[OPTICAL REVIEW Vol. 6, No. 4 (1999) 293-301]

Fractal Roughness Retrieval by Integrated Wavelet Transform

Aristide DOGARIU,1,4 Glenn BOREMAN,1,5 Jun UOZUMI,2,6,* and Toshimitsu ASAKURA3

1School of Optics/CREOL, University of Central Florida, Orlando, Florida 32816, USA, 2Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido, 060-0812 Japan, 3Faculty of Engineering, Hokkai-Gakuen University, Sapporo, Hokkaido, 064-0926 Japan

(Received January 4, 1999; Accepted March 12, 1999)

An integrated-wavelet-transform (IWT) approach is proposed for the study of scattering from slightly rough surfaces that manifest scaling properties over a finite domain of correlation lengths. Instead of collecting angle-resolved intensities, values of the irradiance integrated over increasing areas are used to enhance the contributions of small irradiances at large scattering angles and to reduce the coherent noise. In the case of self-similar surfaces, the scaling behavior of IWT allows investigation of the surface roughness at various length scales. For the realistic case of self-affine surfaces, IWT permits the evaluation of the scaling exponent of the autocorrelation and also offers a direct way to evaluate the necessary length scale of the surface profile.

Key words : Integrated wavelet transform, rough surface, fractal surface, self-similar surface, self-affine surface, autocorrelation, scaling exponent