On the validity domain of approximations to estimation variance of polarization degree, azimuth, and ellipticity

We determine the validity domain of classical approximations to estimation variance of the degree of polarization (DOP), angle of polarization, and ellipticity (EOP), when the measurement matrix of the Stokes vector is a spherical 2 design and noise is additive, white, and Gaussian. We demonstrate that this domain of validity is quite large, so that these approximations can be used safely for back-of-the-envelope calculations. In the presence of strong noise, DOP and EOP approximations show, however, some limits. We thus derive other approximations with extended domain of validity that can account for the dependence of DOP and EOP estimation variance on actual DOP and EOP values. The obtained results are important for design and performance characterization of polarimeters.