On the influence of noise statistics on polarimetric contrast optimization

In active scalar polarimetric imaging systems, the illumination and analysis polarization states are degrees of freedom that can be used to maximize the performance. These optimal states depend on the statistics of the noise that perturbs image acquisition. We investigate the problem of optimization of discrimination ability (contrast) of such imagers in the presence of three different types of noise statistics frequently encountered in optical images (Gaussian, Poisson, and Gamma). To compare these different situations within a common theoretical framework, we use the Bhattacharyya distance and the Fisher ratio as measures of contrast. We show that the optimal states depend on a trade-off between the target/background intensity difference and the average intensity in the acquired image, and that this trade-off depends on the noise statistics. On a few examples, we show that the gain in contrast obtained by implementing the states adapted to the noise statistics actually present in the image can be significant.