76957 20210121114514.0 doi 10.1364/AO.54.006575 sideral 92769 ART-2015-92769 eng (orcid)0000-0002-3698-6719 Ferreira, C. Universidad de Zaragoza Zernike-like systems in polygons and polygonal facets 2015 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 disk. In Opt. Lett. 32, 74 (2007)] we introduced a new Zernike basis for elliptic and annular optical apertures based on an appropriate diffeomorphism between the unit disk and the ellipse and the annulus. Here, we present a generalization of this Zernike basis for a variety of important optical apertures, paying special attention to polygons and the polygonal facets present in segmented mirror telescopes. On the contrary to ad hoc solutions, most of them based on the Gram-Smith orthonormalization method, here we consider a piecewise diffeomorphism that transforms the unit disk into the polygon under consideration. We use this mapping to define a Zernike-like orthonormal system over the polygon. We also consider ensembles of polygonal facets that are essential in the design of segmented mirror telescopes. 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 a typical example of telescope optical aperture are provided. info:eu-repo/grantAgreement/ES/DGA/E99 info:eu-repo/grantAgreement/ES/MINECO/FIS2011-22496 info:eu-repo/grantAgreement/ES/MINECO/FIS2014-58303 info:eu-repo/grantAgreement/ES/MINECO/MTM2014-52859 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.598 2015 OPTICS 45 / 91 = 0.495 2015 Q2 T2 0.837 2015 Electrical and Electronic Engineering 2015 Q1 Engineering (miscellaneous) 2015 Q1 Atomic and Molecular Physics, and Optics 2015 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion López, J.L. (orcid)0000-0002-1328-1716 Navarro, R. (orcid)0000-0002-8021-2745 Pérez Sinusía, E. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 54, 21 (2015), 6575-6583 Appl. opt. (2004) Applied Optics 1559-128X 466132 http://zaguan.unizar.es/record/76957/files/texto_completo.pdf Preprint 70786 http://zaguan.unizar.es/record/76957/files/texto_completo.jpg?subformat=icon icon Preprint oai:zaguan.unizar.es:76957 articulos driver 2021-01-21-10:58:47 ARTICLE