The Turbulence Channel

  • Sherman Karp
  • Robert M. Gagliardi
  • Steven E. Moran
  • Larry B. Stotts
Part of the Applications of Communications Theory book series (ACTH)


In Chapter 4 we examined the guided optical channel or fiber link. In this chapter we consider the turbulent atmosphere as an unguided optical channel. It is well known that turbulence-induced random fluctuations in the atmosphere’s temperature generate corresponding random irregularities in the index of refraction. Upon passing through these irregularities, the wavefronts associated with an optical beam become distorted, the magnitude of the distortions depending on the strength of the turbulence and the length of the atmospheric optical path. Among the effects which are attributable to wavefront distortion and which can seriously degrade the performance of an optical communication system are (1) spreading of the beam beyond that normally caused by diffraction, (2) scintillation of the received intensity, (3) a decrease in the spatial and temporal coherence, and (4) wander of the beam from position to position. Quantification of these effects requires a theoretical understanding of the relationship between the properties of the medium and the transmitted optical radiation.


Atmospheric Turbulence Spatial Coherence Spherical Wave Turbulent Eddy Inertial Subrange 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1 and 2, Academic Press, New York (1978).Google Scholar
  2. 2.
    V. I. Tatarski, Wave Propagation in a Turbulent Medium (translated by R. A. Silverman), McGraw-Hill, New York (1961).Google Scholar
  3. 3.
    V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (translated by Israel Program for Scientific Translations), U.S. Department of Commerce, National Technical Information Service, Springfield, Virginia (1971) [originally published in 1967 ].Google Scholar
  4. 4.
    R. Fante, Electromagnetic beam propagation in turbulent media, Proc. IEEE 63, 1669–1692 (1975).CrossRefGoogle Scholar
  5. 5.
    R. Fante, Electromagnetic beam propagation in turbulent media, an update, Proc. IEEE 68, 1424–1443 (1980).CrossRefGoogle Scholar
  6. 6.
    S. F. Clifford, The classical theory of wave propagation in a turbulent medium, in: Laser Beam Propagation in the Atmosphere (J. W. Strobehn, ed. ), Springer-Verlag (1978).Google Scholar
  7. 7.
    D. Fried, Limiting resolution through the atmosphere, J. Opt. Soc. Am. 56, 1380 (1966).CrossRefGoogle Scholar
  8. 8.
    R. E. Hufnagel and N. R. Stanley, Modulation transfer function associated with image transmission through turbulent media, J. Opt. Soc. Am. 54, 52–61 (1964).CrossRefGoogle Scholar
  9. 9.
    R. E. Hufnagel and N. R. Stanley, Propagation through atmospheric turbulence, in: The Infrared Handbook (W. L. Wolf and G. J. Zissis, eds.), The Environmental Institute of Michigan, Ann Arbor, Michigan (1978).Google Scholar
  10. 10.
    D. Fried, Optical heterodyne detection of an atmospherically distorted wavefront, Proc. IEEE 55, 57–67 (1967).CrossRefGoogle Scholar
  11. 11.
    R. Fante, Propagation of electromagnetic waves through a turbulent plasma using transport theory, IEEE Trans. Antennas Propagat. AP-2, 750–755 (1973).Google Scholar
  12. 12.
    R. Lutomirski and H. Yura, Propagation of a finite optical beam in an inhomogeneous medium, Appl. Opt. 10, 1652–1658 (1971).CrossRefGoogle Scholar
  13. 13.
    Philip M. Morse and Herman Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York (1953), pp. 804–806.zbMATHGoogle Scholar
  14. 14.
    R. Fante, Mutual coherence function and frequency spectrum of a laser beam propagating through atmospheric turbulence, J. Opt. Soc. Am. 64, 592–598 (1974).CrossRefGoogle Scholar
  15. 15.
    H. Yura, Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium, Appl. Opt. 13, 1399–1406 (1972).CrossRefGoogle Scholar
  16. 16.
    G. Parry, Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam, Optical Acta 28, 715–728 (1981).CrossRefGoogle Scholar
  17. 17.
    R. L. Phillips and L. C. Andrews, Measured statistics of laser-light scattering in atmospheric turbulence, J. Opt. Soc. Am. 71, 864–870 (1981).CrossRefGoogle Scholar
  18. 18.
    E. Jakeman and P. N. Pusey, Significance of K-Distributions in Scattering Experiments, Phys. Rev. Lett., 40 (9), 546–550 (1978).CrossRefGoogle Scholar
  19. 19.
    G. Parry and P. N. Pusey, K-distributions in atmospheric propagation of laser light, J. Opt. Soc. Am. 69 (5), 796–798 (1979).CrossRefGoogle Scholar
  20. 20.
    E. Jakeman, On the statistics of K-distributed noise, J. Phys. A: Math. Gen. 13, 31–48 (1980).zbMATHCrossRefGoogle Scholar
  21. 21.
    R. Barakat, Weak-scatter generalization of the K-density function with application to laser scattering in atmospheric turbulence, J. Opt. Soc. Am. A 3, 401–409 (1986).CrossRefGoogle Scholar
  22. 22.
    R. Barakat, Weak-scatter generalization of the K-density function. II. Probability density of total phase, J. Opt. Soc. Am. A 4 (7), 1213–1219 (1987).CrossRefGoogle Scholar
  23. 23.
    E. Jakeman and R. J. A. Tough, Generalized K-distribution: a statistical model for weak scattering, J. Opt. Soc. Am. A 4 (9), 1764–1772 (1987).CrossRefGoogle Scholar
  24. 24.
    D. Fried, Aperture averaging of scintillation, J. Opt. Soc. Am. 57 (1967).Google Scholar
  25. 25.
    Paul H. Deitz and Neal J. Wright, Saturation of scintillation magnitude in near-earth optical propagation, J. Opt. Soc. Am. 59 (5), 527–535 (1969).CrossRefGoogle Scholar
  26. 26.
    H. Yura, Short term average optical-beam spread in a turbulent medium, J. Opt. Soc. Am. 63, 567–572 (1973).CrossRefGoogle Scholar
  27. 27.
    D. Fried, Statistics of geometric representation of wavefront distortion, J. Opt. Soc. Am. 55, 1427 (1965).MathSciNetCrossRefGoogle Scholar
  28. 28.
    H. Hodara, Refractive Index Fluctuations in Seawater, AGARD Lecture Series 61 on Optics of the Sea, Neuilly Sur Seine, France (1973), pp. 2.2–1–2.2.–12.Google Scholar
  29. 29.
    L. Lieberman, The effect of temperature inhomogeneities in the ocean on the propagation of sound, J. Opt. Soc. Am. 23, 563 (1951).Google Scholar
  30. 30.
    R. Fante, Intensity, Coherence and Frequency Spectrum of a Focused Beam in a Random Media, AFCRL Technical Report, AFCRL-TR-7 4–0335, Physical Sciences Research Papers No. 598 (1974).Google Scholar
  31. 31.
    R. D. Anderson and L. Stotts, Underwater measurements of off-axis radiance compared with various analytical treatments of the radiative transfer equation, J. Opt. Soc. Am. 72, 738–746 (1982).CrossRefGoogle Scholar
  32. 32.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York (1965), p. 505.Google Scholar
  33. 33.
    R. M. Gagliardi and S. Karp, Optical Communications, Wiley-Interscience, New York (1976).Google Scholar

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Sherman Karp
    • 1
  • Robert M. Gagliardi
    • 2
  • Steven E. Moran
    • 3
  • Larry B. Stotts
    • 4
  1. 1.Lutronix, Inc.San DiegoUSA
  2. 2.University of Southern CaliforniaLos AngelesUSA
  3. 3.SAICSan DiegoUSA
  4. 4.DARPAArlingtonUSA

Personalised recommendations