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

Abstract

Inasmuch as current fringe analysis techniques used in digital speckle-pattern interferometry (DSPI) yield a phase map modulo 2pi, 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.