A double Kirchhoff approximation for very rough surface scattering using the stochastic functional approach

[1] On the basis of the stochastic functional approach, an analytical derivation for the incoherent scattering angular distribution contributed from the double Kirchhoff solution is presented for very rough surface, that is, with both the surface roughness and the correlation length comparable to the wavelength. By the second-order Kirchhoff approximation and using the propagation shadowing function, the incoherent scattering distribution can be numerically calculated by only the two-dimensional integrals. The numerical calculations are made for the normalized roughness σ/λ = 1.0, 1.5, and 3.5 and the normalized correlation length l/λ = 1.8 and 5.0. The results show that the backscattering enhancement comes from the cross terms in the second-order Kirchhoff approximation. However, in order to obtain the calculations agreement well with the Monte Carlo simulation, the angular shadowing effect should also be included, in addition to the propagation shadowing effect.