Accurate phase retrieval algorithm based on linear correlation in self-calibration phase-shifting interferometry with blind phase shifts

Abstract

The self-calibration algorithm is a powerful phase map reconstruction technique for phase-shifting interferometry with random phase shifts. The existing phase reconstruction algorithms has some restrictions on preconditions including the uniformity of background and the well distributed phase shifts. In this paper, a simple, applicable and accurate phase retrieval algorithm based on linear correlation (LCA) with non-iterative characteristic is proposed to improve this issue. Without pre-filtering, the algorithm searches for optimal linear combination coefficients of the difference intensity map by maximizing the linear correlation, and then phase shifts can be solved by these searched coefficients. Finally, according to the obtained phase shifts, the phase map is readily retrieved by using the matrix form of the linear equations. The whole phase retrieval process has no complicated mathematical transformation, hence it is simply and easily implemented. Good performance of the proposed LCA are verified by reconstructed phase maps from multiple kinds of simulation and experiment interferograms with blind phase shifts, along with the comparisons to that of the popular algorithms. Especially, the proposed algorithm has an excellent accuracy of phase reconstruction when the phase shift distributes unevenly.