000058496 001__ 58496
000058496 005__ 20170117133943.0
000058496 0247_ $$2doi$$a10.1364/OE.22.021263
000058496 0248_ $$2sideral$$a86362
000058496 037__ $$aART-2014-86362
000058496 041__ $$aeng
000058496 100__ $$aNavarro, R.
000058496 245__ $$aGeneralization of Zernike polynomials for regular portions of circles and ellipses
000058496 260__ $$c2014
000058496 5060_ $$aAccess copy available to the general public$$fUnrestricted
000058496 5203_ $$aZernike 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.
000058496 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E99$$9info:eu-repo/grantAgreement/ES/MINECO/FIS2011-22496
000058496 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000058496 590__ $$a3.488$$b2014
000058496 591__ $$aOPTICS$$b9 / 85 = 0.106$$c2014$$dQ1$$eT1
000058496 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000058496 700__ $$aLópez, J.L.
000058496 700__ $$aDíaz, J.A.
000058496 700__ $$0(orcid)0000-0002-1127-3739$$aPérez Sinusía, Ester$$uUniversidad de Zaragoza
000058496 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDepartamento de Matemática Aplicada$$cMatemática Aplicada
000058496 773__ $$g22, 18 (2014), 21263-21279$$pOpt. express$$tOPTICS EXPRESS$$x1094-4087
000058496 8564_ $$s2105584$$uhttp://zaguan.unizar.es/record/58496/files/texto_completo.pdf$$yVersión publicada
000058496 8564_ $$s82839$$uhttp://zaguan.unizar.es/record/58496/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000058496 909CO $$ooai:zaguan.unizar.es:58496$$particulos$$pdriver
000058496 951__ $$a2017-01-16-14:16:31
000058496 980__ $$aARTICLE