Performance comparison of pseudo-inverse and maximum-likelihood estimators of Stokes parameters in the presence of Poisson noise for spherical design-based measurement structures.

Estimation of the Stokes vector from N>4 intensity measurements is usually performed with the pseudo-inverse (PI) estimator, which is optimal when the noise that corrupts the measurements is additive and Gaussian. In the presence of Poisson shot noise, the maximum-likelihood (ML) estimator is different from the PI estimator, but is more complex to implement since it is not closed-form. We compare in this Letter the precisions obtained with the ML and the PI estimators in the presence of Poisson noise when using measurement structures based on spherical designs. We show that, in this case, the gain in precision brought by the ML estimator is real but modest, so that in applications where processing speed is an issue, the PI estimator can be considered sufficient. This result is important in the choice of the inversion strategy for Stokes polarimetry.