  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 consists 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.
