58496 20180531095509.0 doi 10.1364/OE.22.021263 sideral 86362 ART-2014-86362 eng Navarro, R. Generalization of Zernike polynomials for regular portions of circles and ellipses 2014 Access copy available to the general public Unrestricted Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike basis for a variety of important optical apertures. On the contrary to ad hoc solutions, most of them based on the Gram-Schmidt orthonormalization method, here we apply the diffeomorphism (mapping that has a differentiable inverse mapping) that transforms the unit circle into an angular sector of an elliptical annulus. In this way, other apertures, such as ellipses, rings, angular sectors, etc. are also included as particular cases. This generalization, based on in-plane warping of the basis functions, provides a unique solution and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both, the general form and the explicit expressions for most common, elliptical and annular apertures are provided. info:eu-repo/grantAgreement/ES/DGA/E99 info:eu-repo/grantAgreement/ES/MINECO/FIS2011-22496 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 3.488 2014 OPTICS 10 / 86 = 0.116 2014 Q1 T1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion López, J.L. Díaz, J.A. (orcid)0000-0002-8021-2745 Pérez Sinusía, Ester Universidad de Zaragoza 2005 595 Universidad de Zaragoza Departamento de Matemática Aplicada Matemática Aplicada 22, 18 (2014), 21263-21279 Opt. express OPTICS EXPRESS 1094-4087 2105584 http://zaguan.unizar.es/record/58496/files/texto_completo.pdf Versión publicada 82839 http://zaguan.unizar.es/record/58496/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:58496 articulos driver 2018-05-31-09:48:44 ARTICLE