Statistical characteristic of scattering from randomly rough surfaces

An analytical expression for the fourth order moment of the plane wave scattering from two-dimensional randomly rough surface with small roughness is presented based on the Kirchhoff and physical optics approximation. The fourth order moment has been simplified to get the two-position and two-frequency mutual correlation function. With the incidence wavelength 1.06 mum and different root-mean-square (rms) heights, the distributions of FOM changing with the coherence bandwidth frequency difference and scattering angles have been given. It is shown that the rms height of rough surface greatly influences on results and the scattered FOM mainly comes from the specular direction and zero frequency difference with small rms height. If the frequency difference is greater than zero, FOM will quickly decreases to zero in other directions; while at zero frequency, with the increase of rms height, there is also the biggest value which is smaller than that with smaller rms height, and the value in specular direction decreases but others increase, which we call "speckle effect". In addition, the increase of rms height results in the correlation bandwidth narrowing.