Phase-shifting interferometry and maximum-likelihood estimation theory. II. A generalized solution

Abstract

A novel means of quantitatively assessing the performance of a phase-shifting interferometer is further investigated. We show how maximum-likelihood estimation theory can be used to estimate the surface profile from the general case of M noisy, phase-shifted measurements. Monte Carlo experiments show that the maximum-likelihood estimator is unbiased and efficient, achieving the theoretical Cramér–Rao lower bound on the variance of the error. We then use Monte Carlo experiments to compare the performance of the maximum-likelihood estimator with that of two conventional algorithms.

© 1998 Optical Society of America

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