LIMITS OF VALIDITY OF 3 PERTURBATION THEORIES OF THE SPECULAR SCATTERING OF LIGHT FROM ONE-DIMENSIONAL, RANDOMLY ROUGH, DIELECTRIC SURFACES

The reflectivity of p- and s-polarized light incident upon a one-dimen sional, randomly rough, dielectric surface is calculated for several a ngles of incidence, when the plane of incidence is normal to the gener ators of the surface, by a second-order small-amplitude perturbation t heory, by a second-order self-energy perturbation theory, and by a sec ond-order phase perturbation theory. The wavelength of the incident li ght is lambda = 0.6328 mu m, and the dielectric constant of the scatte ring medium is epsilon = 2.25. The surface roughness is characterized by a rms height delta and a transverse correlation length a. From a co mparison of the results of these approximate calculations with those o btained by a numerical simulation approach for each polarization of th e incident light, and for several angles of incidence, curves of delta /lambda as a function of a/lambda are constructed, below which each pe rturbative method is valid with an error that is smaller than 2.5%. It is found that, for a given value of a/lambda, the reflectivity of s- and p-polarized light is given most accurately by the phase perturbati on theory and least accurately by small-amplitude perturbation theory.