Analytical solution of the fourth-moment equation and interpretation as a set of phase screens

An approximate solution for the parabolic fourth-moment equation is found in the form of a multiple convolution over spatial frequencies that is extremely accurate in the case of multiple scatter. The physical significance of this solution is that it represents the extended medium as a large number of equally spaced weak phase-modulated screens. The multiple convolution can be evaluated approximately in closed form as a single integral referred to as the fundamental solution, which is useful for investigating the general behavior of the intensity-fluctuation spectra. It also allows more exact estimates to be made of the multiple convolution. These theoretical results are also compared with numerical simulations of the corresponding propagation experiment.