A novel means of quantitatively assessing the performance of a phase-shifting interferometer is presented. We show how maximum-likelihood estimation theory can be used to estimate the surface-height profile from four noisy phase-shifted measurements. Remarkably, the analytical expression for the maximum-likelihood estimator is identical to the classical four-step algorithm, thereby rooting the traditional method on a statistically sound foundation. Furthermore, a Monte Carlo experiment shows the maximum-likelihood estimator is unbiased and efficient, achieving the theoretical Cramer–Rao lower bound on the variance of the error. This technique is then used to show that the performance is a function of the ratio of the irradiances from each arm, with the optimal performance occurring, not surprisingly, when the irradiances from the two arms are equal.
© 1997 Optical Society of America
Original Manuscript: April 28, 1997
Revised Manuscript: August 1, 1997
Published: December 1, 1997
Eric W. Rogala and Harrison H. Barrett, "Phase-shifting interferometry and maximum-likelihood estimation theory," Appl. Opt. 36, 8871-8876 (1997)