The Statistical Properties of Partially Polarized Light

The focus which the end-point of the electric vector describes at a fixed point in space is an ellipse characterized by three parameters: the sum of the squares of the amplitudes of the two electric vector components, the angle which the major axis makes with the reference coordinate system, and the ratio of the minor to the major axis. The joint and marginal probability densities of these random variables are determined as a function of the degree of polarization. Results are obtained numerically for the mean, variance and marginal probabilities of these random variables as a function of the degree of polarization.