Statistical properties of laser speckle produced in the diffraction field.

The statistical properties (i.e., the probability density function and the average contrast) of laser speckle produced by a weak diffuse object in the diffraction field have been theoretically and experimentally studied with the assumption of the Gaussian statistics for the formation of speckles. The general formulas for the probability density function and the average contrast, which are valid for an entire range of object surface and for the whole diffraction field, are introduced, and their special cases, which have been studied in the past, are derived and discussed. These formulas for the probability density function and the averagae contrast are actually evaluated in the diffraction field of a weak diffuse object illuminated by the Gaussian laser beam. The experimental study has been conducted to verify the above theoretical study, and its results are in good agreement with the theoretical ones. The circularity and noncircularity of the speckle statistics in the diffraction field are discussed on the basis of the theoretical study.