Deng Jian, Wang Kai, Wu Dan, Lv Xiaoxu, Li Chen, Hao Junjie, Qin Jing, Chen Wei
Opt Express. 2015 May 4;23(9):12222-31. doi: 10.1364/OE.23.012222.
Focus on the phase reconstruction from three phase-shifting interferograms with unknown phase shifts, an advanced principal component analysis method is proposed. First, use a simple subtraction operation among interferograms, two intensity difference images are obtained easily. Second, set the center region of the data of intensity difference images to zero, and then construct a covariance matrix to obtain a transformation matrix. Third, two principal components of interferograms can be determined by the Hotelling transform and then phase can be calculated from the two normalized principal components by an arctangent function. By means of the simulation calculation and the experimental research, it is proved that the phase with high precision can be obtained rapidly by the proposed algorithm.
针对从具有未知相移的三幅相移干涉图进行相位重建的问题，提出了一种改进的主成分分析方法。首先，在干涉图之间进行简单的减法运算，很容易得到两幅强度差图像。其次，将强度差图像数据的中心区域设为零，然后构造协方差矩阵以获得变换矩阵。第三，通过霍特林变换确定干涉图的两个主成分，然后通过反正切函数从这两个归一化主成分计算相位。通过模拟计算和实验研究，证明了所提算法能够快速获得高精度的相位。
