Statistical properties of three-dimensional speckle distributions produced by crossed scattered waves

The statistical properties of three-dimensional normal and fractal speckle fields produced by two or three scattered waves crossed orthogonally are studied theoretically. The probability density function and the autocorrelation function of intensity are derived for speckle fields superposed with and without interference. It is shown that the spatial anisotropy of intensity distributions exists even when three scattered waves interfere with one another. This spatial anisotropy affects the power-law distribution of intensity correlation for fractal speckles and leads to intensity patterns that are not self-similar in two or three dimensions. A potential application of the superposed speckle field is proposed.