Scattered fields by rough surfaces

A number of surfaces having the same statistical properties are generated using one stochastic matrix. Additionally, for each surface obtained according to Markov chain, a corresponding Gaussian surface with the same mean and standard deviation is also generated. Utilizing ray-tracing, fields scattered by these surfaces are calculated and compared. It is shown that for rough surfaces generated according to the Markov chain and the Gaussian distribution, the field scatters in a wider range of angles (wider pattern) in proportion to the roughness. The number of the resulting scattering angles for the Gaussian surfaces is larger than those generated according to Markov chain. The reason is that the number of levels which a Markov surface can cover is limited by the order of the stochastic matrix. However, in the Gaussian case, the only limits are the mean and the standard deviation