Yatabe Kohei, Ishikawa Kenji, Oikawa Yasuhiro
Opt Express. 2016 Oct 3;24(20):22881-22891. doi: 10.1364/OE.24.022881.
Phase extraction methods based on the principal component analysis (PCA) can extract objective phase from phase-shifted fringes without any prior knowledge about their shift steps. Although it is fast and easy to implement, many fringe images are needed for extracting the phase accurately from noisy fringes. In this paper, a simple extension of the PCA method for reducing extraction error is proposed. It can effectively reduce influence from random noise, while most of the advantages of the PCA method is inherited because it only modifies the construction process of the data matrix from fringes. Although it takes more time because size of the data matrix to be decomposed is larger, computational time of the proposed method is shown to be reasonably fast by using the iterative singular value decomposition algorithm. Numerical experiments confirmed that the proposed method can reduce extraction error even when the number of interferograms is small.
基于主成分分析（PCA）的相位提取方法可以从相移条纹中提取目标相位，而无需任何关于其相移步长的先验知识。虽然该方法快速且易于实现，但要从噪声条纹中准确提取相位需要许多条纹图像。本文提出了一种用于减少提取误差的PCA方法的简单扩展。它可以有效减少随机噪声的影响，同时继承了PCA方法的大部分优点，因为它只修改了条纹数据矩阵的构建过程。虽然由于要分解的数据矩阵尺寸较大，该方法会花费更多时间，但通过使用迭代奇异值分解算法，所提方法的计算时间显示为相当快。数值实验证实，即使干涉图数量较少，所提方法也能减少提取误差。
