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Title

Direct and inverse discrete Zernike transform

AuthorsNavarro, Rafael; Arines Piferrer, Justo; Rivera, Ricardo CSIC
KeywordsAberration expansions
Wave-front sensing
Wavefront encoding
Aberrations (global)
Issue DateDec-2009
PublisherOptical Society of America
CitationOptics Express 17(26): 24269-24281 (2009)
AbstractAn invertible discrete Zernike transform, DZT is proposed and implemented. Three types of non-redundant samplings, random, hybrid (perturbed deterministic) and deterministic (spiral) are shown to provide completeness of the resulting sampled Zernike polynomial expansion. When completeness is guaranteed, then we can obtain an orthonormal basis, and hence the inversion only requires transposition of the matrix formed by the basis vectors (modes). The discrete Zernike modes are given for different sampling patterns and number of samples. The DZT has been implemented showing better performance, numerical stability and robustness than the standard Zernike expansion in numerical simulations. Non-redundant (critical) sampling along with an invertible transformation can be useful in a wide variety of applications.
DescriptionContiene: 4 ilustraciones, 2 tablas y fórmulas.
Publisher version (URL)http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-26-24269
URIhttp://hdl.handle.net/10261/29832
DOI10.1364/OE.17.024269
ISSN1094-4087
Appears in Collections:(ICMA) Artículos

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