Gram-Charlier distribution in statistical problems of optics

Abstract

In statistical problems of optics to assess the nature of the distribution of random variables and in modern research in the field of signal processing, there is an interest in using Chebyshev-Hermit functions for coding and decoding of signals, since signal components can be described by Gram-Charlier distribution, which has universal properties, can substitute of all known distributions of random variables, and in the case of symmetry takes the form of a Gaussian distribution. A striking feature of skewness and kurtosis is their property of geometric interpretation. It is shown that the application of these parameters in decoding makes it possible to identify the overlapping signals. In statistic problems of rough surface optics, the use of distribution allows to explain some effects, in particular the spectral decomposition of white light observed at grazing angles, and the shift of the maximum specular reflection from the direction of specular luster to the right or left depending on the asymmetry sign.