Exact Analytic Representations for the Integral Characteristics of a Four-Point Coherence Function for Laser Beams in Turbulent Media

Abstract

A new integral-functional equation is derived for the four-dimensional Fourier transform of the four-point coherence function of laser beams in turbulent media and two families of exact analytical solutions of this equation are found. These solutions hold for any level of fluctuations of the refractive index of air. They are used to obtain exact analytic representations of the integral characteristics of the four-point coherence function. In particular, the truncated spectral characteristics of the spatial correlation function of the intensities are found. These representations can be used to test asymptotic, numerical, and other methods for finding this function and to describe its integral properties.