17 January 2008 Light scattering characterization of self-affine fractal surfaces by a new algorithm of Levenberg-Marquardt method
Author Affiliations +
Proceedings Volume 6723, 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment; 67230T (2008) https://doi.org/10.1117/12.783011
Event: 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Large Mirrors and Telescopes, 2007, Chengdu, China
Abstract
Based on the correlation of scattered light intensity profile with self-affine fractal surface parameters of roughness w, the lateral correlation length ζ and roughness exponent α, 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.
© (2008) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Ningyu Zhang, Ningyu Zhang, Chunxiang Liu, Chunxiang Liu, Guiyuan Liu, Guiyuan Liu, Man Liu, Man Liu, Chuanfu Cheng, Chuanfu Cheng, } "Light scattering characterization of self-affine fractal surfaces by a new algorithm of Levenberg-Marquardt method", Proc. SPIE 6723, 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 67230T (17 January 2008); doi: 10.1117/12.783011; https://doi.org/10.1117/12.783011
PROCEEDINGS
6 PAGES


SHARE
RELATED CONTENT


Back to Top