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

• Published in: Applied optics. Optical technology and biomedical optics Vol. 52; no. 27; p. 6636
• Main Authors: Hu, Haofeng, Anna, Guillaume, Goudail, François
• Format: Journal Article
• Language: English
• Published: United States 20.09.2013
• ISSN: 2155-3165
• DOI: 10.1364/AO.52.006636

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.