeexpressedasD = G max = 4πΩ A(A.4)where G max is the maximum value of the far field amplitude radiationpattern computed by GRASP8D = 10 · log ( max |E far | ) ,(A.5)and E far = (|E cp | 2 + |E xp | 2 ), and D is defined in dBi, which isdecibels referenced to an isotropic radiator.5 The meaning of equal area is derived from Maino et al. (2002). ForGaussian elliptical beams, FWHM eff = FWHM E .Page 11 of 12
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A&A 520, A7 (2010)Table 4. Galactic straylight contamination.BEAM POL GI IB GSC (µK) FB GSC (µK)(10 −5 ) % RMS p–p % RMS p–p18 and 23 X 1.652150 0.0634 0.027 0.87 0.330 0.14 0.86Y 1.639975 0.0583 0.025 0.80 0.267 0.11 0.7019 and 22 X 1.569425 0.0662 0.028 0.91 0.400 0.16 1.1Y 1.553854 0.0616 0.026 0.85 0.339 0.14 0.8920 and 21 X 1.513895 0.0761 0.032 1.1 0.448 0.18 1.2Y 1.499650 0.0726 0.031 1.0 0.401 0.16 1.124 X 4.841957 0.0261 0.051 1.3 0.0789 0.088 0.56Y 4.887753 0.0271 0.053 1.3 0.1040 0.12 0.7325 and 26 X 8.468192 0.0472 0.091 2.3 0.0536 0.060 0.38Y 7.977703 0.0734 0.14 3.5 0.0826 0.092 0.5827 and 28 X 10.023255 0.0444 0.30 6.0 0.432 1.1 6.7Y 9.969366 0.0520 0.35 7.0 0.426 1.1 6.6Fig. 14. Co- (top panel) andcross-(bottom panel) polarcomponentsof the 4π beam at 44 GHz (feed horn #24 Y polarized) computed withMrGTD. The maximum level of the main spillover is about –5.4 dBiat φ = 0 ◦ and θ ≃ 85 ◦ for the co-polar component, and the cross-polarcomponent is down to –15 dBi everywhere.Fig. 15. Co- (top panel) andcross-(bottom panel) polarcomponentsofthe 4π beam at 70 GHz (feed horn #23 FM, Y polarized) computed withMrGTD. The maximum level of the main spillover is about –1.8 dBi atφ ≃ 10 ◦ and θ ≃ 85 ◦ for the co-polar component, and the cross-polarcomponent is, in the main spillover region, at about –4.8 dBi.(Gruppuso et al. 2007), provided that the relative uncertainty inthe modelling of the far sidelobes is < ∼ 20%.9. ConclusionsFrom the beginning of the Phase A study to the currentflight configuration, we have reported reported the historyof the optimization of the LFI optical interface. The definition,optimization, and characterization of the LFI feed hornscoupled the <strong>Planck</strong> telescope have been derived by means ofelectromagnetic simulations devoted to maximizing the angularresolution and at the same time minimizing systematic effectsproduced by the sidelobes of the radiation pattern. The positionand orientation of each horn was set taking into accountthe mechanical constraints imposed by the LFI interfaces andthe 4 K reference loads. The feeds and corresponding OMTshave been adjusted in the focal surface in such a way that themain beam polarization directions of the two symmetrically locatedfeed horns in the FPU are at an angle of 45 degrees whenthey observe the same direction in the sky, in order to measurethe Q and U Stokes parameters and thus the linear polarizationof the CMB. Finally, the LFI optical performance computedwith the ideal telescope has been presented. The requirementshave been met and in some cases exceeded. Typical LFI mainbeams have angular resolutions of about 33 ′ ,24 ′ ,and13 ′ ,respectively,at 30 GHz, 44 GHz, and 70 GHz, slightly exceedingthe requirements for the cosmological 70 GHz channel. Thebeams have been delivered to the LFI data processing center andthey are the current baseline data used in the testing of the datareduction pipeline. Of course, the performance in-flight will bePage 10 of 12
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