An approach to inverting experimental light scattering data for obtaining the normalized surface height autocorrelation function of a two-dimensional randomly rough dielectric surface, and its rms height is presented. It is based on the expression for the contribution to the mean differential reflection coefficient from the in-plane, co-polarized, light of s-polarization scattered diffusely from such a surface, obtained by phase perturbation theory. For weakly rough surfaces the reconstructions obtained by this approach are quite accurate.