Extraction of Parameters of Random Self-Affine Fractal Surfaces from Light Scattered Intensity by Levenberg-Marquardt Algorithm

A method for simultaneously extracting the parameters of self-affine fractal surfaces from a single experimental profile of scattered intensity data is proposed. The Levenberg-Marquardt algorithm is introduced to fit the theoretical equation for the scattering intensity profile to the experimental data. A precision system is designed for acquisition of scattering intensity data using the Boxcar integration technique. The surface parameters extracted (root-mean-square roughness w, lateral correlation length ξ, and roughness exponent α) are compared to those obtained using atomic force microscopy.