Abstract

In this paper we study the validity of the small perturbation method for 1-D perfectly conductive random rough surfaces. We have obtained an expression for the diffuse component of the mean scattered intensity up to fourth order in powers of k₀σ for S- waves (k₀ = 2π/λ, a is the rms height). For P-waves it is not possible to obtain the fourth-order term. The perturbative expressions are derived from the Rayleigh hypothesis and also from the extinction theorem. In both cases the final expressions for the mean diffuse intensity are the same. Comparisons with exact numerical results and with those predicted by the Kirchhoff approximation are made. This permits us to establish some criteria on the validity of the perturbative solution, obtaining some new interesting facts. In particular, we show that the total incoherently scattered energy is the parameter that basically determines the applicability of the perturbative solution. Precise curves marking the zones of validity of the second-order perturbative intensity are drawn. Simultaneously, the shape of the diffuse halo as a function of the correlation length T, the angle of incidence θ₀, and the polarization is studied at small k₀σ.

© 1989 Optical Society of America