Analytical Modeling of Electromagnetic Fields Scattered from a Target in the Presence of a Rough Surface

The prediction of electromagnetic fields scattered from a target located above a statistically described rough surface is of interest in multiple applications. The resulting electromagnetic fields must be described statistically given the stochastic nature of the rough surface, making quantities such as field probability density functions and moments (i.e. mean, variance, correlations, etc.) of interest. In time harmonic problems, the associated moments can be taken with or without the inclusion of field phases, resulting in identification of the coherent field (the mean of the complex valued field so that phase is included) and the incoherent power (proportional to the mean of the field amplitude squared). These moments can then be used to identify a coherent radar cross section (RCS) that is associated with the coherent field and a mean RCS that includes both coherent and incoherent contributions.