Abstract
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional randomly rough dielectric surface when the latter is illuminated by $s$-polarized light. This result forms the basis for an approach to inverting experimental light-scattering data to obtain the normalized-surface-height autocorrelation function of the surface. Several parametrized forms of this correlation function, and the minimization of a cost function with respect to the parameters defining these representations, are used in the inversion scheme. This approach also yields the rms height of the surface roughness, and the dielectric constant of the dielectric substrate if it is not known in advance. The input data used in validating this inversion consist of computer simulation results for surfaces defined by exponential and Gaussian surface-height correlation functions, without and with the addition of multiplicative noise, for a single or multiple angles of incidence. The reconstructions obtained by this approach are quite accurate for weakly rough surfaces, and the proposed inversion scheme is computationally efficient.
Highlights
Statistical information about the roughness of a surface is contained in its rms height and in its normalized-surface-height autocorrelation function
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a twodimensional randomly rough dielectric surface when the latter is illuminated by s-polarized light
For the first scattering system we consider, it is assumed that the surface-height autocorrelation function W (|x |) is exponential, Eq (27a), and characterized by a transverse correlation length a = 158.20 nm and an rms height of the surface δ = 9.50 nm
Summary
Statistical information about the roughness of a surface is contained in its rms height and in its normalized-surface-height autocorrelation function. The determination of the rms height of the surface and the normalized-surface-height autocorrelation function was achieved by assuming an expression for the latter function of a particular analytic form and by the determination of the parameters defining it by a least-squares fit of the theoretical mean intensity to the experimental result In contrast to these studies, in this paper we present an approach to the determination of the rms height and the normalized-surface-height autocorrelation function of a twodimensional randomly rough penetrable surface, in particular a dielectric surface, from the inversion of optical scattering data. The dielectric constant of the medium is taken into account in this approach This version of rough-surfacescattering theory was chosen in this study because in a recent comparison between experimental data and the predictions of three perturbation theories for the scattering of electromagnetic radiation from two-dimensional randomly rough metal surfaces, it produced the best results [5]. The paper ends with an appendix detailing the derivation of expressions, central to the present work, for the first few moments of the scattering matrix for s-to-s scattering obtained on the basis of phase perturbation theory
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