  We derive an analytic expression for the height correlation function of a
rough surface based on the inverse wave scattering method of Kirchhoff theory.
The expression directly relates the height correlation function to diffuse
scattered intensity along a linear path at fixed polar angle. We test the
solution by measuring the angular distribution of light scattered from rough
silicon surfaces, and comparing extracted height correlation functions to those
derived from atomic force microscopy (AFM). The results agree closely with AFM
over a wider range of roughness parameters than previous formulations of the
inverse scattering problem, while relying less on large-angle scatter data. Our
expression thus provides an accurate analytical equation for the height
correlation function of a wide range of surfaces based on measurements using a
simple, fast experimental procedure.
