Correlation properties of speckles produced by diffractal-illuminated diffusers

Correlation properties are investigated theoretically for the field scattered by a rough surface which is illuminated by a diffractal produced in the Fraunhofer diffraction region of a random fractal object. In this configuration, the diffractal illuminating the rough surface has a power-law average intensity distribution with a saturated finite value at the center. The second scattering by the rough surface produces another speckle pattern in its Fraunhofer diffraction region. It is shown that the resultant speckled speckles are described by an intensity correlation function expressed by the modified Bessel function. This correlation function approaches a power function for small values of the argument, provided that the fractal dimension of the fractal object is between 1 and 2. Hence, the resultant speckle intensity distribution is considered to be fractal.

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