Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing

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.