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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 5 — May. 1, 2012
  • pp: 832–841

Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence

V. S. Rao Gudimetla, Richard B. Holmes, Carey Smith, and Gregory Needham  »View Author Affiliations

JOSA A, Vol. 29, Issue 5, pp. 832-841 (2012)

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The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments.

© 2012 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.7060) Atmospheric and oceanic optics : Turbulence

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: September 1, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 16, 2012
Published: May 1, 2012

V. S. Rao Gudimetla, Richard B. Holmes, Carey Smith, and Gregory Needham, "Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence," J. Opt. Soc. Am. A 29, 832-841 (2012)

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  1. A. Consortini, L. Ronchi, and L. Stefanutti, “Investigation of atmospheric turbulence by narrow laser beams,” Appl. Opt. 9, 2543–2547 (1970). [CrossRef]
  2. R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the Earth,” IEEE Trans. Antennas Propag. AP-34, 258–261 (1986). [CrossRef]
  3. V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994). [CrossRef]
  4. B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992). [CrossRef]
  5. V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low frequency range,” in Proceedings of International Geoscience and Remote Sensing Symposium, 1996. Remote Sensing for a Sustainable Future (IEEE, 1996), Vol. 1, pp. 22–24.
  6. V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347–354 (1995). [CrossRef]
  7. M. S. Belen’kii, E. Cuellar, K. A. Hughes, and A. V. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006). [CrossRef]
  8. M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, and R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” Proc. SPIE 3762, 396–406 (1999). [CrossRef]
  9. M. Vorontsov, G. W. Carhart, V. S. R. Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, P. Kervan, ed. (Maui Economic Development Board, 2010), pp. 184–195.
  10. A. D. Wheelon, Electromagnetic Scintillation (Cambridge University, 2001), Vol. 1, Chaps. 2 and 4.
  11. Albert D. Wheelon, Electromagnetic Scintillation (Cambridge University, 2001), Vol. 2, Chap. 3.
  12. L. V. Antoshkin, N. N. Botygina, O. N. Emaleev, L. N. Lavrinova, V. P. Lukin, A. P. Rostov, B. V. Fortes, and A. P. Yankov, “Investigation of turbulence spectrum anisotropy in the ground atmospheric layer; preliminary results,” Atmos. Oceanic Opt. 8, 993–996 (1995).
  13. I. Toselli, B. Agrawal, and S. Restaino, “Light propagation through anisotropic turbulence,” J. Opt. Soc. Am. A 28, 483–488 (2011). [CrossRef]
  14. C. Robert, J.-M. Conan, V. Michau, J.-B. Renard, C. Robert, and F. Dalaudier, “Retrieving parameters of the anisotropic refractive index fluctuations spectrum in the stratosphere from balloon-borne observations of stellar scintillation,” J. Opt. Soc. Am. A 25, 379–393 (2008). [CrossRef]
  15. A. P. Aleksandrov, G. M. Grechko, A. S. Gurvich, V. Kan, M. K. H. Manarov, A. I. Pokhomov, Yu. V. Romanenko, S. A. Savchenko, S. I. Serova, and Y. G. Titov, “Spectra of temperature variations in the stratosphere as indicated by satellite-borne observation of the twinkling of stars,” Izv. Atmos. Ocean. Phys. 26, 5–16(1990).
  16. A. S. Gurvich and M. S. Belen’kii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12, 2517–2522 (1995). [CrossRef]
  17. V. E. Ostashev, D. K. Wilson, and G. H. Goedecke, “Spherical wave propagation through inhomogeneous, anisotropic turbulence: log-amplitude and phase correlations,” J. Acoust. Soc. Am. 115, 120–130 (2004). [CrossRef]
  18. V. E. Ostashev and D. K. Wilson, “Log-amplitude and phase fluctuations of a plane wave propagating through anisotropic, inhomogeneous turbulence,” Acta Acust. Acust. (Acta Acustica united with Acustica) 87, 685–694 (2001).
  19. S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, 1978), pp. 9–43.
  20. Larry C. Andrews and R. L. Phillips, Laser Beam Propagation in Random Media (SPIE, 2005).
  21. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, 1965), p. 973.
  22. D. L. Fried and J. D. Cloud, “Propagation of an infinite plane wave in a randomly inhomogeneous medium,” J. Opt. Soc. Am. 56, 1667–1676 (1966). [CrossRef]
  23. Richard J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, 1994).
  24. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988). [CrossRef]
  25. J. M. Martin and S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990). [CrossRef]
  26. J. D. Schmidt, Numerical Simulation Of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

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