Correlation and fractal properties of speckles in the extremely deep Fresnel diffraction region

Based on the Kirchhoff approximation and the theoretical analysis of the random light fields, the speckle intensity distributions in the extremely deep Fresnel diffraction region are simulated. The fractal property of the speckles as well as the relation between the speckle intensity distribution and the corresponding random surface is investigated. We design a microscope system to detect experimentally the speckles in the extremely deep Fresnel diffraction region, and the experimental results prove the conclusions drawn from our simulations.