1991 Fiscal Year Final Research Report Summary
Optical Information Processing of Fractal Objects
| Project/Area Number |
02452078
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理計測・光学
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| Research Institution | Hokkaido University |
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Principal Investigator |
ASAKURA Toshimitsu Hokkaido University, Research Institute of Applied Electricity, Professor, 応用電気研究所, 教授 (70001188)
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| Co-Investigator(Kenkyū-buntansha) |
OKAMOTO Takashi Hokkaido University, Research Institute of Applied Electricity, Research Associa, 応用電気研究所, 助手 (40204036)
UOZUMI Jun Hokkaido University, Research Institute of Applied Electricity, Associate Profes, 応用電気研究所, 助教授 (50184982)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Fractal / Koch curve / Cantor set / Fraunhofer diffraction / Fresnel diffraction / Speckle / Bispectrum / Fractal dimension |
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| Research Abstract |
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.
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