The scattering from curved rough surfaces of an EM wave transmitted through a turbulent medium

A generalized analysis of electromagnetic (EM) wave scattering from rough surfaces yields an expression for mean scattered power flux which is the spatial Fourier transform of the product of three transfer functions: 1) the optical transfer function (OTF) of the propagating medium; 2) the joint characteristic function of the surface roughness; and 3) a coherence involving the mean surface and the wave profile. The solution is applicable to moderately rough surfaces which have rms slopes less than a few degrees. The solution is applied to laser scattering from aluminum and titanium surfaces where the medium is the atmosphere. The randomly rough surface consists of independent "roughness" and "waviness" components which possess a Gaussian autocorrelation. The deterministic surface is quadratic; the laser profile, Gaussian. The atmospheric OTF is modeled into a Gaussian form. For typical parameters, the result decouples into a specular term (depending on turbulence, wave profile, and known surface) and a diffuse component (depending on rough and known surfaces). A slightly spherical incident wave affects only the coherent term.