Scattering of electromagnetic waves from a periodic surface with random roughness

Equations for the scattering of electromagnetic waves from a randomly perturbed periodic surface have been formulated using the extended boundary condition method and solved using the small perturbation method. Surface currents and scattered fields are solved for up to the second order. The results indicate that as the correlation length of the random roughness increases, the bistatic scattering patterns of the scattered fields show several beams associated with each Bragg diffraction direction of the periodic surface. The beam shape becomes broader with smaller correlation length. Results obtained using the Kirchhoff approximation are found to agree well with the present results for the hh and vv polarized backscattering coefficients for small angles of incidence.