## Phase-shifting interferometry and maximum-likelihood estimation theory

Applied Optics, Vol. 36, Issue 34, pp. 8871-8876 (1997)

http://dx.doi.org/10.1364/AO.36.008871

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### Abstract

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

**Citation**

Eric W. Rogala and Harrison H. Barrett, "Phase-shifting interferometry and maximum-likelihood estimation theory," Appl. Opt. **36**, 8871-8876 (1997)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-34-8871

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