Multifractals and dynamic speckle

FEDERICO, A.; KAUFMANN, G. H.

Nimes, Francia

Congreso; Speckle 06; 2006

Ecole des Mines d’ Ales, Francia

In recent years, the fractal theory has been applied to a wide variety of scientific problems. However, this approach has not been used to study dynamic processes through the analysis of temporal sequences of speckle patterns. In this work we present a study of the dynamic speckle phenomenon based on the multifractal theory. This study is carried out by calculating the Hausdorff dimension of the set of singularities of the Hölder exponent. These parameters are determined from the maxima of the wavelet transform modulus of the scattered light intensity along the time axis, for each pixel of the sequence of speckle images. Calculations conducted on experimental data evidence a multifractal structure in the case of a fast drying paint and a bruised fruit. We extend this result by using a synthetic model, which reproduces quite well the first and second spatial statistics of the speckle intensity as well as the correlation coefficient evaluated from a temporal sequence of speckle patterns.