Light scattering characterization of self-affine fractal surfaces by a new algorithm of Levenberg-Marquardt method

Based on the correlation of scattered light intensity profile with self-affine fractal surface parameters of roughness w, the lateral correlation length and roughness exponent a, we propose a new algorithm for the simultaneous extraction of three surface parameters from a single experimental scattered intensity profile data. With this algorithm, the fit of theoretical function to experimental data is used, and Levenberg-Marquardt method is introduced in finding the minimum of sum-squared error. In the iteration of fit process, the gradient and the curvature of sum-squared error function govern a jump of linear-descent to gradient-descent to guarantee the convergence and to accelerate the progress of parameters approaching their real values. In the experiment, we design precision system for the acquisition of scattered intensity data using the integration technique of Boxcar. All the actions in the experiment such as the stepped movement of surfaces, the sampling and the averaging of signals by Boxcar, the readout of the intensity data are also controlled by computer via an analog-to-digital converter. The results of the extracted surface parameters conform well with those by atomic force microscopy.