Two-Scale Kirchhoff Theory: Comparison of Experimental Observations With   Theoretical Prediction
  We introduce a non-perturbative two scale Kirchhoff theory, in the context of light scattering by a rough surface. This is a two scale theory which considers the roughness both in the wavelength scale (small scale) and in the scales much larger than the wavelength of the incident light (large scale). The theory can precisely explain the small peaks which appear at certain scattering angles. These peaks can not be explained by one scale theories. The theory was assessed by calculating the light scattering profiles using the Atomic Force Microscope (AFM) images, as well as surface profilometer scans of a rough surface, and comparing the results with experiments. The theory is in good agreement with the experimental results. 
G. R. Jafari, P. Kaghazchi, R. S. Dariani, A. Iraji zad, S. M.   Mahdavi, M. Reza Rahimi Tabar and N. Taghavinia