Generalization of Zernike polynomials for regular portions of circles and ellipses
Fecha
2014Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Impacto
|
10.1364/oe.22.021263
Resumen
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 diffe ...
[++]
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. [--]
Materias
Zernike polynomials,
Circular optical apertures
Editor
Optical Society of America
Publicado en
Optics Express, Vol. 22, Issue 18, pp. 21263-21279 (2014)
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
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.