Optimal Mueller matrix estimation in the presence of additive and Poisson noise for any number of illumination and analysis states.

We investigate the optimal strategies for estimating the Mueller matrix with arbitrary numbers of illumination and analysis states, in the presence of signal-independent additive noise or signal-dependent Poisson shot noise. We demonstrate that the architectures that minimize and equalize the estimation variances for both types of noise sources are based on spherical designs of order 2 or 3, and we provide closed-form expressions of the estimation precision obtained with these optimal measurement strategies. The obtained results are important to design Mueller polarimeters in practice and assess their fundamental limits in terms of estimation precision.