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Diffraction on Fractals

  • C. Allain
  • M. Cloitre

Abstract

The fractal dimension of an object may be determined through the relation M(r)=rD between its mass M and its radius r or the pair correlation function g(r)=rD−d (d is the dimension of the euclidian space embedding the object). Yet, it is possible to have access to the value of D when studying the variation of the intensity I(q) which is scattered by a fractal at a wavevector q: I(q)=q−D. This relation has been used to interpret several small angle scattering experiments on silica (1). In this paper, we discuss diffraction experiments on deterministic fractal gratings (F). The intensity I(q) at wavevector q is the Optical Fourier Transform (OFT) of the grating F. This allowed a direct determination of D and led us to take in account other geometrical caracteristics of fractals.

Keywords

Structure Factor Fractal Dimension Pair Correlation Function Graphic Plotter Dimensional Fractal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    J.E. Martin, D.W. Schaefer. Phys. Rev. Lett., 53, pp 2457–2460, 1984CrossRefGoogle Scholar
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    J.W. Goodman. Introduction à l’optique de Fourier et à l’holographie p 78, Masson et Cie, Paris,1972Google Scholar
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    B.B. Mandelbrot. The fractal geometry of Nature, chap.8, W.H. Freeman and Company, New York,1982Google Scholar
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    C. Allain, B. Jouhier. J. Phys. Lett., 44,pp L421 - L428, 1983CrossRefGoogle Scholar
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    T. Viscek, J. Phys. A:Math. Gen., 16, pp L647 - L652, 1983CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • C. Allain
    • 1
  • M. Cloitre
    • 1
  1. 1.LHMP UA/CNRS 857 - ESPCIParisFrance

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