The irradiance distribution of light propagating in a multiple scattering medium undergoes spatial spreading. A numerical technique for obtaining two-way (transmitted and received combined) spread functions in configuration space is presented. This formulation is useful for modeling lidar systems in media characterized by a strongly forward scattering function such as the ocean. The theoretical basis is a random walk small angle formalism for Fourier space represen-tations of the spread functions. The assumption of all scatters being independent events allows the expression for the Fourier transform of the photon distribution (i.e. the char-acteristic function) to be written as a product of initial conditions and exponentials of integrals of scattering particle density and the Fourier representation of the local scat-tering function of the medium. The method thus applies to a stratified medium where the direction of variation is along the beam axis. We have developed a numerical method to compute configuration space spread functions utilizing two-dimensional Fast Fourier transforms. The one way results agree well with experimental measurements. When applied to the case of few scatters, our results contrast sharply with Gaussian beam models which only approach validity in a diffusion limit.
Lawrence R. Thebaud,
Stephen J. Gayer,
"Calculation Of LIDAR Beam Spread In Stratified Media", Proc. SPIE 0489, Ocean Optics VII, (27 September 1984); doi: 10.1117/12.943310; https://doi.org/10.1117/12.943310