Method For Reducing The Effect Of Harmonics And Phase Shifting Error In Phase Shifting Interferometry

Large aperture optical components, is of important practical meaning in many fields, such as high power solid-state laser facility, synchrotron radiation light source, astronomy and space optics. At present, the large aperture phase shifting interferometer with non-contact, high-accuracy and high-lateral resolution is considered as the most effective testing method of the large aperture optical components. Two factors will seriously affect the accuracy of the large aperture interferometer. One is the phase shifting error caused by the environmental vibration including mechanical vibration and air turbulence, the other is the harmonics introduced by the interference of multiple-beam or the nonlinearity of system. Therefore, it is of important scientific significance and practical application value to reduce the effect of the harmonics and the phase shifting error in interferometry and to make accurate measurement of optics on-situ. The purpose of this article is to design high accuracy phase shifting algorithms (PSA), and extract the phase information from the fringes with random phase-shift errors and harmonics.This paper contains three parts. The first part introduces the principle of phase shifting interferometry (PSI) and the traditional algorithms. The influence of phase shifting error and harmonics on interferometry is also studied by theoretical analysis and numerical simulation. The second part designs two kinds of iterative phase-shifting algorithms based on the least-squares method. The first iterative algorithm filters out the high-order harmonics by Butterworth low-pass filter in the frequency domain, and then extracts phase information from three frames of fringes with random phase shifts by least squares iterative method. This algorithm can effectively reduce the influence of harmonics and phase shifting error if the fringes have large spatial carrier frequency. The second iterative algorithm directly extracts the phase from fringes with random phase shifts and harmonics. It does not need the requirement of filtering process and large spatial carrier frequency, but it needs2P+1frames of fringes to reduce the effect of P-order harmonics. The validity of the two iterative algorithms is verified by simulation and experiment. In the third part, a non-iterative phase shifting algorithm based on principal component analysis (PCA) is proposed. This PCA method decomposes the interferograms into many uncorrelated quadrature signals called principal components, and then extracts the phase from the principal components without any prior guess about the phase shifts. Numerical simulations demonstrate that the PCA method extracts phase fast and exhibits high accuracy.The designed phase shifting algorithms in this paper can effectively reduce the influence of harmonics and phase shifting error on interferometry, which can improve the performance of the interferometer. In addition, the designed phase shifting algorithms can be applied to fringe analysis in the3D shape measurement, digital holography and other related fields.