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. 2 — Feb. 1, 2006
  • pp: 395–417

Gaussian beam weak scintillation: low-order turbulence effects and applicability of the Rytov method

Gary J. Baker  »View Author Affiliations

JOSA A, Vol. 23, Issue 2, pp. 395-417 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (299 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A generally applicable and computationally efficient description of random irradiance fluctuations induced by single scattering from distributed low-order turbulence (LOT) phase fluctuations is developed for Gaussian beams in the weak scintillation regime. The LOT solution describes irradiance statistics resulting from coarse beam irradiance fluctuations such as beam wander and beam breathing and will generally underestimate the true scintillation owing to the neglect of higher orders. For a subset of beam and turbulence settings that naturally result in non-log-normal irradiance behavior in the weak regime, the LOT solution closely approaches the exact solution and accurately describes the irradiance statistics for any point on the observation plane. For the same settings, beam-wave scintillation theory derived from the Rytov perturbation method yields inaccurate predictions owing to an inherent confinement to log-normal behavior. Examples that naturally exhibit non-log-normal irradiance behavior include focused beams on horizontal paths and collimated beams on ground-to-space paths. The complementary nature of the two scintillation theories (LOT and Rytov) enables a hybrid combination that yields accurate and convenient scintillation predictions for any case exhibiting weak scintillation regardless of irradiance behavior. Comparison of hybrid model predictions with wave optics simulation data reveals excellent agreement.

© 2006 Optical Society of America

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

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: March 7, 2005
Revised Manuscript: July 1, 2005
Manuscript Accepted: July 27, 2005

Gary J. Baker, "Gaussian beam weak scintillation: low-order turbulence effects and applicability of the Rytov method," J. Opt. Soc. Am. A 23, 395-417 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. I. Charnotskii, "Asymptotic analysis of finite beam scintillation in a turbulent medium," Waves Random Media 4, 243-273 (1994). [CrossRef]
  2. V. I. Tatarski, "Light propagation in a medium with random refractive index inhomogeneities in the Markov approximation," Sov. Phys. JETP 29, 1133-1138 (1969).
  3. V. I. Klyatskin and V. I. Tatarski, "The parabolic equation approximation for propagation of waves in a medium with random inhomogeneities," Sov. Phys. JETP 31, 335-339 (1970).
  4. R. Lutomirski and H. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652-1658 (1971). [CrossRef] [PubMed]
  5. V. A. Banakh, G. M. Krekov, and V. L. Mironov, "Intensity variance and spatial correlation of the intensity of wave beams propagating in a turbulent atmosphere," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 17, 252-260 (1974).
  6. V. A. Banakh, G. M. Krekov, V. L. Mironov, S. S. Khmelevtsov, and R. Sh. Tsvik, "Focused laser beam scintillation in the turbulent atmosphere," J. Opt. Soc. Am. 64, 516-518 (1974). [CrossRef]
  7. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669-1692 (1975). [CrossRef]
  8. V. A. Banakh and I. N. Smalikho, "Laser beam propagation along extended vertical and slant paths in the turbulent atmosphere," Atmos. Oceanic. Opt. 5, 233-237 (1992).
  9. R. A. Schmeltzer, "Means, variances, and covariances for laser beam propagation through a random medium," Q. Appl. Math. 24, 339-354 (1967).
  10. D. L. Fried and J. B. Seidman, "Laser-beam scintillation in the atmosphere," J. Opt. Soc. Am. 57, 181-185 (1967). [CrossRef]
  11. D. L. Fried, "Scintillation of a ground-to-space laser illuminator," J. Opt. Soc. Am. 57, 980-983 (1967). [CrossRef]
  12. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.
  13. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarski, Principles of Statistical Radiophysics (Springer-Verlag, 1989), Vol. 4.
  14. J. D. Shelton, "Turbulence-induced scintillation on Gaussian-beam waves: theoretical predictions and observations from a laser-illuminated satellite," J. Opt. Soc. Am. A 12, 2172-2181 (1995). [CrossRef]
  15. L. C. Andrews, R. L. Phillips, and P. T. Yu, "Optical scintillation and fade statistics for a satellite-communications system," Appl. Opt. 34, 7742-7751 (1995) L. C. Andrews, R. L. Phillips, and P. T. Yu,[errata, Appl. Opt. 36, S.6068 (1997)]. [CrossRef] [PubMed]
  16. J. R. Dunphy and J. R. Kerr, "Turbulence effects on target illumination by laser sources: phenomenological analysis and experimental results," Appl. Opt. 16, 1345-1358 (1977). [CrossRef] [PubMed]
  17. F. Dios, J. A. Rubio, A. Rodriguez, and A. Comeron, "Scintillation and beam-wander analysis in an optical ground station-satellite uplink," Appl. Opt. 43, 3866-3873 (2004). [CrossRef] [PubMed]
  18. G. J. Baker and R. S. Benson, "Gaussian beam scintillation on ground-to-space paths: The importance of beam wander," in Free Space Laser Communications IV, J.C.Ricklin and D.G.Voelz, eds., Proc. SPIE 5550, 225-235 (2004).
  19. G. J. Baker and R. S. Benson, "Laser scintillation on ground to space paths: a hybrid model for beam wander effects," in Proceedings of AMOS Technical Conference (AFRL/Det 15, 2004), pp. 205-212.
  20. M. E. Gracheva, and A. S. Gurvich, "On strong fluctuations of the intensity of light when propagating in the lower layer of the atmosphere," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 8, 717-724 (1965).
  21. M. E. Gracheva, "Research into the statistical properties of the strong fluctuations of light when propagated in the lower layer of the atmosphere," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 10, 775-787 (1967).
  22. V. L. Mironov, G. Ya. Patrushev, V. V. Pokasov, and L. I. Shchavlev, "Measurements of intensity fluctuations in light beams having angular diversity," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 18, 450-452 (1975).
  23. R. L. Phillips and L. C. Andrews, "Measured statistics of laser light scattering in atmospheric turbulence," J. Opt. Soc. Am. 71, 1440-1445 (1981). [CrossRef]
  24. A. Consortini, F. Cochetti, J. H. Churnside, and R. J. Hill, "Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation," J. Opt. Soc. Am. A 10, 2354-2362 (1993). [CrossRef]
  25. J. R. Kerr and R. Eiss, "Transmitter-size and focus effects on scintillation," J. Opt. Soc. Am. 62, 682-684 (1972). [CrossRef]
  26. J. R. Kerr and J. R. Dunphy, "Experimental effects of finite transmitter aperture on scintillation," J. Opt. Soc. Am. 63, 1-8 (1973). [CrossRef]
  27. A. Ishimaru, "The beam wave case and remote sensing," in Laser Beam Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer-Verlag, 1978), Chap. 5.
  28. R. Jüngling, "Simulation gerichteter ausbreitung optischer wellen in turbulenter atmosphäre," Diploma thesis (Institute for Nuclear Theory, Westphalien Wilhelms University, 2001), http://lmb.informatik.uni-freiburg.de/people/juengling/pubs/.
  29. G. J. Baker and R. S. Benson, "Gaussian beam weak scintillation on ground to space paths; compact descriptions and Rytov method applicability," Opt. Eng. (Bellingham) 44, 106002 (2005). [CrossRef]
  30. W. B. Miller, J. C. Ricklin, and L. C. Andrews, "Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam," J. Opt. Soc. Am. A 11, 2719-2726 (1994). [CrossRef]
  31. R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523-1545 (1970). [CrossRef]
  32. P. J. Titterton, "Power reduction and fluctuations caused by narrow laser beam motion in far field," Appl. Opt. 12, 423-425 (1973). [CrossRef] [PubMed]
  33. J. H. Churnside and R. J. Lataitis, "Wander of an optical beam in the turbulent atmosphere," Appl. Opt. 29, 926-930 (1990). [CrossRef] [PubMed]
  34. A. E. Siegman, Lasers (University Science, 1986).
  35. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  36. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976). [CrossRef]
  37. M. C. Roggermann and B. Welsh, Imaging through Turbulence (CRC Press, 1996).
  38. V. I. Klyatskin and A. I. Kon, "On the displacement of spatially bounded light beams in a turbulent medium in the Markovian random process approximation," Radiophys. Quantum Electron. 15, 1056-1061 (1972). [CrossRef]
  39. J. W. Goodman, Statistical Optics (Wiley, 1985).
  40. P. A. Lightsey, "Scintillation in ground-to-space and retroreflected laser beams," Opt. Eng. (Bellingham) 33, 2535-2543 (1994). [CrossRef]
  41. D. L. Fried, "Statistics of laser beam fade induced by pointing jitter," Appl. Opt. 12, 422-423 (1973). [CrossRef] [PubMed]
  42. G. J. Baker, "Gaussian beam weak scintillation: A tour of the D1 region," in Atmospheric Propagation II, C.Y.Young and G.C.Gilbreath eds., Proc. SPIE 5793, 17-27 (2005).
  43. A. M. Obukhov, "Effect of weak inhomogeneities in the atmosphere on sound and light propagation," Izv. Akad. Nauk Ser. Geofiz. 2, 155-165 (1953).
  44. J. W. Strohbehn, "Line of sight wave propagation through the turbulent atmosphere," Proc. IEEE 56, 1301-1318 (1968). [CrossRef]
  45. J. R. Dunphy and J. R. Kerr, "Atmospheric beam-wander cancellation by a fast-tracking transmitter," J. Opt. Soc. Am. 64, 1015-1016 (1974). [CrossRef]
  46. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).
  47. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001). [CrossRef]
  48. J. A. Arnaud and H. Kogelnik, "Gaussian light beams with general astigmatism," Appl. Opt. 8, 1687-1693 (1969). [CrossRef] [PubMed]
  49. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  50. B. J. Herman and L. A. Strugala, "Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence," in Propagation of High-Energy Laser Beams through the Earth's Atmosphere, Proc. SPIE 1221, 183-192 (1990).
  51. E. M. Johansson and D. T. Gavel, "Simulation of stellar speckle imaging," in Amplitude and Intensity Spatial Interferometry II, J.B.Breckenridge, ed., Proc. SPIE2200, 372-383 (1994).
  52. E. Nichelatti and G. Possi, "Improved beam propagation method equations," Appl. Opt. 37, 9-21 (1998). [CrossRef]
  53. R. Frehlich, "Simulation of laser propagation in a turbulent atmosphere," Appl. Opt. 39, 393-397 (2000). [CrossRef]
  54. R. A. Johnston and R. G. Lane, "Modeling scintillation from an aperiodic Kolmogorov phase screen," Appl. Opt. 39, 4761-4769 (2000). [CrossRef]
  55. A. Belmonte, "Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance," Appl. Opt. 39, 5426-5444 (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