Research Of Random Phase-Shifting Algorithm Based On Principal Component Analysis And Its Application

The random phase-shifting interferometry is a research focus recently and it has an important application value for on-situ measurement of optics. The reported theoretical models and analytic methods of the random phase-shifting interferometry have some limitations and the accuracy and the efficiency of on-situ measurement need to be improved. In this paper, a random phase-shifting algorithm based on principal component analysis(PCA) is studied. The basic law and the error source of the algorithm are analyzed, and then the algorithm is improved. Finally, the PCA algorithm is applied to the dynamic interferometry and some meaningful results are obtained as follows:The first part introduces the principles of phase shifting interferometry (PSI), the traditional algorithms, and the random phase-shifting algorithm based on principal component analysis. The simulation result shows that the PCA algorithm is accurate and non-iterative.The second part analyzes two problems of the PCA algorithm,the sign ambiguity and the reliability of the extracted phase by principal component analysis. To solve these problems, we analyzed the relationship between the extracted phase shifts and the global sign and the accuracy of the extracted phase. Then the sign ambiguity and the reliability of extracted phase are determined and valued by analyzing the extracted phase shifts. For the case that the reliability of extracted phase is low, a method combining the principal component analysis (PCA) and the least squares method (LSM) is proposed to improve the accuracy of the extracted phase. The method estimates the initial phase by PCA, and then reduces the residual phase error by LSM with several iterations. The validity of the extended-PCA algorithms is verified by simulation and experiment.The third part studies the application of the improved random phase-shifting alogrithm based on PCA.Firstly, a software about interferogram analysis based on Matlab is developed. The improved PCA algorithm is applied in the commercial Fizeau interferometer and it improves the accuracy of the interferometer. Secondly, a novel phase shifter calibration method based principle component analysis (PCA) is proposed to cope with nonlinear phase shifts of piezoelectric ceramic transducer. Optical experiments show that the proposed method is effective and efficient and it is meaningful to accurate interferometer..Thirdly,, The improved PCA algorithm is applied to the reference sphere calibration based on ball average. Numerical simulation shows the proposed method is more accurate and efficient than the traditional 13-step phase-shifting algorithm..The paper completely introduces the random phase-shifting algorithm based on PCA. It deeply analyzes the existing problems and then proposes effective methods to solve them. Finally, it extends the application of the improved algorithm. The results of this paper will provide a theoretical guide to the accurate interferometry and present a new insight and a new method for the on-situ measurement, thus it is of great scientific and practical meaning to optical shop testing.