OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 6 — Jun. 1, 1976
  • pp: 536–546

An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness

J. Carl Leader  »View Author Affiliations

JOSA, Vol. 66, Issue 6, pp. 536-546 (1976)

View Full Text Article

Acrobat PDF (1276 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An expression is derived for the mutual coherence function of laser radiation scattered from a rough surface. The rough surface is described by the superposition of two random-height distributions. The expression descibes the correlation of the radiation amplitude at spatially separated far-field points caused by the scattering from spatially separate surface elements. Numerical predictions of this mutual interaction or coherent contribution to the mutual coherence function are computed for a square surface area and typical values of the surface statistical parameters. These results are compared with the scattering cross section of a flat surface area and the degree of coherence of a perfectly diffuse surface. The functional form of the incoherent contribution to the mutual coherence function, resulting from the integration of the radiation that is diffracted by the surface irregularities, is deduced from an analysis of the single scale of roughness scattering problem. The derived mutual coherence function is shown to reduce to the proper functional form for the ideal limiting cases of a perfectly flat surface and a perfectly diffuse scattering area.

© 1976 Optical Society of America

J. Carl Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536-546 (1976)

Sort:  Author  |  Journal  |  Reset


  1. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
  2. H. T. Yura, Appl. Opt. 13, 150 (1974).
  3. R. B. Crane, J. Opt. Soc. Am. 60, 1658 (1970).
  4. H. H. Arsenault, J. Opt. Soc. Am. 61, 1425 (1971).
  5. B. I. Semyonov, Radio Eng. Electron. Phys. (USSR) 11, 1179 (1966).
  6. P. Beckmann, Proc. IEEE 53, 1012 (1965).
  7. A. K. Fung and H-L Chan, IEEE Trans. Antennas Propag. AP-17, 590 (1969).
  8. J. W. Wright, IEEE Trans. Antennas Propag. AP-16, 217 (1968).
  9. D. E. Barrick and W. H. Peake, Rad. Sci. 3, 865 (1968).
  10. Portions of this section's development were presented by the author at the 1973 International IEEE Antennas and Propagation Symposium and USNC/URSI Meeting, Boulder, Colo. 22–24 Aug. 1973. These portions are outlined in McDonnell Aircraft Co. Paper No. MCAIR 73-020.
  11. J. C. Leader, J. Appl. Phys. 42, 4808 (1971).
  12. J. C. Leader, J. Opt. Soc. Am. 62, 1356 (1972).
  13. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N.J., 1964) p. 40.
  14. J. C. Leader, "Polarization Discrimination in Remote Sensing," AGARD Electromagnetic Propagation Panel Symposium of Electromagnetic Wave Propagation Involving Irregular Surfaces and Inhomogeneous Media, The Hague, Netherlands (March 1974), AGARD Conference Proceedings No. 144.
  15. L. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).
  16. Goldfischer calculated the irradiance correlation function R12 = 〈I1 I2〉, which is related to the degree of coherence by R12 = 〈I1〉 〈I2〉[1 + 2| γ12 | 2] for Gaussian fluctuation statistics.
  17. J. E. Seltzer, IEEE Trans. Antennas Propag. AP-20, 726 (1972).
  18. D. E. Barrick, IEEE Trans. Antennas Propag. AP-16, 449 (1968).

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