Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters with Eight Intensity Measurements

Abstract

We demonstrate that the ellipsometric parameters of the isotropic samples can be measured by a partial polarimeter with only eight intensity measurements. Under the Gaussian and Poisson noises, we propose the optimal measurement matrices for the polarization state generator and the polarization state analyzer that minimize the total estimation variance of eight nonzero Mueller elements related to the ellipsometric parameters. In addition, since considering only four of the eight elements, the estimation variance can be further reduced, and we also introduce two proper criteria to find the optimal measurement matrices that robustly minimize the total estimation variance for these four Mueller elements. Compared with the existing measurement matrices based on 16 intensity measurements, our proposed matrices can effectively decrease the total estimation variance and, thus, improve the measurement precision of the Mueller matrix and ellipsometric parameters with only eight measurements. Furthermore, the proposed optimal measurement matrices do not depend on the Mueller elements of samples and thus not on the ellipsometric measurements.