A Study Of Phase Unwrapping And Application In Phase Measurement Profilometry

Phase unwrapping is a common problem in many phase measuring techniques, such as optical metrology, magnetic resonance imaging, synthetic aperture radar interferometric imaging, etc. One can only obtain the wrap phase in the (-π,π] interval due to using the arctangent function in these applications. This procedure of retrieving the continuous phase from the wrap phase is called phase unwrapping. In practice, phase unwrapping is usually a difficult inverse problem because of noise degrading real data, invalid data in the shadow regions and undersampling of data in regions where phase changes rapidly. There is no solution suitable to all the problems of phase unwrapping though many algorithms have been presented in the recent 20 years.In this paper, many popular phase unwrapping algorithms have been studied, Firstly, and their main ideas, advantages, disadvantages and suitable conditions are presented. Secondly, six of them are thoroughly compared through performing on computer-generated wrap phases. Finally, two improved phase unwrapping algorithms are developed: minimum cost flow phase unwrapping algorithm based on second difference weights and phase unwrapping algorithm based on simulated annealing. The former combines phase second difference and minimum cost flow algorithm and takes phase second difference as weight;the latter uses a cost function based on phase second-order differences, which is minimized by simulated annealing. Simulation computation shows: the former can avoid local incomplete unwrapping problem that cuts close on themselves in branch cut algorithm and reduce the errors caused by least square unwrapping algorithm. Comparing with the unweighted minimum cost flow algorithm, it also improves the phase unwrapping precision. The latter is very effective for undersampled and noise undersampled wrapped phase.The phase unwrapping results on real data in phase measurement profilometry verify also the validity of them.