  An approach is presented for the inversion of experimental in-plane,
co-polarized light scattering data in p and s polarization to obtain the
normalized surface-height autocorrelation function and the rms-roughness of a
two-dimensional randomly rough metal surface. The approach is based on an
expression, obtained on the basis of second-order phase perturbation theory,
for the contribution to the mean differential reflection coefficient from the
light scattered diffusely by the rough surface. The inversion scheme is
validated by using several sets of computer generated scattering data for rough
silver surfaces defined by Gaussian surface height correlation functions. The
reconstructions obtained by this approach are found to be rather accurate for
weakly rough surfaces illuminated by p- and s-polarized incident light; this is
also true in cases where the contributions to the input data from multiple
scattering of surface plasmon polaritons is not insignificant. Finally, the
inversion scheme is applied to experimental scattering data obtained for
characterized two-dimensional randomly rough gold surfaces, and the results
obtained in this way, compare favorably to what is obtained by directly
analyzing the surface morphology. Such results testify to the attractiveness of
the computationally efficient inversion scheme that we propose.
