The mathematics of estimating overdetermined polarization parameters is worked out within the context of the inverse modeling of linearly polarized light, and as the primary new result the general solution is presented for estimators of the linear Stokes parameters from any number of measurements. The utility of the general solution is explored in several illustrative examples including the canonical case of two orthogonal pairs. In addition to the actual utility of these estimators in Stokes analysis, the pedagogical discussion illustrates many of the considerations involved in solving the ill-posed problem of overdetermined parameter estimation. Finally, suggestions are made for using a rapidly rotating polarizer for continuously updating polarization estimates.
John Furey, John Furey,
"Estimators for overdetermined linear Stokes parameters", Proc. SPIE 9853, Polarization: Measurement, Analysis, and Remote Sensing XII, 985306 (4 May 2016); doi: 10.1117/12.2225992; https://doi.org/10.1117/12.2225992