基于加权最小二乘法的鲁棒无包裹相位恢复方法
Robust Wrapping-free Phase Retrieval Method Based on Weighted Least-square Method
摘要：
对于许多轮廓术技术，相位展开是最具挑战性的过程之一。为了回避相位展开过程，Perciante et.等人[Appl Opt 2015; 54（10）：3018-23]提出了一种基于图案的空间导数的直接积分来检索相位的无包裹方法。但它只适用于被测物体相位连续的情况，这意味着它可能无法处理含有复杂奇异性的条纹图，如噪声、阴影、剪切和表面不连续等。针对这一问题，本文提出了一种基于Perciante方法和加权最小二乘法相结合的鲁棒无包裹相位恢复方法。该方法从干涉条纹图中得到所需相位的两个偏导数，同时采用直接相位差法消除载波。利用微分方差相关图（DVCM）确定相位奇异点，并从反向DVCM的二进制掩码中获得加权系数。仿真和实验证明了该方法的有效性。通过与Perciante方法的对比分析，表明该方法可用于测量具有各种奇异源的物体。
英文摘要：
For many profilometry techniques, phase unwrapping is one of the most challenging process. In order to sidestep the phase unwrapping process, Perciante et. al [Appl Opt 2015; 54(10):3018-23] proposed a wrapping-free method based on the direct integration of the spatial derivatives of the patterns to retrieve the phase. But it is only applicable for the case of the phase continuity for the tested object, which means it may fail to handle fringe patterns containing complicated singularities, such as noise, shadow, shears and surface discontinuity. In view of this problems, a robust wrapping-free phase retrieval method is proposed in this paper, which is based on combined Perciante's method and weighted least-squares method. Two partial derivatives of the desired phase is obtained from the fringe patterns, meanwhile the carrier is eliminated using direct phase difference method. The phase singularities are determined using 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. Results are analyzed and compared with those of Perciante's method, demonstrating that the proposed method can be available for measuring objects with some kinds of singularities sources.
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