Fast temporal phase unwrapping method for the fringe reflection technique based on the orthogonal grid fringes

In traditional temporal phase unwrapping (TPU) algorithms, wrapped phases with different spatial frequencies are obtained from several groups of phase shift fringes to calculate the unwrapped phase. Therefore, the necessary quantity of captured fringes is very large, especially for the fringe reflection technique (FRT), since a pair of phases should be unwrapped to get the slopes of two perpendicular directions. In this paper, we propose a fast TPU algorithm based on the orthogonal grid fringes by which only one image is needed to extract the two integer phases for each frequency instead of two groups of phase shift fringes, and then they can be added into the wrapped phases separately to complete the unwrapping. There are ridge errors in the direct unwrapped phases, but they are significantly suppressed by our pseudo-phase-shift strategy without any extra captured fringes. The proposed method is robust and effective where the fringe amount used for unwrapping is only 1/4 of the previous similar algorithm and 1/6-1/8 of the traditional TPU methods. The detailed comparison of measurement time is also given, which demonstrate that the FRT measurement can be accelerated in most cases by our method. The algorithm is validated by the experiments, which still works well for the severely defocusing fringes or complex specimen.