Optical reflectivity of thin rough films: application to ellipsometric measurements on liquid films

Equations to calculate the optical properties of a flat but rough interface are given. This interface is supposed to be much thinner than the wavelength of the light, and made of N-1 layers of refractive indices n{m} (for layer m ) between two media of refractive indices n{0} and n{N}. The interfaces separating two layers are rough. The roughness is supposed to have weak slopes (mid R:nablaZmid R:(z)1). These equations can be solved very simply for any N values. The explicit solution for N=2 (one rough layer) is given for the incidence angle equal to the Brewster angle in order to apply the result to ellipsometric measurements, specially on liquid interfaces whose roughness originates from thermal fluctuations and is depending on a small number of parameters.