一种改进的施密特正交化两步相移算法

An Improved Two-Step Phase-Shifting Algorithm Based on Gram-Schmidt Orthonormalization

提出了一种基于施密特正交化的两步相移算法的改进方法。通过高斯高通滤波器滤除干涉图的直流项,再将两幅滤波后的干涉图的强度进行施密特正交化,并根据两个正交向量的模之间的反正弦关系提取相移量。在两步相移干涉测量中,当两幅干涉图之间的相移量值确定后,可以通过一个反正切函数来恢复待测相位。模拟计算和实验研究的结果表明:与现有的几种两步相移算法相比,所提出的方法不仅可以准确地提取相移量,并且可以快速地恢复待测相位,在相位测量领域具有广泛的应用前景。

An improved two-step phase-shifting algorithm based on the Gram-Schmidt orthonormalization is proposed. After removing the direct current of the interferograms by a Gaussian high-pass filter and orthonormalizing the intensity of the two-frame filtered interferograms by Gram-Schmidt process, the phase shift can be extracted by an arcsine function according to the relationship between two orthogonal vector norms. In the two-step phase-shifting interferometry, as long as the phase shift value between two-frame interferograms is determined, the measured phase can be retrieved by an arctangent function. This method can not only extract the accurate phase shift value, but also retrieve the phase rapidly. By means of computer simulation and experiment, and comparing the performance of this method with several two-step phase-shifting algorithms, the result proves the effectiveness and the advantage of the proposed method in the phase measurement.