OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 65, Iss. 8 — Aug. 1, 1975
  • pp: 942–948

Beam wander in a turbulent medium: An application of Ehrenfest’s theorem

Richard J. Cook  »View Author Affiliations

JOSA, Vol. 65, Issue 8, pp. 942-948 (1975)

View Full Text Article

Acrobat PDF (747 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Beam wander of a finite optical beam propagating in a turbulent medium is investigated theoretically. Using the optical analog of Ehrenfest’s theorem, it is shown that the centroid of a finite beam propagates as a paraxial ray in a certain effective refractive index that depends on the irradiance profile of the beam. Ray statistics in the effective refractive index are studied for arbitrary irradiance profiles and new results are obtained for the variance of spot displacement and beam angle of arrival. These results are then applied to the particular cases of focused and collimated gaussian beams in atmospheric turbulence with a modified Von Karman power spectrum to yield the functional dependence of spot dancing and angle-of-arrival statistics on the inner and outer scales of turbulence and on the Fresnel number for focused gaussian beams.

Richard J. Cook, "Beam wander in a turbulent medium: An application of Ehrenfest’s theorem," J. Opt. Soc. Am. 65, 942-948 (1975)

Sort:  Author  |  Journal  |  Reset


  1. L. I. Schiff, Quantum Mechanics, 2nd ed. (McGraw-Hill, New York, 1955), p. 25.
  2. P. Beckmann, Radio Sci. 69D, 629 (1965).
  3. L. A. Chernow, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill, New York, 1960), Ch. 2.
  4. J. B. Keller, Proc. Symp. Appl. Math. 13, 226 (1962).
  5. T. Chiba, Appl. Opt. 10, 2456 (1971).

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