On the performance of the physicality-constrained maximum-likelihood estimation of Stokes vector

Abstract

We address the estimation of the Stokes vectors taking into account the physical realizability constraint. We propose a fast method for computing the constrained maximum-likelihood (CML) estimator for any measurement matrix, and we compare its performance with the classical empirical physicality-constrained estimator. We show that when the measurement matrix is based on four polarization states spanning a regular tetrahedron on the Poincaré sphere, the two estimators are very similar, but the CML provides a better estimation of the intensity. For an arbitrary measurement matrix, the CML estimator does not always yield better estimation performance than the empirical one: their comparative performances depend on the measurement matrix, the actual Stokes vector and the signal-to-noise ratio.