Phase unwrapping with the branch-cut method has been successfully used in many different applications in recent years. Most methods to set the branch cuts minimize the overall cut length. However, this technique fails in different cases, since this criterion is based mainly on statistical examinations. We show how the orientation and direction of the phase map help to create additional physical criteria that can be used to optimize the setting of the branch cuts. We show how these new criteria can be implemented into an energy function that will be minimized by a simulated annealing algorithm in order of a correct setting of the branch cuts. Finally, we present experimental results from electronic speckle pattern interferometry and digital holography phase maps.
The branch-cut method is a powerful tool for correct unwrapping of phase maps in optical metrology. However, this method encounters the problem of the correct setting of the cuts, which belongs to the class of nondeterministic-polynomial-time-complete problems. Simulated annealing is an algorithm used to solve problems of this kind in a polynomial-time execution. However, the algorithm still requires an enormous calculation time if the number of discontinuity sources and thus the number of branch cuts is high. We illustrate the motivation for the use of this algorithm and show how the running time can be severely reduced by use of reverse simulated annealing, starting from the nearest-neighbor solution to find a proper initial configuration, and by clustering of discontinuity sources.
The phase-shifting technique is used in optical metrology to evaluate the local phase of a fringe pattern. Accurate calibration of the shifting device is often essential but sometimes hardly possible because of deviations of the fringe pattern from the ideal sinusoidal shape and because of a nonconstant phase shift between consecutive frames. We introduce a new technique for calculating the phase shift between frames even in the presence of high noise and nonsinusoidal fringe patterns. In addition, this technique permits the identification of different error sources such as low signal-to-noise ratio, higher harmonics contained in the fringe pattern, and nonconstant phase shift.
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