Influence of noise statistics on optimizing the distribution of integration time for degree of linear polarization polarimetry

The problem of optimizing the distribution of integration time for the degree of linear polarization (DOLP) polarimetry with different types of noise statistics (Gaussian additive, Poisson shot, and gamma speckle) is investigated, in order to decrease the variance of estimator. It is found that if the total integration time of intensity measurements is fixed, the variance of DOLP estimator depends on the distribution of integration time in the presence of Gaussian noise and Poisson shot noise, whereas for the gamma noise, the variance does not depend on the distribution of integration time. We deduce the closed-form solutions of the optimal distribution of the integration time for Gaussian additive and Poisson shot noise within a common theoretical framework. In addition, we investigate the consequence of misjudging the noise statistics, and it is found that the degree of optimization only decays slightly if the noise statistics are misjudged. This characteristic indicates that it is not essential to know the statistics of the noise in advance.