Robust weighted least-squares phase-unwrapping algorithm

Abstract

Phase unwrapping is one of the key steps of optical interferogram analysis.However,implementing phase-unwrapping algorithm(PUA) can be challenging,and the accuracy may be low when it is used to handle fringe patterns containing complicated singularities, such as noise, shadow, shears and surface discontinuity. When weighted least-squares unwrapping approach is adopted to unwrap the phase,the weighting coefficients are designed and defined to distinguish the singularities regions and normal regions in wrapped phase patterns.The weighting coefficients corresponding to the singularities are given zero-weighted, the singularities will not affect the unwrapping.But weighted least-squares unwrapping approach has the smooth effect on the final phase map.In view of this problem, a Robust Weighted leastsquares phase-unwrapping algorithm is proposed in this paper, which is based on combining the phase correction operation and weighted least-squares(WLS) method.In our method, Two partial derivatives of the wrapped phase are obtained from the fringe patterns. The phase singularities are determined using reliability, and the weighting coefficient is obtained from the binary mask from the reliability mask generated by thresholding method. The Weighted leastsquares phase-unwrapping was solved using the preconditioned conjugate gradient (PCG) method,The result of WLS is used to estimate the fringe order directly.The spatial phase unwrapping algorithm is applied to correct the phase with residual wraps by. Experiments are conducted to prove the validity of the proposed method. Results are analyzed and compared with the other least-squares methods, The experimental results demonstrate that the performance of proposed method.