Integral equation for scattering by a rough surface

The single integral equation method for scattering by dielectrics reduces the memory requirements for an electromagnetic scattering calculation from those of other common methods to those for a perfect conductor. This is especially important for three-dimensional finite scatterers for which the number of patches covering the surface needs to be large enough to obtain accurate results. Special considerations apply to particular configurations, such as the scattering by a rough surface represented by a measured square area, which we assume is embedded in a plane interface. The exact computation described can be used to determine the validity of approximate statistical methods, which are not necessarily accurate when the wavelength of the light is comparable to the feature size or when the surface is not a perfect conductor. We consider a homogeneous dielectric that fills a half space and has a rough surface.