Bayesian maximum likelihood estimator of phase retardation for quantitative polarization-sensitive optical coherence tomography

This paper presents the theory and numerical implementation of a maximum likelihood estimator for local phase retardation (i.e., birefringence) measured using Jones-matrix-based polarization sensitive optical coherence tomography. Previous studies have shown conventional mean estimations of phase retardation and birefringence are significantly biased in the presence of system noise. Our estimator design is based on a Bayes' rule that relates the distributions of the measured birefringence under a particular true birefringence and the true birefringence under a particular measured birefringence. We used a Monte-Carlo method to calculate the likelihood function that describes the relationship between the distributions and numerically implement the estimator. Our numerical and experimental results show that the proposed estimator was asymptotically unbiased even with low signal-to-noise ratio and/or for the true phase retardations close to the edge of the measurement range. The estimator revealed detailed clinical features when applied to the in vivo anterior human eye.