Electromagnetic scattering by hemispherical bosses on a infinite plane surface

An analytic solution to the problem of multiple scattering of a plane electromagnetic wave by an array of hemispherical bosses on a perfectly conducting infinite plane surface is obtained by using the solution of the scattering by an array of full spheres, on the basis of an image technique. The solution of this problem is relevant in analyzing the scattering by 3-D rough surfaces. The system considered is replaced by the array of complete spheres in the absence of the conducting plane, but with the given incident plane wave and also a supplementary image plane wave, chosen such that the boundary conditions for the total field are satisfied at all the points where the conducting plane is located in the original problem. Numerical results are presented for the normalized backscattering cross section versus the incident angle for different systems of spheres.>