Analytic height correlation function of rough surfaces derived from light scattering

TL;DR

This paper presents an analytical expression linking the height correlation function of rough surfaces to light scattering data, validated against AFM measurements, enabling quick and accurate surface roughness characterization.

Contribution

It introduces a new analytical formula for the height correlation function derived from inverse wave scattering, improving accuracy and applicability over previous methods.

Findings

Close agreement with AFM measurements across various roughness parameters

Requires less large-angle scatter data than previous models

Provides a fast, simple experimental procedure for surface analysis

Abstract

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.