OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 21 — Jul. 20, 2011
  • pp: 3907–3917

Spatial coherence function of partially coherent Gaussian beams in atmospheric turbulence

Daniel J. Wheeler and Jason D. Schmidt  »View Author Affiliations

Applied Optics, Vol. 50, Issue 21, pp. 3907-3917 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (454 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We introduce a new method of estimating the coherence function of a Gaussian–Schell model beam in the inertial subrange of atmospheric turbulence. It is compared with the previously published methods based on either the quadratic approximation of the parabolic equation or an assumed independence between the source’s randomness and the atmosphere using effective beam parameters. This new method, which combines the results of the previous two methods to account for any random source/atmospheric coupling, was shown to more accurately estimate both the coherence radius and coherence functional shape across much of the relevant parameter space. The regions of the parameter space where one method or another is the most accurate in estimating the coherence radius are identified along with the maximum absolute estimation error in each region. By selecting the appropriate estimation method for a given set of conditions, the absolute estimation error can generally be kept to less than 5%, with a maximum error of 7%. We also show that the true coherence function is more Gaussian than expected, with the exponential power tending toward 9 / 5 rather than the theoretical value of 5 / 3 in very strong turbulence regardless of the nature of the source coherence.

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(030.1640) Coherence and statistical optics : Coherence

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: March 10, 2011
Manuscript Accepted: June 8, 2011
Published: July 13, 2011

Daniel J. Wheeler and Jason D. Schmidt, "Spatial coherence function of partially coherent Gaussian beams in atmospheric turbulence," Appl. Opt. 50, 3907-3917 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Department of Commerce, 1971).
  2. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005). [CrossRef]
  3. T. Weyrauch, M. A. Vorontsov, J. W. Gowens, II, and T. G. Bifano, “Fiber coupling with adaptive optics for free-space optical communication,” Proc. SPIE 4489, 177–184 (2002). [CrossRef]
  4. Y. Dikmelik and F. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44, 4946–4952 (2005). [CrossRef] [PubMed]
  5. M. Toyoshima, “Maximum fiber coupling efficiency and optimum beam size in the presence of random angular jitter for free-space laser systems and their applications,” J. Opt. Soc. Am. A 23, 2246–2250 (2006). [CrossRef]
  6. J. Ma, F. Zhao, L. Tan, S. Yu, and Y. Yang, “Degradation of single-mode fiber coupling efficiency due to localized wavefront aberrations in free-space laser communications,” Opt. Eng. 49, 045004 (2010). [CrossRef]
  7. S. Shaklan and F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2334–2338 (1988). [CrossRef] [PubMed]
  8. C. Ruilier and F. Cassaing, “Coupling of large telescopes and single-mode waveguides: application to stellar interferometry,” J. Opt. Soc. Am. A 18, 143–149 (2001). [CrossRef]
  9. D. K. Jacob, M. B. Mark, and B. D. Duncan, “Heterodyne ladar system efficiency enhancement using single-mode optical fiber mixers,” Opt. Eng. 34, 3122–3129 (1995). [CrossRef]
  10. P. J. Winzer and W. R. Leeb, “Fiber coupling efficiency for random light and its applications to lidar,” Opt. Lett. 23, 986–988 (1998). [CrossRef]
  11. T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112–126(2004). [CrossRef]
  12. D. J. Wheeler and J. D. Schmidt, “Coupling of Gaussian Schell-model beams into single-mode optical fibers,” J. Opt. Soc. Am. A 281224–1238 (2011). [CrossRef]
  13. M. S. Belen’kii and V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980). [CrossRef]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  15. J. C. Leader, “Atmospheric propagation of partially coherent radiation,” J. Opt. Soc. Am. 68, 175–185 (1978). [CrossRef]
  16. S. C. H. Wang and M. A. Plonus, “Optical beam propagation for a partially coherent source in the turbulent atmosphere,” J. Opt. Soc. Am. 69, 1297–1304 (1979). [CrossRef]
  17. J. Wu, “Propagation of a Gaussian–Schell beam through turbulent media,” J. Mod. Opt. 37, 671–684 (1990). [CrossRef]
  18. G. Gbur and E. Wolf, “Spreading of partially coherent beams in random media,” J. Opt. Soc. Am. A 19, 1592–1598(2002). [CrossRef]
  19. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19, 1794–1802 (2002). [CrossRef]
  20. T. Shirai, A. Dogariu, and E. Wolf, “Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A 20, 1094–1102 (2003). [CrossRef]
  21. O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43, 330–341 (2004). [CrossRef]
  22. H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent general beams in atmospheric turbulence,” J. Opt. Soc. Am. A 24, 2891–2901 (2007). [CrossRef]
  23. X. Ji and X. Li, “Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through atmospheric turbulence,” J. Opt. 12, 035403 (2010). [CrossRef]
  24. K. Drexler, M. Roggemann, and D. Voelz, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng. 50, 025002(2011). [CrossRef]
  25. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2005).
  26. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005). [CrossRef]
  27. Because the fields used to calculate Γ are taken at the same instant in time, it can alternatively be referred to as the mutual intensity J instead of the MCF . However, to maintain consistency with other published literature , we are referring to it in this paper as the MCF. Consequently, the time dependence of the field E is ignored.
  28. J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).
  29. D. A. de Wolf, “Saturation of irradiance fluctuations due to turbulent atmosphere,” J. Opt. Soc. Am. 58, 461–466 (1968). [CrossRef]
  30. M. Beran, “Propagation of a finite beam in a random medium,” J. Opt. Soc. Am. 60, 518–521 (1970). [CrossRef]
  31. R. F. Lutomirski and H. T. Yura, “Propagation of a finite optical beam in an inhomogeneous medium,” Appl. Opt. 10, 1652–1658 (1971). [CrossRef] [PubMed]
  32. J. Wilbur and P. Brown, “Second moment of a wave propagating in a random medium,” J. Opt. Soc. Am. 61, 1051–1059(1971). [CrossRef]
  33. K. Furutsu, “Statistical theory of wave propagation in a random medium and the irradiance distribution function,” J. Opt. Soc. Am. 62, 240–254 (1972). [CrossRef]
  34. R. L. Fante, “Mutual coherence function and frequency spectrum of a laser beam propagating through atmospheric turbulence,” J. Opt. Soc. Am. 64, 592–598 (1974). [CrossRef]
  35. R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979). [CrossRef]
  36. M. J. Beran, “Coherence equations governing propagation through random media,” Radio Sci. 10, 15–21 (1975). [CrossRef]
  37. H. T. Yura, “Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium,” Appl. Opt. 11, 1399–1406 (1972). [CrossRef] [PubMed]
  38. A. N. Kolmogorov, “The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers,” C. R. Acad. Sci. U.S.S.R. 30, 301–305 (1941).
  39. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).
  40. L. C. Andrews, W. B. Miller, and J. C. Ricklin, “Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence,” J. Opt. Soc. Am. A 11, 1653–1660 (1994). [CrossRef]
  41. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence, 2nd ed. (SPIE, 2007). [CrossRef]
  42. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited