Analytic height correlation function of rough surfaces derived from light scattering

摘要

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