Optimal distribution of integration time in degree of linear polarization polarimetry based on the expected variance

Previous study shows that if the total integration time of intensity measurements is fixed, the variance of DOLP estimator depends on the distribution of the degree of linear polarization for two intensity measurements. However, the optimal time dependents on the quantity being measured. In this paper, the expected variance is used to define a cost function for optimization of the estimator, which overcomes the above limitation. Actually, minimizing the expected variance is equivalent to minimizing the noise power of estimator, so as to improve the precision of the estimator. We also deduce the closed-form solution of the optimal distribution of the integration time for additive Gaussian noise by employing Lagrange multiplier method. According to the theoretical analyses, it is shown that the variance of DOLP estimator can be decreased for most values of DOLP without prior knowledge, and the proposed method statistically improve the measurement accuracy of the polarimetry system.