Orthogonal basis with a conicoid first mode for shape specification of optical surfaces
Ver/
Fecha
2016Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
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10.1364/OE.24.005448
Resumen
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational ...
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A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational symmetry is obtained applying an appropriate change of variables to Legendre polynomials, whereas the system for general freeform case is obtained applying a similar procedure to spherical harmonics. Numerical comparisons with standard systems, such as Forbes and Zernike polynomials, are performed and discussed. [--]
Materias
Orthogonal functions,
Optical surfaces,
Conicoids
Editor
Optical Society of America
Publicado en
Optics Express, vol. 24, issue 5, pp. 5448-5462 (2016)
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 MTM2014-52859 and FIS2014-58303.