## Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps

Applied Optics, Vol. 37, Issue 14, pp. 3076-3084 (1998)

http://dx.doi.org/10.1364/AO.37.003076

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### Abstract

Inasmuch as current fringe analysis techniques used in digital speckle-pattern interferometry (DSPI) yield a phase map modulo 2π, phase unwrapping is the final step of any data evaluation process. The performance of a recently published algorithm used to unwrap DSPI phase maps is investigated. The algorithm is based on a least-squares minimization technique that is solvable by the discrete cosine transform. When phase inconsistencies are present, they are handled by exclusion of invalid pixels from the unwrapping process through the assignment of zero-valued weights. Then the weighted unwrapping problem is solved in an iterative manner by a preconditioned conjugate-gradient method. The evaluation is carried out with computer-simulated DSPI phase maps, an approach that permits the generation of phase fields without inconsistencies, which are then used to calculate phase deviations as a function of the iteration number. Real data are also used to illustrate the performance of the algorithm.

© 1998 Optical Society of America

**OCIS Codes**

(100.5070) Image processing : Phase retrieval

(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.6160) Instrumentation, measurement, and metrology : Speckle interferometry

**History**

Original Manuscript: October 1, 1997

Revised Manuscript: January 7, 1998

Published: May 10, 1998

**Citation**

Guillermo H. Kaufmann, Gustavo E. Galizzi, and Pablo D. Ruiz, "Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps," Appl. Opt. **37**, 3076-3084 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-14-3076

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