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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 8 — Apr. 17, 2006
  • pp: 3204–3213

Half-quadratic cost function for computing arbitrary phase shifts and phase: Adaptive out of step phase shifting

Mariano Rivera, Rocky Bizuet, Amalia Martinez, and Juan A. Rayas  »View Author Affiliations

Optics Express, Vol. 14, Issue 8, pp. 3204-3213 (2006)

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We present a phase shifting robust method for irregular and unknown phase steps. The method is formulated as the minimization of a half-quadratic (robust) regularized cost function for simultaneously computing phase maps and arbitrary phase shifts. The convergence to, at least, a local minimum is guaranteed. The algorithm can be understood as a phase refinement strategy that uses as initial guess a coarsely computed phase and coarsely estimated phase shifts. Such a coarse phase is assumed to be corrupted with artifacts produced by the use of a phase shifting algorithm but with imprecise phase steps. The refinement is achieved by iterating alternated minimization of the cost function for computing the phase map correction, an outliers rejection map and the phase shifts correction, respectively. The method performance is demonstrated by comparison with standard filtering and arbitrary phase steps detecting algorithms.

© 2006 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Image Processing

Original Manuscript: February 22, 2006
Revised Manuscript: April 4, 2006
Manuscript Accepted: April 11, 2006
Published: April 17, 2006

Mariano Rivera, Rocky Bizuet, Amalia Martinez, and Juan A. Rayas, "Half-quadratic cost function for computing arbitrary phase shifts and phase: Adaptive out of step phase shifting," Opt. Express 14, 3204-3213 (2006)

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