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

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 Cramer-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. (C) 1998 Optical Society of America OCIS codes: 120.0120, 120.3180, 100.2650, 000.5490.