An Analytical Formulation for the Coherent Scattered Field of a Target Above a Randomly Rough Surface

An analytical solution for the coherent field scattered from an arbitrary object above a rough surface using the bistatic response of the object in free space is presented. The method allows the computation of the mean scattered field for an object above a rough surface without the need for costly Monte Carlo simulations. Assuming the first-order scattering from the object and decomposing the illuminating field into free space and rough surface scattered components, predicted by the first-order small-slope approximation, the ensemble average scattered field can be described using a four-path model interpretation. The resulting field contributions for the first three paths have the form of an object above a flat dielectric interface with an additional reflection loss arising from surface roughness, while the contribution of the fourth path requires an additional correction term that depends on the surface roughness power spectral density function. The effects of this coherent correction term on the results are investigated.