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Zernike-like systems in polygons and polygonal facets

AutorFerreira, Chelo; López, José L.; Navarro, Rafael; Pérez Sinusía, Ester
Fecha de publicación2015
EditorOptical Society of America
CitaciónApplied Optics 54(21): 6575-6583 (2015)
ResumenZernike 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.
DescripciónarXiv:1506.07396v1
Versión del editorhttps://doi.org/10.1364/AO.54.006575
URIhttp://hdl.handle.net/10261/147805
DOI10.1364/AO.54.006575
Identificadoresdoi: 10.1364/AO.54.006575
e-issn: 2155-3165
issn: 1559-128X
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