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A&A 520, A8 (2010)Table B.1. Main beam characteristics as a function of frequency for the 30 GHz channel, for the Y-polarisation (main arm) of feed horn LFI-27.Frequency Edge TaperaD feed FWHM e b τ c D d XPD e d f S g(GHz) (dB @ 22 ◦ ) (dBi) (arcmin) ( ◦ ) (dBi) (dB) (%) (%)27.0 18.59 20.42 32.80 1.32 −89.9 51.06 27.09 0.556 0.8727.2 19.11 20.51 32.80 1.32 −89.9 51.06 27.19 0.542 0.8027.4 19.64 20.59 32.75 1.32 −89.9 51.08 27.26 0.531 0.7527.6 20.18 20.67 32.74 1.33 −89.9 51.09 27.30 0.521 0.7127.8 20.74 20.75 32.72 1.34 −89.9 51.10 27.38 0.510 0.6628.0 21.33 20.84 32.72 1.34 −89.9 51.10 27.47 0.498 0.6228.2 21.97 20.93 32.66 1.35 −90.0 51.10 27.56 0.487 0.5928.4 22.65 21.01 32.73 1.36 −90.0 51.10 27.61 0.477 0.5628.6 23.40 21.09 32.77 1.36 −90.0 51.09 27.68 0.467 0.5528.8 24.21 21.17 32.80 1.37 −90.0 51.08 27.80 0.457 0.5329.0 25.08 21.25 32.91 1.38 90.0 51.08 27.95 0.447 0.5329.2 26.01 21.34 32.98 1.38 90.0 51.06 28.10 0.437 0.5329.4 27.04 21.42 33.05 1.39 90.0 51.04 28.19 0.430 0.5329.6 28.19 21.51 33.08 1.40 90.0 51.03 28.28 0.424 0.5429.8 29.35 21.59 33.15 1.40 90.0 51.01 28.41 0.418 0.5530.0 30.43 21.67 33.23 1.41 89.9 51.00 28.31 0.412 0.5830.2 31.52 21.74 33.35 1.41 89.9 50.98 28.20 0.405 0.6230.4 32.74 21.80 33.42 1.41 89.9 50.95 28.17 0.399 0.6530.6 33.80 21.88 33.50 1.41 89.9 50.93 28.18 0.393 0.6730.8 34.56 21.96 33.58 1.42 89.9 50.92 28.13 0.388 0.6931.0 34.77 22.03 33.63 1.41 89.9 50.91 28.01 0.384 0.7331.2 34.57 22.10 33.63 1.41 89.9 50.90 27.96 0.379 0.7731.4 34.40 22.16 33.70 1.40 89.9 50.89 28.04 0.371 0.7931.6 34.42 22.22 33.70 1.40 89.9 50.89 28.30 0.363 0.8031.8 34.46 22.27 33.66 1.40 90.0 50.89 28.58 0.356 0.8032.0 34.57 22.31 33.62 1.39 90.0 50.89 28.88 0.349 0.8032.2 35.12 22.36 33.62 1.39 −90.0 50.90 29.20 0.343 0.8032.4 36.44 22.41 33.62 1.39 −90.0 50.90 29.38 0.341 0.8032.6 38.60 22.45 33.68 1.41 −89.9 50.90 29.07 0.342 0.7932.8 40.77 22.49 33.80 1.42 −89.9 50.88 28.63 0.347 0.7833.0 41.00 22.54 34.02 1.44 −89.9 50.86 28.36 0.350 0.79Notes. (a) feed directivity; (b) ellipticity; (c) rotation angle of the polarisation ellipse; (d) main beam directivity; (e) cross polar discrimination factor;( f ) main beam depolarisation parameter; (g) spillover.Fig. B.2. Feed horn taper at 22 ◦ (corresponding approximately to theedge of the primary mirror) versus frequency.Fig. B.3. Full width at −3, −10, and −20 dB from the main beam powerpeak. No significant trend with the frequency is evident from thesecurves.25 dB, within the specification; iii) a spread of about 6% is evidentin the FWHM, followingthetrendoftheedgetapervalue;iv) the spillover initially decreases because the main lobe getsnarrower, then it increases due to the growth of the first sidelobeup to 10 dB higher, and finally, between 32 and 33 GHz itPage 24 of 26
-40-50-40-40-30-3-10-10-30-30-40-50-40-40-30J. P. Leahy et al.: Planck pre-launch status: Expected LFI polarisation capability-500.02-500.01-40-50-50-40-40-50-60-40-40-50-40-40-500.02-30-20-30-40-300.01-20-40-200.00-100.00-30-20-3-6-10-30-40-3-40-50-6-0.01-20-10-50-40-0.01-30-20-30-10-3-6-50-40-50-30-50-50-20-40-0.02-60-50-50-50-60-60-60-60-60-60-50-0.02-40-40-30-40-40-50-50-60-50-0.02 -0.01 0.00 0.01 0.02-0.02 -0.01 0.00 0.01 0.020.02-50-50-60-50-60-40-50-50-500.02-50-40-60-50-40-30-40-50-40-50-500.01-50-30-20-500.01-50-40-20-50-500.00-40-50-600.00-40-30-20-3-6-10-20-30-3-6-40-50-0.01-20-30-10-40-0.01-3-10-6-20-30-40-50-0.02-50-50-0.02-40-50-50-50-0.02 -0.01 0.00 0.01 0.02-50-40-40-0.02 -0.01 0.00 0.01 0.02-50-600.02-50-40-500.02-40-40-40-30-40-40-200.01-300.01-30-20-20-400.00-400.00-30-3-6-20-10-10-6-40-0.01-20-50-0.01-20-30-3-6-10-0.02-50-50-50-30-40-50-0.02-30-30-20-40-0.02 -0.01 0.00 0.01 0.02-40-40-0.02 -0.01 0.00 0.01 0.02-40Fig. B.4. Main beam at 27 GHz (first row), 33 GHz (second row), andaveraged main beam over the nominal 27–33 GHz bandpass. (thirdrow). Co-polar pattern is on the left side and cross-polar pattern is onthe right side. Colour scale goes from −90 to 0 dB. Contours (dotted) ofafittedbivariateGaussianaresuperimposed;thefittedaveragedFWHMare 32.09, 33.10, and 32.53 arcmin, respectively.decreases again because the sidelobe gets narrower and the firstminimum become more evident; v) thebeamdepolarisation 15decreases with frequency.The effective band-averaged beam will be weighted by thebandpass and the brightness spectrum, whereas uniform weightshave been used for the patterns analysed here. Weighted-averagebeams will be used for the final analysis but are not availablefor this pre-launch analysis since the time-consuming physicalopticssimulations required have only been completed for onepolarisation of one horn in each band, and only within the nominalpassband whereas the actual response is significant over awider frequency range, as shown by Zonca et al. (2009). Theresults presented here suffice to show that beamshape variationacross the band is a second-order effect, and therefore justifiesour separation of bandpass and beam effects on the polarisationin the main text.15 Defined as in Sandri et al. (2010); in our notation, d = 1 −√〈WQ 〉 2 + 〈W U 〉 2 + 〈W V 〉 2 /〈W I 〉.Fig. B.5. Feed horn directivity, main beam directivity, and XPD (toppanel), FWHM (central panel), spillover and depolarisation parameter(bottom panel).Acknowledgements. J.P.L. thanks Johan Hamaker for a fruitful collaboration(Hamaker & Leahy 2004) whichhassignificantlyinfluencedthepresentationinthis paper. J.P.L. also thanks the Osservatorio Astronomico di Trieste for hospitalitywhile much of this paper was written. We thank the referee for a perceptivereview. The Planck-LFI project is developed by an International Consortium ledby Italy and involving Canada, Finland, Germany, Norway, Spain, Switzerland,UK, USA. The Italian contribution to Planck is supported by the Italian SpaceAgency (ASI). The UK contribution is supported by the Science and TechnologyFacilities Council (STFC). The Finnish contribution is supported by the FinnishFunding Agency for Technology and Innovation (Tekes) and the Academy ofFinland. The Canadian contribution is supported by the Canadian Space Agency.We wish to thank people of the Herschel/Planck Project of ESA, ASI, THALESAlenia Space Industries, and the LFI Consortium that are involved in activitiesrelated to optical simulations and the measurement and modelling of theradiometer performance. We acknowledge the use of the Planck sky model, developedby the Component Separation Working Group (WG2) of the PlanckCollaboration. We thank the members of the Planck CTP working group for thepreparation and validation of the Trieste simulations. Some of the results in thispaper have been derived using the HEALPix (Gorski et al. 1999). We acknowledgethe use of the Legacy Archive for Microwave Background Data Analysis(LAMBDA). Support for LAMBDA is provided by the NASA Office of SpaceScience. This research has made use of NASA’s Astrophysics Data System. Weacknowledge partial support of the NASA LTSA Grant NNG04CG90G.ReferencesArmitage-Caplan, C., & Wandelt, B. D. 2009, ApJS, 181, 533Ashdown, M. A. J., Baccigalupi, C., Balbi, A., et al. 2007, A&A, 471, 361Ashdown, M. A. J., Baccigalupi, C., Bartlett, J. G., et al. 2009, A&A, 493, 753Battaglia, P., Francheschet, C., Zonca, A., et al. 2009, JINST, 4, T12014Berkhuijsen, E. M. 1975, A&A, 40, 311Bersanelli, M., Mandolesi, N., Butler, R. C., et al. 2010, A&A, 520, A4Bietenholz, M. F., & Kronberg, P. P. 1991, ApJ, 368, 231Page 25 of 26
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A&A 520, E1 (2010)DOI: 10.1051/0004
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ABSTRACTThe European Space Agency
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A&A 520, A1 (2010)three frequency c
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A&A 520, A1 (2010)- University of C
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A&A 520, A1 (2010)57 Instituto de A
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