Application of the rigorous method to x-ray and neutron beam scattering on rough surfaces

The paper presents a comprehensive numerical analysis of x-ray and neutron scattering from finite-conducting rough surfaces which is performed in the frame of the boundary integral equation method in a rigorous formulation for high ratios of characteristic dimension to wavelength. The single integral equation obtained involves boundary integrals of the single and double layer potentials. A more general treatment of the energy conservation law applicable to absorption gratings and rough mirrors is considered. In order to compute the scattering intensity of rough surfaces using the forward electromagnetic solver, Monte Carlo simulation is employed to average the deterministic diffraction grating efficiency due to individual surfaces over an ensemble of realizations. Some rules appropriate for numerical implementation of the theory at small wavelength-to-period ratios are presented. The difference between the rigorous approach and approximations can be clearly seen in specular reflectances of Au mirrors with different roughness parameters at wavelengths where grazing incidence occurs at close to or larger than the critical angle. This difference may give rise to wrong estimates of rms roughness and correlation length if they are obtained by comparing experimental data with calculations. Besides, the rigorous approach permits taking into account any known roughness statistics and allows exact computation of diffuse scattering.