The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum

The validity of the Kirchhoff approximation for rough surface scattering is examined by comparison with exact results obtained by solving an integral equation. The pressure release boundary condition is assumed. The field quantity calculated is the bistatic scattering cross section, which is obtained with a Monte Carlo technique. The accuracy of correcting the Kirchhoff scattering cross section for shadowing is also addressed. The surface realizations used are randomly rough with a Gaussian roughness spectrum and have height variations in only one direction. The surface correlation length is found to be the most important parameter in defining the valid region of the Kirchhoff approximation away from the low grazing angle region. A procedure is given that provides a quantitative measure of the accuracy of the shadow-corrected approximation when the root-mean-square (rms) slope angle of the surface γ is ≲20° and when the incident grazing angle θ is ≳2γ. Examples with θ≲2γ are also discussed.