Assessing and optimizing the performance of a phase-shifting interferometer capable of measuring the complex index of refraction and the surface profile of a test surface

A novel interferometer based upon a conventional phase-shifting design is further investigated. This interferometer is capable of measuring both the real and imaginary parts of the complex index of refraction and the surface profile of a test surface. Maximum-likelihood estimation theory is shown to be an effective means of extracting the three parameters of interest from the measured data. Cramér–Rao lower bounds are introduced as a means of quantitatively assessing the performance of the system. Furthermore, it is shown that as the design parameters are optimized, the results approach the theoretical performance limit. We conclude by developing the underlying theory behind the relationship of the complex-index-of-refraction estimates to the surface-profile estimate.