Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix

We consider the Mueller matrix ellipsometry (MME) measuring the ellipsometric parameters of the isotropic sample and the anisotropic sample under certain conditions in the presence of either Gaussian additive noise or Poisson shot noise. In this case, the ellipsometric parameters only relate to partial elements in Mueller matrix, and we optimize the instrument matrices of polarization state generator (PSG) and analyzer (PSA) to minimize the total measurement variance for these elements, in order to decrease the variance of the estimator of ellipsometric parameters. Compared with the previous instrument matrices, the optimal instrument matrices in this paper can effectively decrease the measurement variance and thus statistically improve the measurement precision of the ellipsometric parameters. In addition, it is found that the optimal instrument matrices for Poisson shot noise are same to those for Gaussian additive noise, and furthermore, the optimal instrument matrices do not depend on the ellipsometric parameters to be measured, which means that the optimal instrument matrices of MME proposed in this paper can be widely applied in various cases.