Influence of the surface profile on the roughness contribution to the ellipticity coefficient

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Abstract
The light reflection on a fluid interface is considered for determination of the intrinsic surface profile and roughness. An integral equation derived for the electric displacement vector in the surface layer is iterated to second order in the dielectric permittivity difference Δε of the coexisting phases. The ellipticity coefficient at the Brewster angle of incidence is obtained generally for an arbitrary profile and roughness spectrum assuming their spatial dimensions to be significantly less than the light wavelength. The roughness contribution to the ellipticity coefficient is shown to depend crucially on the surface profile. The ellipticity coefficient value calculated with the Fisk-Widom profile and roughness within the capillary-wave model essentially coincides with that measured in the critical region, contrary to the sharp-boundary result. The dependence of the ellipticity on the capillary-short-wave cutoff changes from linear to logarithmic due to the finiteness of the profile thickness. The term of second order in Δε violates a symmetry with respect to the permutation of coexisting phases.