Estimation variance of dual-rotating-retarder Mueller matrix polarimeter in the presence of Gaussian thermal noise and poisson shot noise

摘要

In this paper, the close-form functions of estimation variances on the elements of the measured Mueller matrix for a dual-rotating-retarder Mueller matrix polarimeter with a rotating frequency ratio of 5 omega :N omega (N = 1, 2, 3, 4, 6, 7, 8, 9) are addressed by theoretical analysis and simulations in the presence of additive Gaussian noise and signal-dependent Poisson shot noise, which are two dominant types of noise in the most commonly used detectors. The results provide a clear insight into the estimation precision of each Mueller matrix element. It is found that (1) estimation variances on each element of the Mueller matrix are heavily dependent on the retardances of the retarders and inversely proportional to the number of measurements; (2) for Gaussian noise, estimation variances are independent of rotating frequency ratio and dual 130.18 degrees retardances can minimize the total variance of the 16 estimated Mueller matrix elements at a fixed number of measurements; (3) for Poisson noise, the estimation variances are only dependent on four elements of the Mueller matrix under test when the rotating frequency ratio of 5 omega :7 omega is used; (4) the retardance in the range from 126.43 degrees -133.54 degrees can result in a nearly-minimum total variance for both Gaussian and Poisson noise, whatever the observed Mueller matrix. These results are important for designing dual-rotating-retarder Mueller matrix polarimeters aimed at different types of applications and for assessing their performance.