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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 3 — Mar. 1, 1998
  • pp: 669–674

Diffraction analysis of random fractal fields

T. Alieva and F. Agullo-Lopez  »View Author Affiliations


JOSA A, Vol. 15, Issue 3, pp. 669-674 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000669


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Abstract

It is shown that optical diffraction can be used to reveal the scaling features not only of deterministic but also of random fractal fields and to determine their main characteristics. The analysis of fractals can be experimentally realized through first-order optical systems.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics

Citation
T. Alieva and F. Agullo-Lopez, "Diffraction analysis of random fractal fields," J. Opt. Soc. Am. A 15, 669-674 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-3-669


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References

  1. B. B. Mandelbrot, The Fractal Geometry of Nature, 2nd ed. (Freeman, New York, 1982), Chap. 1, pp. 1–5.
  2. A. Lakhtakia, N. S. Holter, V. K. Varadan, and V. V. Varadan, “Self-similarity in diffraction by a self-similar fractal screen,” IEEE Trans. Antennas Propag. AP-35, 236–239 (1987).
  3. C. Allain and M. Cloitre, “Optical diffraction on fractals,” Phys. Rev. B 33, 3566–3569 (1986).
  4. Y. Kim, H. Grebel, and D. L. Jaggard, “Diffraction by fractally serrated apertures,” J. Opt. Soc. Am. A 8, 20–26 (1991).
  5. Y. Sakurada, J. Uozumi, and T. Asakura, “Fresnel diffraction by one-dimensional regular fractals,” Pure Appl. Opt. 1, 29–40 (1992).
  6. J. Uozumi, Y. Sakurada, and T. Asakura, “Fraunhofer diffraction from apertures bounded by regular fractals,” J. Mod. Opt. 42, 2309–2322 (1995), and references therein.
  7. T. Alieva and F. Agullo-Lopez, “Optical wave propagation of fractal fields,” Opt. Commun. 125, 267–274 (1996).
  8. M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
  9. T. Alieva, “Fractional Fourier transform as a tool for investigation of fractal objects,” J. Opt. Soc. Am. A 13, 1189–1192 (1996).
  10. R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, Berkeley, Calif., 1966), Chap. 4, pp. 217–268.
  11. K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979), pp. 381–393.
  12. M. Nazarathy and J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982).
  13. C. Gomez-Reino, “GRIN optics and its application in optical connections,” Int. J. Optoelectron. 7, 607–680 (1992).
  14. D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transformations and their optical implementation. I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).
  15. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
  16. T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
  17. T. Alieva and F. Agullo-Lopez, “Reconstruction of the optical correlation function in a quadratic refractive index medium,” Opt. Commun. 114, 161–169 (1995).
  18. S. Abe and J. T. Sheridan, “Almost-Fourier and almost-Fresnel transformations,” Opt. Commun. 113, 385–388 (1995).
  19. M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
  20. A. W. Lohmann and B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transform,” J. Opt. Soc. Am. A 11, 1798–1801 (1994).
  21. M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).
  22. J. Feder, Fractals (Plenum, New York, 1988), Chap. 14, pp. 227–237.

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