Optical Information Processing of Fractal Objects

分形物体的光学信息处理

基本信息

批准号：
02452078
负责人：
ASAKURA Toshimitsu
金额：
$ 3.78万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (B)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-02452078/
关键词：
Fractal Koch curve Cantor set Fraunhofer diffraction Fresnel diffraction Speckle Bispectrum Fractal dimension フ-リェ空間

项目摘要

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.

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光学。（2）由于随机分形而引起的衍射场的统计：通过计算机仿真技术分析了随机分形的一些统计特性。结果表明，由于非骨骼对象，由于随机分形引起的集成斑点强度的普通斑点未知的特性。（3）由于Cantor集合引起的菲涅耳衍射：Cantor衍射场的特性是Cantor Set的特性，这是典型的自同时在一维空间上的自同时分类。数值分析表明，强度分布具有周期性和自相似性，这取决于对象的物体性质和繁殖距离。（4）Cantor Set的双光谱：作为一种新的空间，频率分析的方法，Cantor Set的双偏度被数字研究了。显示了双光谱比功率光谱的优势，用于对被添加剂噪声污染的分形对象进行维数分析。（5）光学信息处理作为分形维估计器的光学处理：研究优势和问题，以通过光学傅立叶变换，光学相关技术和角度功率光谱来估计分形维度。特别地，讨论了量表范围，对象的差距和噪声对估计误差的影响，并显示了用于选择分形维的方法的准则。