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An expression is obtained on the basis of phase perturbation theory for thecontribution to the mean differential reflection coefficient from the in-planeco-polarized component of the light scattered diffusely from a two-dimensionalrandomly rough dielectric surface when the latter is illuminated by s-polarizedlight. This result forms the basis for an approach to inverting experimentallight scattering data to obtain the normalized surface height autocorrelationfunction of the surface. Several parametrized forms of this correlationfunction, and the minimization of a cost function with respect to theparameters defining these representations, are used in the inversion scheme.This approach also yields the rms height of the surface roughness, and thedielectric constant of the dielectric substrate if it is not known in advance.The input data used in validating this inversion consists of computersimulation results for surfaces defined by exponential and Gaussian surfaceheight correlation functions, without and with the addition of multiplicativenoise, for a single or multiple angles of incidence. The reconstructionsobtained by this approach are quite accurate for weakly rough surfaces, and theproposed inversion scheme is computationally efficient.

physical review. a/physical review, a

Determination of the normalized surface height autocorrelation function  of a two-dimensional randomly rough dielectric surface by the inversion of  light scattering data