Length Scales Analysis of Wave Scattering from Rough Surfaces

The aim is to study surface characteristics through scattered wave intensity in frame work of the Kirchhoff wave theory. There are three length scales which scaling behavior between them play role in rough surface scattering, wave-length (λ) of the incident wave, the roughness (σ) and the correlation length (ξ) of the surface. In this work we show the effective role of the correlation length in surface scattering. Up to now, some of the reports for wave scattering from rough surfaces are based on the product of the wave number and surface roughness kσ without consideration to correlation length. For λx, correlation length has no effects on the properties of the scattered wave and kσ is the appropriate parameter to study the rough surfaces scattering problem. But, if ξ and λ are in comparable range, scattered wave depends on how kσ is chosen by k or σ. In this case, kσ is not suitable to present wave scattering from rough surface. In other word, for a constant ka, scattered wave could depend on any of the parameters k or σ. To justify our statements we compare our theoretical results with experimental data for the intensity profile obtained from a self-affine rough surface. We show that by changing the parameters ξ, λ, σ, and the Hurst exponent, the intensity profiles obtained by theory and numerical estimation overlap when λ is much longer than ξ. But interestingly, the profiles start to diverge when ξ tends to λ. This provides a good understanding of the role of the characteristics of the surface on the profile of scattered intensity.