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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 2 — Feb. 1, 2006
  • pp: 288–297

Wavefront reconstruction from its gradients

Amos Talmi and Erez N. Ribak  »View Author Affiliations


JOSA A, Vol. 23, Issue 2, pp. 288-297 (2006)
http://dx.doi.org/10.1364/JOSAA.23.000288


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Abstract

Wavefronts reconstructed from measured gradients are composed of a straightforward integration of the measured data, plus a correction term that disappears when there are no measurement errors. For regions of any shape, this term is a solution of Poisson’s equation with Dirichlet conditions ( V = 0 on the boundaries). We show that for rectangular regions, the correct solution is not a periodic one, but one expressed with Fourier cosine series. The correct solution has a lower variance than the periodic Fourier transform solution. Similar formulas exist for a circular region with obscuration. We present a near-optimal solution that is much faster than fast-Fourier-transform methods. By use of diagonal multigrid methods, a single iteration brings the correction term to within a standard deviation of 0.08, two iterations, to within 0.0064, etc.

© 2006 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.5070) Image processing : Phase retrieval

ToC Category:
Image Processing

History
Original Manuscript: April 22, 2005
Manuscript Accepted: June 5, 2005

Citation
Amos Talmi and Erez N. Ribak, "Wavefront reconstruction from its gradients," J. Opt. Soc. Am. A 23, 288-297 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-2-288


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  22. A MATLAB program with these examples can be read at physics.technion.ac.il/~eribak/s2p/.

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