Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts

A non-iterative method based on principal component analysis (PCA) is presented to directly extract the phase from multiple-beam Fizeau interferograms with random phase shifts. The PCA method is the approach that decomposes the multiple-beam Fizeau interferograms into many uncorrelated quadrature signals and then applies principal component analysis algorithm to extract the measured phase without any prior guess about the phase shifts. Some factors that affect the performance of the proposed method are analyzed and discussed. Numerical simulations and experiments demonstrate that the proposed method extracts phase fast and exhibits high precision. The method can be applied in high precision interferometry.