Optimal polarimeter structures for estimating polarization degree, angle, and ellipticity in the presence of additive noise.

In polarimetry, it is well known that measurement matrices based on spherical 2 designs optimize Stokes vector estimation in the presence of additive noise. We investigate the optimal matrices for estimation of the degree of polarization (DOP), the angle of polarization (AOP), and the ellipticity (EOP), which are nonlinear functions of the Stokes vector. We demonstrate that spherical 2 designs also optimize DOP and EOP estimation, but not AOP estimation, for which optimal structures consist of linear analyzers forming a regular polygon on the equator of the Poincaré sphere.