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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 22 — Aug. 1, 2002
  • pp: 4620–4629

Fractal description of rough surfaces

Oleg V. Angelsky, Dmitry N. Burkovets, Alexander V. Kovalchuk, and Steen G. Hanson  »View Author Affiliations


Applied Optics, Vol. 41, Issue 22, pp. 4620-4629 (2002)
http://dx.doi.org/10.1364/AO.41.004620


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Abstract

The multifractal description of rough surfaces is discussed and the mechanisms for generation of fractal and multifractal height distributions of inhomogeneities for rough surfaces are simulated. The original technique for estimating the spectrum of singularities is proposed for the study of these distributions.

© 2002 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(170.6960) Medical optics and biotechnology : Tomography
(180.1790) Microscopy : Confocal microscopy
(240.5770) Optics at surfaces : Roughness
(290.0290) Scattering : Scattering

History
Original Manuscript: November 12, 2001
Revised Manuscript: March 14, 2002
Published: August 1, 2002

Citation
Oleg V. Angelsky, Dmitry N. Burkovets, Alexander V. Kovalchuk, and Steen G. Hanson, "Fractal description of rough surfaces," Appl. Opt. 41, 4620-4629 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-22-4620


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References

  1. M. Francon, Laser Speckle and Applications in Optics (Academic, New York, 1979).
  2. J. Uozumi, N. Asakura, Fractal Optics (Hokkaido University Press, Sapporo, Japan, 1995).
  3. M. V. Berry, J. H. Hannay, “Topography of random surfaces,” Nature 273, 573–576 (1978). [CrossRef]
  4. M. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Bahan, ed. (North-Holland, Amsterdam, 1981).
  5. J. F. Nye, M. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974). [CrossRef]
  6. M. S. Soskin, M. V. Vasnetsov, “Nonlinear singular optics,” Pure Appl. Opt. 7, 301–311 (1998). [CrossRef]
  7. O. V. Angelsky, S. G. Hanson, P. P. Maksimyak, Use of Optical Correlation Techniques for Characterizing Scattering Objects and Media, Vol. PM71 of SPIE Press Monograph Series (SPIE Press, Bellingham, Wash., 1999).
  8. A. S. Toporets, Optics of Rough Surfaces (Mashinostroenie, Leningrad, 1988), in Russian.
  9. J. M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  10. P. Beckmann, A. Spizzichino, Reflection of Electromagnetic Waves from Rough Surfaces (Basingstoke, Macmillan, London, 1963).
  11. A. Arneodo, G. Grasseau, M. Holschneider, “Wavelet transform of multifractals,” Phys. Rev. Lett. 61, 2281–2284 (1988). [CrossRef] [PubMed]
  12. M. Berry, I. Marzoli, W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–44 (2001).
  13. P. Hall, S. Davies, “On direction invariance of fractal dimension on a surface,” Appl. Phys. A 60, 271–274 (1995). [CrossRef]
  14. M. Hasegawa, J. Liu, Y. Konishi, “Characterization of engineering surfaces by fractal analysis,” Int. J. Jpn. Soc. Prec. Eng. 27, 192–196 (1993).
  15. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988). [CrossRef] [PubMed]
  16. J. Kertész, T. Vicsek, “Self-affine surfaces,” in Fractals in Science, A. Bunde, S. Havlin, eds. (Springer-Verlag, Berlin, 1994). [CrossRef]
  17. T. Vicsek, “Dynamics of growing self-affine surfaces,” in From Statistical Physics to Chaos, G. Györgyi, I. Kondor, L. Sasvári, T. Tél, eds. (World Scientific, Singapore, 1992).
  18. A. Dogariu, J. Uozumi, T. Asakura, “Sources of error in optical measurements of fractal dimension,” Pure Appl. Opt. 2, 339–350 (1993). [CrossRef]
  19. A. Dogariu, J. Uozumi, T. Asakura, “Angular power spectra of fractal structures,” J. Mod. Opt. 41, 729–738 (1994). [CrossRef]
  20. Y.-P. Zhao, C.-F. Cheng, G.-C. Wang, T.-M. Lu, “Power law behavior in diffraction from fractal surfaces,” Surf. Sci. Lett. 409, L703–L708 (1998). [CrossRef]
  21. O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Appl. Opt. 40, 5693–5707 (2001). [CrossRef]
  22. V. G. Zakharov, “Elaboration and application of wavelet-analysis to nonlinear hydrodynamical systems,” Ph.D. dissertation (Institute of Mechanics of Continua, Ural Division, Russian Academy of Sciences, Perm, Russia, 1997), in Russian.
  23. B. B. Mandelbrot, Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1984).
  24. N. M. Astafyeva, “Wavelet-analysis: theoretical principles and application examples,” Usp. Phys. Nauk 166, 1145–1170 (1996), in Russian. [CrossRef]
  25. A. Arneodo, “Wavelet analysis of fractals: from the mathematical concept to experimental reality,” in Wavelets: Theory and Application, M. Y. Hussaini, ed. (Oxford University, New York, 1996), pp. 352–497.

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