Analytical expression for wave scattering from exponential height correlated rough surfaces

Wave scattering from rough surfaces in addition to inverse scattering is an interesting approach to obtaining surface topography properties in various fields. Analytical expressions in wave scattering from some known rough surfaces not only help us to understand scattering phenomena, but can also prove adequate as a criterion to measure the information for empirical rough surfaces. For a rough surface with an exponential height correlation function, we derive an analytical expression for the diffused part and expand it in two asymptotic regimes. We consider one surface as slightly rough and the other as very rough based on the framework of the Kirchhoff theory. Finally, we have measured the role of various Hurst exponents and correlation lengths on the scattering intensity in self-affine surfaces. We have shown that by increasing the Hurst exponent from H 0 to H = 1, diffuse scattering decreases with scattering angle.