Ade, P.A.R. and Aghanim, N. and Arnaud, M. and Ashdown, M. and Atrio-Barandela, F. and Aumont, J. and Baccigalupi, C. and Balbi, A. and Banday, A.J. and Barreiro, R.B. and Bartlett, J.G. and Battaner, E. and Benabed, K. and Benoit, A. and Bernard, J.-P. and Bersanelli, M. and Bhatia, R. and Bikmaev, I. and Bobin, J. and Böhringer, H. and Bonaldi, A. and Bond, J.R. and Borgani, S. and Borrill, J. and Bouchet, F.R. and Bourdin, H. and Brown, M.L. and Burenin, R. and Burigana, C. and Cabella, P. and Cardoso, J.-F. and Carvalho, P. and Castex, G. and Catalano, A. and Cayon, L. and Chamballu, A. and Chiang, L.-Y. and Chon, G. and Christensen, P.R. and Churazov, E. and Clements, D.L. and Colafrancesco, S. and Colombi, S. and Colombo, L.P.L. and Comis, B. and Coulais, A. and Crill, B.P. and Cuttaia, F. and Da Silva, A. and Dahle, H. and Danese, L. and Davis, R.J. and De Bernardis, P. and de Gasperis, G. and de Zotti, G. and Delabrouille, J. and Démoclès, J. and Desert, F.-X. and Diego, J.M. and Dolag, K. and Dole, H. and Donzelli, S. and Dore, O. and Dorl, U. and Douspis, M. and Dupac, X. and Efstathiou, G. and Enßlin, T.A. and Eriksen, H.K. and Finelli, F. and Flores-Cacho, I. and Forni, O. and Fosalba, P. and Frailis, M. and Franceschi, E. and Frommert, M. and Galeotta, S. and Ganga, K. and Genova-Santos, R.T. and Giard, M. and Giraud-Héraud, Y. and Gonzalez-Nuevo, J. and Gorski, K.M. and Gregorio, A. and Gruppuso, A. and Hansen, F.K. and Harrison, D. and Hempel, A. and Henrot-Versille, S. and Hernandez-Monteagudo, C. and Herranz, D. and Hildebrandt, S.R. and Hivon, E. and Hobson, M. and Holmes, W.A. and Hurier, G. and Jaffe, A.H. and Jaffe, T.R. and Jagemann, T. and Jones, W.C. and Juvela, M. and Keihanen, E. and Khamitov, I. and Kisner, T.S. and Kneissl, R. and Knoche, J. and Knox, L. and Kunz, M. and Kurki-Suonio, H. and Lagache, G. and Lahteenmaki, A. and Lamarre, J.-M. and Lasenby, A. and Lawrence, C.R. and Le Jeune, M. and Leonardi, R. and Liddle, A. and Lilje, P.B. and Lopez-Caniego, M. and Luzzi, G. and Macias-Perez, J.F. and Maino, D. and Mandolesi, N. and Maris, M. and Marleau, F. and Marshall, D.J. and Martinez-Gonzalez, E. and Masi, S. and Massardi, M. and Matarrese, S. and Mazzotta, P. and Mei, S. and Melchiorri, A. and Melin, J.-B. and Mendes, L. and Mennella, A. and Mitra, S. and Miville-Deschenes, M.-A. and Moneti, A. and Montier, L. and Morgante, G. and Mortlock, D. and Munshi, D. and Murphy, J.Anthony and Naselsky, P. and Nati, F. and Natoli, P. and Norgaard-Nielsen, H.U. and Noviello, F. and Novikov, D. and Novikov, I. and Osborne, S. and Pajot, F. and Paoletti, D. and Pasian, F. and Patanchon, G. and Perdereau, O. and Perotto, L. and Perrotta, F. and Piacentini, F. and Piat, M. and Pierpaoli, E. and Piffaretti, R. and Plaszczynski, S. and Pointecouteau, E. and Polenta, G. and Ponthieu, N. and Popa, L. and Poutanen, T. and Pratt, G.W. and Prunet, S. and Puget, J.-L. and Rachen, J.P. and Reach, W.T. and Rebolo, R. and Reinecke, M. and Remazeilles, M. and Renault, C. and Ricciardi, S. and Riller, T. and Ristorcelli, I. and Rocha, G. and Roman, M. and Rosset, C. and Rossetti, M. and Rubino-Martin, J.A. and Rusholme, B. and Sandri, M. and Savini, G. and Scott, D. and Smoot, G.F. and Starck, J.-L. and Sudiwala, R. and Sunyaev, R. and Sutton, D. and Suur-Uski, A.-S. and Sygnet, J.-F. and Tauber, J.A. and Terenzi, L. and Toffolatti, L. and Tomasi, M. and Tristram, M. and Toffolatti, L. and Tomasi, M. and Tristram, M. and Tuovinen, J. and Valenziano, L. and Van Tent, B. and Varis, J. and Vielva, P. and Villa, F. and Vittorio, N. and Wade, L.A. and Wandelt, B.D. and Welikala, N. and White, S.D.M. and White, M. and Yvon, D. and Zacchei, A. and Zonca, A. (2013) Planck intermediate results (Corrigendum) V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect. Astronomy & Astrophysics, 558 (C2). ISSN 0004-6361

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Abstract

We have developed an approximate technique, based on the principles of multi-mode Gaussian optics, for studying the behaviour of shaped off-axis mirrors. We describe a mirror as an inclined phase-transforming plane, where the phase transformation across the plane is determined by the depth of the mirror as a function of position. The scattering matrix is calculated in the usual way by evaluating the overlap integrals over some surface for which the amplitudes and phases of the incoming and outgoing fields are known; because, however, the modes are not orthogonal over the surface of interest, a system of linear equations has to be solved. We demonstrate the “thin-mirror” technique by studying the behaviour of paraboloidal and ellipsoidal mirros, and we show how the performance of measured and approximate surfaces can be assessed.

Item Type:	Article
Keywords:	cosmology: observations; galaxies: clusters: general; galaxies: clusters: intracluster medium; submillimeter: general; X-rays: general; errata, addenda;
Academic Unit:	Faculty of Science and Engineering > Experimental Physics
Item ID:	14304
Identification Number:	https://doi.org/10.1051/0004-6361/201220040e
Depositing User:	Dr. Anthony Murphy
Date Deposited:	01 Apr 2021 16:17
Journal or Publication Title:	Astronomy & Astrophysics
Publisher:	EDP Sciences
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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