Estimation precision of full polarimetric parameters in the presence of additive and Poisson noise

The final product of polarimetric measurements is often such polarimetric parameters as degree of polarization (DOP), angle of polarization (AOP) and ellipticity (EOP). Since these parameters are nonlinear functions of the Stokes vector, it is difficult to derive closed-form expressions of their variances. We derive approximate but accurate expressions of the estimation variances of DOP, AOP, and EOP in the presence of both additive and Poisson noise for optimal spherical design-based Stokes polarimeters. These original closed-from expressions provide a clear insight into the physical parameters that govern the estimation precision of each polarimetric parameter. They are validated through optical experiments on a real-world polarimeter. These expressions are important for designing and sizing polarimeters or polarimetric imagers aimed at different types of applications, and for assessing their performance.