(27) Phase Singularity Distribution of Fractal Speckles
J. Uozumi
Proc. 2nd International Conference on Optics and Laser Applications (ICOLA'07), pp.16-20
Statistical properties have been investigated recently for fractal speckles, which are scattered wavefields having fractal intensity distributions. Such speckles can be produced by illuminating a diffuser by a coherent beam having a radial intensity profile obeying a negative power function. The particularities of fractal speckles are power-law correlation tail, multi-scale speckle grains and statistically self-similar intensity distribution. It is also known that such an intensity distribution is not a simple fractal but a multifractal, which consists of subsets characterized by different fractal dimensions and is characterized by a multifractal dimension. Although, interesting properties of intensity statistics have been revealed for fractal speckles so far as explained above, phase statistics have not been studied well. In this paper, as an intriguing topic of phase properties, the spatial distribution of phase singularities is investigated by means of computer simulations. Fractal speckles are simulated on a computer by assuming a coherent power-law illumination of a rough and fine plane diffuser and observation of the speckle in a Fourier transform plane. Phase singularities are extracted numerically from the spatial distribution of complex amplitudes, and their spatial distribution are examined for several different exponent values of the power-law illumination beam. As a result, it is found that the spatial distribution of the phase singularities is again not a simple fractal but a multifractal. This stands in marked contrast to phase singularities of ordinary speckles, which are distributed uniformly.
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