OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 25, Iss. 12 — Dec. 1, 2008
  • pp: 3030–3042

Statistical properties of three-dimensional speckle distributions produced by crossed scattered waves

Takashi Okamoto and Shuhei Fujita  »View Author Affiliations

JOSA A, Vol. 25, Issue 12, pp. 3030-3042 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (878 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The statistical properties of three-dimensional normal and fractal speckle fields produced by two or three scattered waves crossed orthogonally are studied theoretically. The probability density function and the autocorrelation function of intensity are derived for speckle fields superposed with and without interference. It is shown that the spatial anisotropy of intensity distributions exists even when three scattered waves interfere with one another. This spatial anisotropy affects the power-law distribution of intensity correlation for fractal speckles and leads to intensity patterns that are not self-similar in two or three dimensions. A potential application of the superposed speckle field is proposed.

© 2008 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(220.3740) Optical design and fabrication : Lithography

ToC Category:
Coherence and Statistical Optics

Original Manuscript: August 1, 2008
Revised Manuscript: October 7, 2008
Manuscript Accepted: October 10, 2008
Published: November 19, 2008

Takashi Okamoto and Shuhei Fujita, "Statistical properties of three-dimensional speckle distributions produced by crossed scattered waves," J. Opt. Soc. Am. A 25, 3030-3042 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60-64 (1997). [CrossRef]
  2. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56 (2000). [CrossRef] [PubMed]
  3. S. Shoji and S. Kawata, “Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin,” Appl. Phys. Lett. 76, 2668-2670 (2000). [CrossRef]
  4. T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725-727 (2001). [CrossRef]
  5. L. Leushacke and M. Kirchner, “Three-dimensional correlation coefficient of speckle intensity for rectangular and circular apertures,” J. Opt. Soc. Am. A 7, 827-832 (1990). [CrossRef]
  6. T. Okamoto and T. Asakura, “The statistics of dynamic speckles,” in Progress in Optics, Vol. 34, E.Wolf, ed. (Elsevier, 1995), pp. 183-248. [CrossRef]
  7. M. Kowalczyk and E. Bernabeu, “Space-time correlation properties of dynamic laser speckle in the near diffraction field of a longitudinally moving diffuse object,” J. Opt. Soc. Am. A 6, 758-764 (1989). [CrossRef]
  8. T. Yoshimura and S. Iwamoto, “Dynamic properties of three-dimensional speckles,” J. Opt. Soc. Am. A 10, 324-328 (1993). [CrossRef]
  9. H. T. Yura, S. G. Hanson, R. S. Hanson, and B. Rose, “Three-dimensional speckle dynamics in paraxial optical systems,” J. Opt. Soc. Am. A 16, 1402-1412 (1999). [CrossRef]
  10. H. T. Yura, S. G. Hanson, and M. L. Jakobsen, “Speckle dynamics resulting from multiple interfering beams,” J. Opt. Soc. Am. A 25, 318-326 (2008). [CrossRef]
  11. J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156, 350-358 (1998). [CrossRef]
  12. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007), Chap. 3.
  13. E. Kolenovic, W. Osten, and W. Juptner, “Non-linear speckle phase changes in the image plane caused by out of plane displacement,” Opt. Commun. 171, 333-344 (1999). [CrossRef]
  14. W. Kim, V. P. Safonov, V. M. Shalaev, and R. L. Armstrong, “Fractals in microcavities: giant coupled, multiplicative enhancement of optical responses,” Phys. Rev. Lett. 82, 4811-4814 (1999). [CrossRef]
  15. T. Okamoto and A. Fukuyama, “Light amplification from cantor and asymmetric multilayer resonators,” Opt. Express 13, 8122-8127 (2005). [CrossRef] [PubMed]
  16. J. Uozumi, “Fractality of the optical fields scattered by power-law-illuminated diffusers,” Proc. SPIE 4607, 257-267 (2001). [CrossRef]
  17. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359-367 (2008). [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