Fractality of speckle intensity fluctuations

Coherent-light diffraction on random phase screens with fractal properties leads to the formation of speckle patterns with peculiarities in correlation characteristics in the small-scale region. Such peculiarities are manifested in asymptotic behavior in intensity autocorrelation and structure functions in the vicinity of the zero values of their arguments. Intensity fluctuations in the far and the near diffraction zones are also characterized by values of fractal (Hausdorff-Besicovitch) dimensions D(HB), differing from the corresponding Euclidean dimension. Relationships between the exponential factors of the structure functions of boundary field phase and scattered-light intensity fluctuations as well as between values of D(HB) have been obtained as a result of speckle-formation analysis for different conditions. Their dependencies on the illumination and observation conditions obtained in experiments with fractallike scatterers (rough glass plates) are in satisfactory agreement with theoretical results.