Abstract

Multiple angles of incidence have been employed in both ellipsometry and reflectometry as a means of obtaining several independent measurements for multiparameter estimation of optical constants. However, we know of no systematic investigation into the determination of a set of incidence angles and polarizations that are optimal in terms of reducing both random and systematic errors and minimizing correlations among the measurements. Several researchers have found configurations that give good results for certain problems by using physical arguments, but a general procedure that applies to all cases has not been developed. We show that the multidimensional Cramer–Rao (CR) bound gives a quantitative measure of the random errors, systematic errors, and correlations in one canonical expression; hence it is an ideal candidate for selecting an optimal experimental configuration. Maximum-likelihood estimation theory is used for the inversion problem because the estimation error is known to approach the CR bounds asymptotically. Numerical examples are given to demonstrate the procedure.

© 1991 Optical Society of America

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