Correlation properties of three dimensional superposed fractal speckle distributions

The statistical properties of three-dimensional fractal speckle fields produced by three speckle waves crossed orthogonally are studied theoretically. The analytical expressions are derived for the intensity correlation of the superposed speckle fields, and the theoretical results are verified by means of computer simulations. It is shown that the spatial anisotropy of intensity distributions, which exists in each speckle field, remains even when three speckle waves are interfered with one another. This spatial anisotropy affects the power law distribution of intensity correlations for fractal speckle fields, and leads to speckle patterns that are not self-similar in two or three dimensions. As an application of the superposed speckle field, we propose a method to fabricate a disordered medium by illuminating photopolymer with multiple laser speckle waves.