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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

  • Vol. 19, Iss. 7 — Jul. 1, 2002
  • pp: 1319–1333

Discrete Green’s methods and their application to two-dimensional phase unwrapping

Stefano Marano, Francesco Palmieri, and Giorgio Franceschetti  »View Author Affiliations


JOSA A, Vol. 19, Issue 7, pp. 1319-1333 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001319


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Abstract

A fully self-contained discrete framework with discrete equivalents of Stokes’s, Gauss’s, and Green’s theorems is presented. The formulation is analogous to that of continuous operators, but totally discrete in nature, and the exact relationships derived are shown to hold provided that a set of predefined rules is followed in building discrete contours and domains. The method allows for an analytical rigor that is not guaranteed if one translates the classical continuous formulations onto a discretized approximated framework. We clarify several issues related to the use of discrete operators, which may play a crucial role in specific applications such as the two-dimensional phase-unwrapping problem, chosen as our main application example, and we show that reconstruction on irregular domains and/or in the presence of undersampling and noise is better formulated in the discrete framework than in the continuous domain.

© 2002 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.0100) Image processing : Image processing
(100.2960) Image processing : Image analysis
(100.5070) Image processing : Phase retrieval

History
Original Manuscript: August 17, 2001
Revised Manuscript: December 17, 2001
Manuscript Accepted: December 17, 2001
Published: July 1, 2002

Citation
Stefano Marano, Francesco Palmieri, and Giorgio Franceschetti, "Discrete Green’s methods and their application to two-dimensional phase unwrapping," J. Opt. Soc. Am. A 19, 1319-1333 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-7-1319

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