We analyze the estimation precision of the parameter of the orthogonal state contrast image (OSCI) under coherent illumination. This parameter represents the degree of polarization of the light if the materials that compose the scene are purely depolarizing. Two different estimation modes are considered, depending on the uniformity of the illumination of the scene. We first determine lower bounds on the estimation precision in both cases by computing the Cramer–Rao lower bounds (CRLBs) for unbiased estimation. This allows us to compare the potential precision that can be reached in each mode. We then consider the estimators based on empirical averaging of the data, and we show that there are cases where they are strongly biased. We thus propose and characterize another estimator based on the natural representation of the OSCI, which is asymptotically unbiased and whose variance is close to the unbiased CRLB.
© 2005 Optical Society of America
Original Manuscript: January 19, 2005
Revised Manuscript: April 26, 2005
Manuscript Accepted: April 26, 2005
Published: November 1, 2005
Nicolas Roux, François Goudail, and Philippe Réfrégier, "Cramer–Rao lower bounds on the estimation of the degree of polarization in coherent imaging systems," J. Opt. Soc. Am. A 22, 2532-2541 (2005)