OSA's Digital Library

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


View Full Text Article

Enhanced HTML    Acrobat PDF (244 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited