Application of the integral equation method of smoothing to random surface scattering

The integral equation method of smoothing is applied to the magnetic field integral equation weighted by the exponential exp (jk1 zeta) where zeta is the stochastic surface height. An integral equation in coordinate space for the average of the product of the surface current and the exponential factor is developed. The exact closed-form solution of this integral equation is obtained based on the specularity of the average scattered field. The complex amplitude of the average scattered field is thus determined by an algebraic equation which clearly shows the effects of multiple scattering on the surface. In addition, it is shown how the incoherent scattered power can be obtained using this method. Comparisons with the Kirchhoff approximation and the dishonest approach are presented, and the first-order smoothing result is shown to be superior to both.