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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 24269–24281

Direct and inverse discrete Zernike transform

Rafael Navarro, Justo Arines, and Ricardo Rivera  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 24269-24281 (2009)
http://dx.doi.org/10.1364/OE.17.024269


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Abstract

An 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.

© 2009 OSA

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.1010) Optical design and fabrication : Aberrations (global)
(080.1005) Geometric optics : Aberration expansions
(110.7348) Imaging systems : Wavefront encoding

History
Original Manuscript: July 9, 2009
Revised Manuscript: November 20, 2009
Manuscript Accepted: December 4, 2009
Published: December 18, 2009

Citation
Rafael Navarro, Justo Arines, and Ricardo Rivera, "Direct and inverse discrete Zernike transform," Opt. Express 17, 24269-24281 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-24269


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