Bi-frequency correlation properties of the scattered intensity from dielectric rough surfaces.

The analytical expression for the Bi-frequency correlation function of the intensity scattered from two-dimensional dielectric randomly rough surfaces obeying Gaussian distribution are presented based on the scalar Kirchhoff approximation theory with the root-mean-square (rms) slope of the surface less than 0.25 and the Gaussian moment theorem. The results show that the bi-frequency correlation properties of the scattered intensity closely depend on the incident and scattered conditions as well as on the statistical parameters and complex refractive index of the surface. Especially, the correlation function mainly comes from the specular direction, and the coherence bandwidth and the function decrease with the increase of the roughness of the rough surface. In addition, comparing with the real part, the imagery of the complex refractive index has a greater impact on the bi-frequency correlation function.