Optimal configurations of full-Stokes polarimeter with immunity to both Poisson and Gaussian noise

For a full-Stokes polarimeter (FSP), generally there are two types of noise, signal-dependent Poisson shot noise and signal-independent additive Gaussian noise, which will degrade the signal-to-noise ratio on the measured Stokes parameters. The relation between the immunity to Gaussian noise and the condition of the measurement matrix has been widely studied in the recent literature. In this paper, we present a new merit function and use it to achieve optimal configurations with immunity to both types of noise. The numerical results show that, for the FSP consisting of variable retarders followed by a fixed polarizer, the four measurement channels immune to these two types of noise can be optimally composed by a 102.2 degrees retardance with a pair of azimuths +/- 71.9 degrees and a 142.1 degrees retardance with a pair of azimuths +/- 34.95 degrees, or by two quarter-wave plates with four pairs of azimuths (+/- 70.15 degrees, +/- 87.84 degrees) and (+/- 42.82 degrees, +/- 19.14 degrees). The tolerances of the retardances or azimuths in the optimized configurations are evaluated for practical manufacturing, assembling and alignment.