Planck Collaboration, P. A. R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown, F. Atrio-Barandela, J. Aumont, C. Baccigalupi, A. J. Banday, R. B. Barreiro, E. Battaner, K. Benabed, A. Benoît, A. Benoit-Lévy, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. Bobin, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, J. W. Bowyer, M. Bridges, M. Bucher, C. Burigana, J. -F. Cardoso, A. Catalano, A. Challinor, A. Chamballu, R. -R. Chary, L. -Y Chiang, H. C. Chiang, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, F. Couchot, A. Coulais, B. P. Crill, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, F. -X. Désert, J. M. Diego, H. Dole, S. Donzelli, O. Doré, M. Douspis, J. Dunkley, X. Dupac, G. Efstathiou, T. A. Enßlin, H. K. Eriksen, F. Finelli, O. Forni, M. Frailis, A. A. Fraisse, E. Franceschi, S. Galeotta, K. Ganga, M. Giard, Y. Giraud-Héraud, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, J. Haissinski, F. K. Hansen, D. Hanson, D. Harrison, S. Henrot-Versillé, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, Z. Hou, W. Hovest, K. M. Huffenberger, T. R. Jaffe, A. H. Jaffe, W. C. Jones, M. Juvela, E. Keihänen, R. Keskitalo, T. S. Kisner, R. Kneissl, J. Knoche, L. Knox, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, R. J. Laureijs, C. R. Lawrence, R. Leonardi, C. Leroy, J. Lesgourgues, M. Liguori, P. B. Lilje, M. Linden-Vørnle, M. López-Caniego, P. M. Lubin, J. F. Macías-Pérez, C. J. MacTavish, B. Maffei, N. Mandolesi, M. Maris, D. J. Marshall, P. G. Martin, E. Martínez-González, S. Masi, S. Matarrese, T. Matsumura, F. Matthai, P. Mazzotta, P. McGehee, A. Melchiorri, L. Mendes, A. Mennella, M. Migliaccio, S. Mitra, M. -A. Miville-Deschênes, A. Moneti, L. Montier, G. Morgante, D. Mortlock, D. Munshi, J. A. Murphy, P. Naselsky, F. Nati, P. Natoli, C. B. Netterfield, H. U. Nørgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, S. Osborne, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, D. Paoletti, F. Pasian, G. Patanchon, O. Perdereau, L. Perotto, F. Perrotta, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, E. Pointecouteau, A. M. Polegre, G. Polenta, N. Ponthieu, L. Popa, T. Poutanen, G. W. Pratt, G. Prézeau, S. Prunet, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, C. Renault, S. Ricciardi, T. Riller, I. Ristorcelli, G. Rocha, C. Rosset, G. Roudier, M. Rowan-Robinson, B. Rusholme, M. Sandri, D. Santos, A. Sauvé, G. Savini, E. P. S. Shellard, L. D. Spencer, J. -L. Starck, V. Stolyarov, R. Stompor, R. Sudiwala, F. Sureau, D. Sutton, A. -S. Suur-Uski, J. -F. Sygnet, J. A. Tauber, D. Tavagnacco, L. Terenzi, M. Tomasi, M. Tristram, M. Tucci, G. Umana, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, L. A. Wade, B. D. Wandelt, D. Yvon, A. Zacchei, A. Zonca
This paper characterizes the effective beams, the effective beam window functions (EBWF) and the associated errors for the Planck High Frequency Instrument (HFI) detectors. The effective beam is the angular response including the effect of the optics, detectors, data processing and the scan strategy. The EBWF is the representation of this beam in the harmonic domain that is required to recover an unbiased measurement of the Cosmic Microwave Background (CMB) angular power spectrum. The HFI is a scanning instrument and its effective beams are the convolution of the optical response of the telescope and feeds, the processing of the time-ordered data and deconvolution of the bolometric and electronic time response, and the merging of several surveys to produce maps. The time response transfer functions are measured with observations of Jupiter and Saturn and by minimizing survey difference residuals. The scanning beam is the post-deconvolution angular response of the instrument, and is characterized with observations of Mars. The main beam solid angles are determined to better than 0.5% at each HFI frequency band. Observations of Jupiter and Saturn limit near sidelobes to ~0.1% of the total solid angle. Time response residuals remain as long tails in the scanning beams, but contribute <0.1% of the total solid angle. The bias and uncertainty in the beam products are estimated with ensembles of simulated planet observations that include the impact of instrumental noise and known systematic effects. The correlation structure of these ensembles is well-described by 5 error eigenmodes and is sub-dominant to sample variance and instrumental noise in the harmonic domain. A suite of consistency tests provide confidence that the error model represents a sufficient description of the data. The total error in the EBWF is <1% at 100 GHz up to multipole 1500, and <0.5% at 143 and 217 GHz up to 2000.
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http://arxiv.org/abs/1303.5068
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