Optical study of the fractional Fourier transforms for a regular fractal pattern

Shaotong Feng

doi:10.1117/12.483247

16 September 2002 Optical study of the fractional Fourier transforms for a regular fractal pattern

Shaotong Feng

Author Affiliations +

Proceedings Volume 4929, Optical Information Processing Technology; (2002) https://doi.org/10.1117/12.483247
Event: Photonics Asia, 2002, Shanghai, China

Abstract

In this paper we have successfully applied optical diffraction method to the study of fractional Fourier transforms of a regular fractal pattern—a snowflake. Fractals may be divided into two kinds: the 1stkind is called regular fractal which may be generated artificially according to a set of mathematical rules and it exhibits strict self-similarity; while the 2nd kind is called irregular fractal in which strict self-similarity is replaced by statistical self-similarity. We have obtained fractional Fourier transforms of a snowflake by optical method as an example of regular fractal. Different orders of fractional Fourier transforms are obtained. These are compared with ordinary Fourier transform of the same pattern. These experimental results are discussed in the light of the fractional Fourier transform for pattern recognition. These results may be readily extended to the case of irregular fractals which closely correspond to most of natural patterns.

Citation Download Citation

Shaotong Feng "Optical study of the fractional Fourier transforms for a regular fractal pattern", Proc. SPIE 4929, Optical Information Processing Technology, (16 September 2002); https://doi.org/10.1117/12.483247

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

;

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE