Zernike-like systems in polygons and polygonal facets

arXiv:1506.07396v1

Detalhes bibliográficos
Autores: Ferreira, Chelo, López, José L., Navarro, Rafael, Pérez Sinusía, Ester
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2015
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/147805
Acesso em linha:http://hdl.handle.net/10261/147805
Access Level:acceso abierto
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spelling Zernike-like systems in polygons and polygonal facetsFerreira, CheloLópez, José L.Navarro, RafaelPérez Sinusía, EsterarXiv:1506.07396v1Zernike 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.European Union (FIS2011-22496); Government of Aragón (E99); Spanish Ministry of Economía y Competitividad (FIS2014-58303), (MTM2014-52859); State University of Navarra.Peer ReviewedOptical Society of AmericaUniversidad de NavarraGobierno de AragónUniversidad Pública de NavarraMinisterio de Economía y Competitividad (España)European CommissionConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2017201720152017info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/147805reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2014-52859-Pinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/FIS2014-58303-Phttps://doi.org/10.1364/AO.54.006575Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1478052026-05-22T06:33:51Z
dc.title.none.fl_str_mv Zernike-like systems in polygons and polygonal facets
title Zernike-like systems in polygons and polygonal facets
spellingShingle Zernike-like systems in polygons and polygonal facets
Ferreira, Chelo
title_short Zernike-like systems in polygons and polygonal facets
title_full Zernike-like systems in polygons and polygonal facets
title_fullStr Zernike-like systems in polygons and polygonal facets
title_full_unstemmed Zernike-like systems in polygons and polygonal facets
title_sort Zernike-like systems in polygons and polygonal facets
dc.creator.none.fl_str_mv Ferreira, Chelo
López, José L.
Navarro, Rafael
Pérez Sinusía, Ester
author Ferreira, Chelo
author_facet Ferreira, Chelo
López, José L.
Navarro, Rafael
Pérez Sinusía, Ester
author_role author
author2 López, José L.
Navarro, Rafael
Pérez Sinusía, Ester
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad de Navarra
Gobierno de Aragón
Universidad Pública de Navarra
Ministerio de Economía y Competitividad (España)
European Commission
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
description arXiv:1506.07396v1
publishDate 2015
dc.date.none.fl_str_mv 2015
2017
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/147805
url http://hdl.handle.net/10261/147805
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2014-52859-P
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/FIS2014-58303-P
https://doi.org/10.1364/AO.54.006575
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Optical Society of America
publisher.none.fl_str_mv Optical Society of America
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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