Optical Information Processing of Fractal Objects

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The aim of the project is to reveal properties of diffraction field produced by fractal objects illuminated by coherent radiation such as laser light and to develop new techniques for optical information processing of fractal objects.(1) Fraunhofer diffraction due to regular fractals : Properties of Fraunhofer diffraction region produced by regular self-similar fractals were studied experimentally and theoretically on the basis of Fourier optics.(2) Statistics of diffraction field due to random fractals : Some statistical properties of speckles produced in the Fraunhofer diffraction field of random fractals were analyzed by means of computer simulation technique. It was shown that the integrated speckle intensity due to random fractals have a property unknown for ordinary speckles due to non-fractal objects.(3) Fresnel diffraction due to Cantor set : Properties of Fresnel diffraction field were studied for Cantor set that is a typical self-similar fractal on one-dimensional space. Numerical analysis showed that intensity distributions have periodicity and self-similarity, which vary depending upon object properties and propagation distance from the object.(4) Bispectrum of Cantor set : As a new method of spatial, frequency analysis, bispectra of the Cantor set was investigated numerically. An advantage of bispectra over power spectra was shown for the dimensional analysis of fractal objects contaminated by additive noise.(5) Optical information processing as fractal dimension estimators : Advantages and problems were investigated for estimation of fractal dimension by means of optical Fourier transform, optical correlation technique, and angular power spectrum. In particular, effects of scale range, lacularity and noise of objects on the estimation errors were discussed and guidelines were shown for selection of method to estimate fractal dimension.