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

Ningyu Zhang; Chunxiang Liu; Guiyuan Liu; Man Liu; Chuanfu Cheng

doi:10.1117/12.783011

17 January 2008 Light scattering characterization of self-affine fractal surfaces by a new algorithm of Levenberg-Marquardt method

Ningyu Zhang, Chunxiang Liu, Guiyuan Liu, Man Liu, Chuanfu Cheng

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.

Citation Download Citation

Ningyu Zhang, Chunxiang Liu, Guiyuan Liu, Man Liu, and 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); https://doi.org/10.1117/12.783011

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
6 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Fractal analysis

Light scattering

Atomic force microscopy

Scattering

Correlation function

Data acquisition

Algorithms

Show All Keywords

Keywords/Phrases

Search In:

Publication Years