The Multi-Scale and the Multi-Fractality Properties of Speckles on Rough Screen Surfaces

With a microscopic imaging system composed of microscopic objective, lens and CCD, we observe the complicated structures in the speckle fields on the surface of a rough screen. It is found that such structures contain ridge stripes, large platform-like grains, and shivy grains, exhibiting multiple scales in size and multiple fractalities. Simulations shows these structures are formed by different parts of the rough surface. The experimental curve of the autocorrelation function of the speckle intensity includes the three parts of the central peak, the transition part and the long tail part. Using the sum of self-affine fractal models with different scales and fractalities, we propose theoretically a triple-scale autocorrelation function to describe the speckle field. Fit of this autocorrelation function to the experimental curve gives the values of such parameters as average speckle sizes and fractalities in different scales of the speckle structures.