Zernike-like systems in polygons and polygonal facets
| dc.contributor.author | Ferreira González, Chelo | |
| dc.contributor.author | López García, José Luis | |
| dc.contributor.author | Navarro, Rafael | |
| dc.contributor.author | Pérez Sinusía, Ester | |
| dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
| dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
| dc.contributor.funder | Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa | es |
| dc.date.accessioned | 2018-12-14T12:04:12Z | |
| dc.date.available | 2018-12-14T12:04:12Z | |
| dc.date.issued | 2015 | |
| dc.description.abstract | 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 [Diaz et all, 2014] 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 piece-wise 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. | en |
| dc.description.sponsorship | This research was supported by the Spanish Ministry of Economía y Competitividad and the European Union, grant FIS2011-22496, and by the Government of Aragón, research group E99. The financial support of the State University of Navarra is also acknowledged. | en |
| dc.format.extent | 17 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1364/AO.54.006575 | |
| dc.identifier.issn | 1559-128X (Print) | |
| dc.identifier.issn | 2155-3165 (Electronics) | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/31769 | |
| dc.language.iso | eng | en |
| dc.publisher | Optical Society of America | en |
| dc.relation.ispartof | Applied Optics Vol. 54, Issue 21, pp. 6575-6583 (2015) | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//FIS2011-22496/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1364/AO.54.006575 | |
| dc.rights | © 2015 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Zernike polynomials | en |
| dc.subject | Orthonormal systems | en |
| dc.subject | Polygonal facets | en |
| dc.subject | Segmented mirror telescopes | en |
| dc.title | Zernike-like systems in polygons and polygonal facets | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
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