Robust wrapping-free phase retrieval method based on weighted least squares method

Abstract

Phase unwrapping is one of the most challenging processes in many profilometry techniques. To sidestep the phase unwrapping process, Perciante et al. (2015) proposed a wrapping-free method to retrieve the phase based on the direct integration of the spatial derivatives of the fringe patterns. However, this method is only applicable to objects with phase continuity, so it may fail to handle fringe patterns containing complicated singularities such as noise, shadows, shears and surface discontinuities. In the light of this problems, a robust wrapping-free phase retrieval method is proposed that is based on the combined use of Perciante's method and the weighted least squares method. Two partial derivatives of the desired phase are obtained from the fringe patterns, while the carrier is eliminated using the direct phase difference method. The phase singularities are determined using a derivative variance correlation map (DVCM), and the weighting coefficient is obtained from the binary mask of the reverse DVCM. Simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Perciante's method demonstrating that in addition to maintaining the advantage of sidestepping the phase unwrapping process, the proposed method is available for measuring objects with some types of singularities sources.