Abstract
By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.
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References
Lohmann, A. W., Image rotation, Wigner rotation and the fractional Fourier transform, J. Opt. Soc. Am. (A), 1993, 10(10): 2181–2186.
Mandelbrot, B. B., Fractal Geometry of Nature, New York: Freeman, 1983.
Alieva, T., Fractional Fourier transform as a tool for investigation of fractal objects, J. Opt. Soc. Am. (A). 1996, 13(6): 1189–1192.
Meakin, P., Fractals, Scaling and Growth Far From Equilibrium, Cambridge: Cambridge University Press, 1998.
Mandelbrot, B. B., Van Ness, J. W., Fractional Brownian motions, fractional noises and applications, SIAM Rev., 1968, 10:422–437.
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Feng, S., Han, D. & Ding, H. Experimental determination of Hurst exponent of the self-affine fractal patterns with optical fractional Fourier transform. Sci China Ser G: Phy & Ast 47, 485–491 (2004). https://doi.org/10.1360/03yw0245
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DOI: https://doi.org/10.1360/03yw0245