Adaptive mask generating algorithm based on the fuzzy set theory for the weighted least-squares phase unwrapping

Abstract In the digital speckle pattern interferometry (DSPI), accurate phase unwrapping is essential for quantitative phase measurement. In this paper, a novel adaptive mask generating algorithm based on the fuzzy set theory is proposed, which can automatically calculate an optimal threshold for the reliability masked weighted least-squares phase unwrapping. The reliability map of a wrapped phase map is firstly calculated based on the second differences of each pixel. Then, the fuzzy interval of the threshold is determined according to reliability values of the residues and standard deviation of the reliability map, and a membership function describing the fuzzy threshold is established to map the reliability values to the interval of [0, 1]. At last, the membership matrix is used to perform weighted average processing on the reliability map to automatically calculate the optimal threshold for generating a 0-1 mask. Two sets of simulated phase maps under different noise levels and fringe abnormal conditions are generated to evaluate and the accuracy of the adaptive threshold and the performance of the proposed algorithm. Experimental phase data of deformation dynamic measurement in DSPI is adopted to verify the effectiveness of the proposed algorithm. Simulation and experimental results show that the algorithm can adaptively calculate an optimal threshold of different wrapped phase maps, which is very close to the threshold elaborately selected by manual intervention, and can provide a reliable and accurate unwrapping phase for actual phase measurement.