OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1491–1502

Fluctuation correlation of the scattered intensity from two-dimensional rough surfaces

Geng Zhang and Zhensen Wu  »View Author Affiliations

Optics Express, Vol. 20, Issue 2, pp. 1491-1502 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1588 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The fourth-order moment of the scattered light, namely, the correlation function of the scattered intensity fluctuation from two-dimensional optically weak homogeneous and isotropic rough surfaces obeying Gaussian distribution are investigated based on Beckmann theory and Gaussian moment theorem. Analytical and numerical results are given for the correlation functions of the scattered intensity fluctuation. Also two important special cases, two-frequency correlation and angular correlation, are discussed, as well as the influence of the incident and observation conditions and the characteristic parameters of the rough surfaces on the correlation function which could lead to a more clear understanding of the scattering property of the rough surface and provide a theoretical basis for the 3D target recognition.

© 2012 OSA

OCIS Codes
(260.0260) Physical optics : Physical optics
(290.1350) Scattering : Backscattering
(140.3538) Lasers and laser optics : Lasers, pulsed

ToC Category:

Original Manuscript: November 2, 2011
Revised Manuscript: December 13, 2011
Manuscript Accepted: December 13, 2011
Published: January 9, 2012

Geng Zhang and Zhensen Wu, "Fluctuation correlation of the scattered intensity from two-dimensional rough surfaces," Opt. Express 20, 1491-1502 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).
  2. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  3. W. Zhensen and C. Suomin, “Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies,” Int. J. Infrared Millim. Waves13(4), 537–549 (1992). [CrossRef]
  4. G. Zhang and Z. S. Wu, “Two-frequency mutual coherence function of scattering from arbitrarily shaped rough objects,” Opt. Express19(8), 7007–7019 (2011). [CrossRef] [PubMed]
  5. E. Bahar and S. Chakrabarti, “Scattering and depolarization by large conducting spheres with rough surfaces,” Appl. Opt.24(12), 1820–1825 (1985). [CrossRef] [PubMed]
  6. E. Bahar and M. A. Fitzwater, “Scattering and depolarization by conducting cylinders with rough surfaces,” Appl. Opt.25(11), 1826–1832 (1986). [CrossRef] [PubMed]
  7. A. Ishimaru, L. Ailes-Sengers, P. Phu, and D. Winebrenner, “Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces,” Waves Random Media4(2), 139–148 (1994). [CrossRef]
  8. P. Phu, A. Ishimaru, and Y. Kuga, “Controlied milimeter-wave experiments and numerical simulations on the enhanced backscattering from one-dimensional very rough surfaces,” Radio Sci.28(4), 533–548 (1993). [CrossRef]
  9. C. Hui, W. Zhensen, and B. Lu, “Infrared laser pulse scattering from randomly rough surfaces,” Int. J. Infrared Millim. Waves25(8), 1211–1219 (2004). [CrossRef]
  10. D. J. Schertler and N. George, “Backscattering cross section of a tilted, roughened disk,” J. Opt. Soc. Am. A9(11), 2056–2066 (1992). [CrossRef]
  11. D. J. Schertler and N. George, “Backscattering cross section of a roughened sphere,” J. Opt. Soc. Am. A11(8), 2286–2297 (1994). [CrossRef]
  12. T. Michel and K. A. O'Donnell, “Angular correlation functions of amplitudes scattered from a one-dimensional, perfectly conducting rough surface,” J. Opt. Soc. Am. A9(8), 1374–1384 (1992). [CrossRef]
  13. G. Zhang, L. Tsang, and Y. Kuga, “Studies of the angular correlation function of scattering by random rough surfaces with and without a buried object,” IEEE Trans. Geosci. Rem. Sens.35(2), 444–453 (1997). [CrossRef]
  14. G. Zhang, L. Tsang, and K. Pak, “Angular correlation function and scattering coefficient of electromagnetic waves scattered by a buried object under a two-dimensional rough surface,” J. Opt. Soc. Am. A15(12), 2995–3002 (1998). [CrossRef]
  15. C. T. C. Le, Y. Kuga, and A. Ishimaru, “Angular correlation function based on the second-order Kirchhoff approximation and comparison with experiments,” J. Opt. Soc. Am. A13(5), 1057–1067 (1996). [CrossRef]
  16. Y. Kuga, C. T. C. Le, A. Ishimaru, and L. Ailes-Sengers, “Analytical, experimental, and numerical studies of angular memory signatures of waves scattered from one-dimensional rough surfaces,” IEEE Trans. Geosci. Rem. Sens.34(6), 1300–1307 (1996). [CrossRef]
  17. C. T. C. Le, A. Ishimaru, Y. Kuga, and J.-H. Yea, “Angular memory and frequency interferometry for mean height profiling of a rough surface,” IEEE Trans. Geosci. Rem. Sens.36(1), 61–71 (1998). [CrossRef]
  18. Z. S. Xu, J. Wu, Z. S. Wu, and Q. Li, “Solution for the fourth moment equation of waves in random continuum under strong fluctuations: general theory and plane wave solution,” IEEE Trans. Antenn. Propag.55(6), 1613–1621 (2007). [CrossRef]
  19. M. E. Knotts, T. R. Michel, and K. A. O’Donnell, “Angular correlation functions of polarized intensities scattered from a one-dimensionally rough surface,” J. Opt. Soc. Am. A9(10), 1822–1831 (1992). [CrossRef]
  20. M. Nieto-Vesperinas and J. A. Sanchez-Gil, “Intensity angular correlations of light multiply scattered from random rough surfaces,” J. Opt. Soc. Am. A10(1), 150–157 (1993). [CrossRef]
  21. V. N. Bronnikov and M. M. Kalugin, “Measuring the parameters of vibrations and surface roughness, using the frequency spectrum of the intensity fluctuations of scattered radiation,” J. Opt. Technol.76(11), 697–701 (2009). [CrossRef]
  22. M. J. Wang, Z. S. Wu, Y. L. Li, X. A. Zhang, and H. Zhang, “The fourth order moment statistical characteristic of the laser pulse scattering on random rough surface,” Acta. Physica. Sinica.58(4), 2390–2396 (2009).
  23. Y. Xin, Y. J. He, Y. R. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett.35(23), 4000–4002 (2010). [CrossRef] [PubMed]
  24. H. C. Jacks and O. Korotkova, “Intensity-intensity fluctuations of stochastic fields produced upon weak scattering,” J. Opt. Soc. Am. A28(6), 1139–1144 (2011). [CrossRef] [PubMed]
  25. W. Zhen-Sen and Z. Geng, “Intensity correlation function of light scattering from a weakly one-dimensional random rough surface,” Chin. Phys. Lett.26(11), 114208 (2009). [CrossRef]
  26. L. G. Shirley and N. George, “Speckle from a cascade of two thin diffusers,” J. Opt. Soc. Am. A6(6), 765–781 (1989). [CrossRef]
  27. J. S. Gradshteyn and J. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1965).

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