OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 35, Iss. 22 — Aug. 1, 1996
  • pp: 4325–4333

Fractality of speckle intensity fluctuations

Dmitry A. Zimnyakov and Valery V. Tuchin  »View Author Affiliations

Applied Optics, Vol. 35, Issue 22, pp. 4325-4333 (1996)

View Full Text Article

Enhanced HTML    Acrobat PDF (394 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Coherent-light diffraction on random phase screens with fractal properties leads to the formation of speckle patterns with peculiarities in correlation characteristics in the small-scale region. Such peculiarities are manifested in asymptotic behavior in intensity autocorrelation and structure functions in the vicinity of the zero values of their arguments. Intensity fluctuations in the far and the near diffraction zones are also characterized by values of fractal (Hausdorff–Besicovitch) dimensions DHB, differing from the corresponding Euclidean dimension. Relationships between the exponential factors of the structure functions of boundary field phase and scattered-light intensity fluctuations as well as between values of DHB have been obtained as a result of speckle-formation analysis for different conditions. Their dependencies on the illumination and observation conditions obtained in experiments with fractallike scatterers (rough glass plates) are in satisfactory agreement with theoretical results.

© 1996 Optical Society of America

Original Manuscript: October 4, 1995
Published: August 1, 1996

Dmitry A. Zimnyakov and Valery V. Tuchin, "Fractality of speckle intensity fluctuations," Appl. Opt. 35, 4325-4333 (1996)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. V. Berry, “Diffractals,” J. Phys. A 12, 781–797 (1979). [CrossRef]
  2. C. Allain, M. Cloitre, “Optical diffraction on fractals,” Phys. Rev. B 33, 3566–3569 (1986). [CrossRef]
  3. O. V. Angelsky, P. P. Maksimyak, T. O. Perun, “Dimensionality in optical fields and signals,” Appl. Opt. 32, 6066–6071 (1993). [CrossRef] [PubMed]
  4. E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of precision machined surfaces,” Opt. Eng. 24, 388–396 (1985).
  5. M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986). [CrossRef]
  6. E. Jakeman, “Fresnel scattering by a corrigated random surface with fractal slope,” J. Opt. Soc. Am. 72, 1034–1041 (1982). [CrossRef]
  7. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988). [CrossRef] [PubMed]
  8. D. L. Jaggard, Y. Kim, “Diffraction by bandlimited fractal screens,” J. Opt. Soc. Am. A 4, 1055–1062 (1987). [CrossRef]
  9. J. F. Benzoni, S. Sarkar, D. Sherrington, “Random phase screens,” J. Opt. Soc. Am. A 4, 17–26 (1987). [CrossRef]
  10. S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarsky, Introduction to Statistical Radiophysics. Part 2. Random Fields (Nauka, Moscow, 1978), p. 464 (in Russian).
  11. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–49 (1979). [CrossRef]
  12. D. A. Zimnyakov, V. V. Tuchin, S. R. Utz, “Investigation of statistical properties of partially developed speckles for diagnostics of human skin structural changes,” Opt. Spectrosc. USSR 76, 838–844 (1994).
  13. V. V. Tuchin, D. A. Zimnyakov, G. G. Akchurin, A. A. Mishin, I. L. Kon, “Coherence-domain optical methods for cell and tissue structure and function monitoring,” in Laser Chemistry, Biophysics, and Biomedicine, V. N. Zadkov, ed., Proc. SPIE2802, 152–163 (1996).
  14. V. V. Tuchin, S. R. Utz, I. V. Yaroslavsky, “Tissue optics, light distribution and spectroscopy,” Opt. Eng. 33, 3178–3188 (1994). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited