OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 1 — Jan. 1, 2006
  • pp: 73–80

Statistics of specular points at a randomly rough surface

Iosif M. Fuks and Mikhail I. Charnotskii  »View Author Affiliations

JOSA A, Vol. 23, Issue 1, pp. 73-80 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (152 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Statistical parameters are obtained for an ensemble of specular points at a randomly rough Gaussian statistically isotropic surface at normal incidence. The joint probability density functions (PDFs) of specular point heights and total curvátures are derived separately for maxima, minima, and saddle points. The joint PDFs of brightness and surface elevations of specular points of different types are obtained analytically in an explicit form.

© 2006 Optical Society of America

OCIS Codes
(030.5770) Coherence and statistical optics : Roughness
(080.2720) Geometric optics : Mathematical methods (general)
(240.6700) Optics at surfaces : Surfaces
(290.1350) Scattering : Backscattering
(290.5880) Scattering : Scattering, rough surfaces

ToC Category:
Coherence and Statistical Optics

Iosif M. Fuks and Mikhail I. Charnotskii, "Statistics of specular points at a randomly rough surface," J. Opt. Soc. Am. A 23, 73-80 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. Zeng, J. Kondev, D. McNamara, and A. A. Middleton, "Statistical topography of glassy interfaces," Phys. Rev. Lett. 80, 109-112 (1998). [CrossRef]
  2. A. S. Balankin and O. Sussarey, "A new statistical distribution for self-affine crack roughness parameters," Philos. Mag. Lett. 79, 629-637 (1999). [CrossRef]
  3. P. Lehmann, "Surface roughness measurement based on the intensity correlation function of scattered light under speckle-pattern illumination," Appl. Opt. 38, 1144-1152 (1999). [CrossRef]
  4. M. Elias and M. Menu, "Experimental characterization of a random metallic rough surface by spectrometric measurements in the visible range," Opt. Commun. 180, 191-198 (2000). [CrossRef]
  5. F. P. Quintian, M. A. Rebollo, R. G. Berlasso, and N. G. Gaggiolli, "A valuable method for online wire quality control: light scattering from cylindrical rough surface," in Proc. SPIE 4399, 328-334 (2003). [CrossRef]
  6. C. Cox and W. Munk, "Measurement of roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am. 44, 838-850 (1954). [CrossRef]
  7. C. Cox and W. Munk, "Statistics of sea surface derived from the sun's glitter," J. Mar. Res. 13, 198-227 (1954).
  8. O. I. Yordanov and M. A. Michalev, "Statistics of specular points on a non-Gaussian random surface," J. Opt. Soc. Am. A 6, 1578-1583 (1989). [CrossRef]
  9. G. L. Stamm and L. A. Harris, "Sea echo measurements made with 1.06-µm laser radiation," Appl. Opt. 13, 2477-2479 (1974). [CrossRef] [PubMed]
  10. J. L. Bufton, F. E. Hoge, and R. N. Swift, "Airborne measurements of laser backscatter from the ocean surface," Appl. Opt. 22, 2603-2618 (1983). [CrossRef] [PubMed]
  11. J. A. Reagan and D. A. Zielinskie, "Spaceborne lidar remote sensing techniques aided by surface return," Opt. Eng. 30, 96-102 (1991). [CrossRef]
  12. J. H. Churnside, S. G. Handson, and J. W. Wilson, "Determination of ocean wave spectra from images of backscattered incoherent light," Appl. Opt. 34, 962-968 (1995). [CrossRef] [PubMed]
  13. M. S. Longuet-Higgins, "The statistical analysis of a random, moving surface," Philos. Trans. R. Soc. London, Ser. A 249, 321-387 (1957). [CrossRef]
  14. M. S. Longuet-Higgins, "The statistical distribution of the curvature of a random Gaussian surface," Proc. Cambridge Philos. Soc. 54, 439-454 (1958). [CrossRef]
  15. M. S. Longuet-Higgins, "The distribution of the sizes of images reflected in a random surface," Proc. Cambridge Philos. Soc. 55, 91-100 (1959). [CrossRef]
  16. M. S. Longuet-Higgins, "Reflection and refraction at a random moving surface," J. Opt. Soc. Am. 50, 838-856 (1960). [CrossRef]
  17. M. S. Longuet-Higgins, "The statistical geometry of random surfaces," in Hydrodynamic Instability, in Proceedings of the 13th Symposium on Applied Mathematics (American Mathematical Society. 1962), Vol. 13, pp. 105-143
  18. R. J. Adler, The Geometry of Random Fields (Wiley, 1981).
  19. R. G. Gardachov, "The probability density of the total curvature of a uniform random Gaussian sea surface in the specular points," Int. J. Remote Sens. 21, 2917-2926 (2000). [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