Effect of retroreflection on a Fizeau phase-shifting interferometer

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.

Algorithm for multiple-beam Fizeau interferograms with arbitrary phase shifts

The objective of this paper is to describe a novel method for phase extraction from multiple-beam Fizeau interferograms with arbitrary phase shifts. The approach begins with applying FFT method to estimate the phase shifts and then utilizes least-squares iterative algorithm to extract phase and phase shifts simultaneously. If the spatial carrier frequency of the fringes is high enough to separate the phase of the first-order maximum in the Fourier domain, the proposed method requires only two iterative cycles to accurately extract phase information from seven multiple-beam Fizeau interferograms with arbitrary phase shifts. Numerical simulations and experiments demonstrate the effectiveness of the proposed algorithm. A comprehensive analysis of the influences of systematic errors (spatial carrier frequency, reflectivity coefficient, and random noise) on the evaluation of phase shifts and phase is presented. The method has applications in high precision interferometry.

Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile

The spectrum of the intensity profile of multiple-beam Fizeau interferograms is presented. Knowledge of this spectrum provides valuable information about the characteristics of Fizeau interferograms, allowing one to calculate the phase error when the Fizeau profile is evaluated by means of two-beam phase-stepping algorithms, as is usual for low-reflectivity coefficients.