Optical Information Processing of Fractal Objects

该项目的目的是揭示分形物体在激光等相干辐射照射下产生的衍射场的性质，并开发分形物体光学信息处理的新技术。(1)规则分形产生的夫琅和费衍射：基于傅立叶光学，从实验和理论上研究了规则自相似分形产生的夫琅和费衍射区的性质。(2)随机分形衍射场的统计特性：利用计算机模拟技术分析了随机分形夫琅和费衍射场产生的散斑的统计特性。结果表明，由于随机分形的散斑积分强度有一个属性未知的普通散斑由于非分形对象。(3)康托集的菲涅耳衍射：研究了一维空间上典型的自相似分形康托集的菲涅耳衍射场的性质。数值分析表明，强度分布具有周期性和自相似性，这取决于对象的属性和传播距离的对象。(4)Cantor集的双谱：对Cantor集的双谱作为一种新的空间、频率分析方法进行了数值研究。对于加性噪声污染的分形目标的维数分析，双谱比功率谱具有更大的优势。(5)光学信息处理作为分形维数的估计：研究了利用光学傅里叶变换、光学相关技术和角功率谱估计分形维数的优点和问题。特别讨论了目标的尺度范围、稀疏性和噪声对估计误差的影响，为分形维数估计方法的选择提供了指导。

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.