Abstract

An analytical expression for the log-amplitude correlation function for plane wave propagation through anisotropic non-Kolmogorov turbulent atmosphere is derived. The closed-form analytic results are based on the Rytov approximation. These results agree well with wave optics simulation based on the more general Fresnel approximation as well as with numerical evaluations, for low-to-moderate strengths of turbulence. The new expression reduces correctly to the previously published analytic expressions for the cases of plane wave propagation through both nonisotropic Kolmogorov turbulence and isotropic non-Kolmogorov turbulence cases. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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 Geoscience and Remote Sensing Symposium, 1996. IGARSS ’96. Remote Sensing for a Sustainable Future (IEEE, 1996), 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 (1995).
    [CrossRef]
  7. 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).
  8. M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
    [CrossRef]
  9. 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]
  10. M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
    [CrossRef]
  11. M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
    [CrossRef]
  12. J. R. Kerr, “Experiments on turbulence characteristics and multiwavelength scintillation phenomena,” J. Opt. Soc. Am. 62, 1040–1049 (1972).
    [CrossRef]
  13. J. R. Dunphy and J. R. Kerr, “Scintillation measurements for large integrated-path turbulence,” J. Opt. Soc. Am. 63, 981–986 (1973).
    [CrossRef]
  14. A. D. Wheelon, in Electromagnetic Scintillation I: Geometrical Optics (Cambridge University, 2001), Chaps. 2 and 4.
  15. A. D. Wheelon, in Electromagnetic Scintillation II. Weak Scattering (Cambridge University, 2001), Chap. 3.
  16. M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).
  17. F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of sheets in the atmospheric temperature field,” J. Atmos. Sci. 51, 237–248 (1994).
    [CrossRef]
  18. 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]
  19. A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
    [CrossRef]
  20. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
    [CrossRef]
  21. D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
    [CrossRef]
  22. 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).
  23. R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
    [CrossRef]
  24. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [CrossRef]
  25. S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996).
  26. L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express 18, 451–462 (2010).
    [CrossRef]
  27. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
    [CrossRef]
  28. T. S. McKechnie, “Atmospheric turbulence and the resolution limits of large ground-based telescopes,” J. Opt. Soc. Am. A 9, 1937–1954 (1992).
    [CrossRef]
  29. E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004).
    [CrossRef]
  30. C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
    [CrossRef]
  31. G. D. Boreman and C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 13, 517–522(1996).
    [CrossRef]
  32. A. S. Gurvich and I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108(D5), article 4166, ACL 6-1–ACL 6-4 (2003).
    [CrossRef]
  33. 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]
  34. M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20, 1359–1361 (1995).
    [CrossRef]
  35. 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]
  36. V. E. Ostashev and D. K. Wilson, “Log-amplitude and phase fluctuations of a plane wave propagating through anisotropic, inhomogeneous turbulence,” Acta Acust. Acust. 87, 685–694 (2001).
  37. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
    [CrossRef]
  38. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
    [CrossRef]
  39. I. Toselli, B. Agrawal, and S. Restaino, “Light propagation through anisotropic turbulence,” J. Opt. Soc. Am. A 28, 483–488 (2011).
    [CrossRef]
  40. J. Cang and X. Liu, “Scintillation index and performance analysis of wireless optical links over non-Kolmogorov weak turbulence based on generalized atmospheric spectral model,” Opt. Express 19, 19067–19077 (2011).
    [CrossRef]
  41. R. Gudimetla, R. B. Holmes, C. Smith, and G. 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).
    [CrossRef]
  42. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, 1994).
  43. J. M. Martin and Stanley M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef]
  44. 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]
  45. J. D. Schmidt, Numerical Simulation Of Optical Wave Propagation With Examples in MATLAB (SPIE, 2010).

2012 (1)

2011 (2)

2010 (1)

2008 (2)

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]

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

2007 (2)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

2006 (1)

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[CrossRef]

2005 (1)

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

2004 (2)

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]

E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004).
[CrossRef]

2003 (1)

A. S. Gurvich and I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108(D5), article 4166, ACL 6-1–ACL 6-4 (2003).
[CrossRef]

2001 (1)

V. E. Ostashev and D. K. Wilson, “Log-amplitude and phase fluctuations of a plane wave propagating through anisotropic, inhomogeneous turbulence,” Acta Acust. Acust. 87, 685–694 (2001).

2000 (1)

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

1999 (2)

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]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[CrossRef]

1997 (1)

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

1996 (2)

G. D. Boreman and C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 13, 517–522(1996).
[CrossRef]

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996).

1995 (6)

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]

M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20, 1359–1361 (1995).
[CrossRef]

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[CrossRef]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347 (1995).
[CrossRef]

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).

1994 (3)

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of sheets in the atmospheric temperature field,” J. Atmos. Sci. 51, 237–248 (1994).
[CrossRef]

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994).
[CrossRef]

1993 (1)

1992 (2)

T. S. McKechnie, “Atmospheric turbulence and the resolution limits of large ground-based telescopes,” J. Opt. Soc. Am. A 9, 1937–1954 (1992).
[CrossRef]

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

1990 (2)

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).

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]

1988 (1)

1986 (1)

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]

1973 (1)

1972 (1)

1970 (1)

Agrawal, B.

Aleksandrov, A. P.

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).

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
[CrossRef]

Antoshkin, L. V.

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).

Barchers, J. D.

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]

Beland, R. R.

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[CrossRef]

Belen’kii, M. S.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[CrossRef]

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]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

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]

M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20, 1359–1361 (1995).
[CrossRef]

Beresnev, L. A.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Bishop, K. P.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Boreman, G. D.

Botygina, N. N.

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).

Brown, J. M.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[CrossRef]

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]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Cang, J.

Carhart, G. W.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Chkhetiani, O. G.

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996).

Chunchuzov, I. P.

A. S. Gurvich and I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108(D5), article 4166, ACL 6-1–ACL 6-4 (2003).
[CrossRef]

Conan, J.-M.

Consortini, A.

Crochet, M.

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of sheets in the atmospheric temperature field,” J. Atmos. Sci. 51, 237–248 (1994).
[CrossRef]

Cuellar, E.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[CrossRef]

Dainty, C.

Dalaudier, F.

Du, W.

Dunphy, J. R.

Emaleev, O. N.

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).

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

Flatté, S. M.

Flatté, Stanley M.

Fortes, B. V.

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).

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

Fugate, R. Q.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[CrossRef]

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]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Goedecke, G. H.

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]

Golbraikh, E.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004).
[CrossRef]

Grechko, G. M.

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).

Gudimetla, R.

Gurvich, A. S.

A. S. Gurvich and I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108(D5), article 4166, ACL 6-1–ACL 6-4 (2003).
[CrossRef]

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]

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).

Han, Q.

Holmes, R. B.

Hughes, K. A.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[CrossRef]

Jiang, W.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

Kan, V.

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).

Karis, S. J.

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[CrossRef]

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]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Keating, D. B.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Kerr, J. R.

Kopeika, N. S.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004).
[CrossRef]

Kupershmidt, I.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

Kyrazis, D. T.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Lachinova, S. L.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Lavrinova, L. N.

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).

Ling, N.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

Liu, J.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Liu, X.

Lukin, V. P.

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).

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347 (1995).
[CrossRef]

V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994).
[CrossRef]

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low frequency range,” in Geoscience and Remote Sensing Symposium, 1996. IGARSS ’96. Remote Sensing for a Sustainable Future (IEEE, 1996), pp. 22–24.

Ma, J.

Manarov, M. K. H.

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).

Manning, R. M.

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]

Martin, J. M.

McKechnie, T. S.

Michau, V.

Miller, W. B.

Moiseev, S. S.

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996).

Needham, G.

Osmon, C. L.

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]

Ostashev, V. E.

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]

V. E. Ostashev and D. K. Wilson, “Log-amplitude and phase fluctuations of a plane wave propagating through anisotropic, inhomogeneous turbulence,” Acta Acust. Acust. 87, 685–694 (2001).

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

Pokhomov, A. I.

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).

Preble, A. J.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Rao, C.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

Rao Gudimetla, V. S.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Rehder, K.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Renard, J.-B.

Restaino, S.

Ricklin, J. C.

Riker, J. F.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Robert, C.

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Romanenko, Yu. V.

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).

Ronchi, L.

Rostov, A. P.

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).

Rye, V. A.

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[CrossRef]

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, 1994).

Savchenko, S. A.

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).

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation Of Optical Wave Propagation With Examples in MATLAB (SPIE, 2010).

Serova, S. I.

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).

Shtemler, Y.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

Sidi, C.

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of sheets in the atmospheric temperature field,” J. Atmos. Sci. 51, 237–248 (1994).
[CrossRef]

Smith, C.

Stefanutti, L.

Stevenson, E.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Tan, L.

Titov, Y. G.

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).

Toselli, I.

I. Toselli, B. Agrawal, and S. Restaino, “Light propagation through anisotropic turbulence,” J. Opt. Soc. Am. A 28, 483–488 (2011).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

Vernin, J.

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of sheets in the atmospheric temperature field,” J. Atmos. Sci. 51, 237–248 (1994).
[CrossRef]

Virtser, A.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

Vorontsov, M.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

Weyrauch, T.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

Wheelon, A. D.

A. D. Wheelon, in Electromagnetic Scintillation I: Geometrical Optics (Cambridge University, 2001), Chaps. 2 and 4.

A. D. Wheelon, in Electromagnetic Scintillation II. Weak Scattering (Cambridge University, 2001), Chap. 3.

Wilson, D. K.

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]

V. E. Ostashev and D. K. Wilson, “Log-amplitude and phase fluctuations of a plane wave propagating through anisotropic, inhomogeneous turbulence,” Acta Acust. Acust. 87, 685–694 (2001).

Wissler, J.

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

Yankov, A. P.

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).

Yu, S.

Zilberman, A.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

Acta Acust. Acust. (1)

V. E. Ostashev and D. K. Wilson, “Log-amplitude and phase fluctuations of a plane wave propagating through anisotropic, inhomogeneous turbulence,” Acta Acust. Acust. 87, 685–694 (2001).

Appl. Opt. (3)

Atmos. Oceanic Opt. (1)

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).

Atmos. Res. (1)

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88, 66–77 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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]

Izv. Atmos. Ocean. Phys. (1)

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).

J. Acoust. Soc. Am. (1)

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]

J. Atmos. Sci. (1)

F. Dalaudier, C. Sidi, M. Crochet, and J. Vernin, “Direct evidence of sheets in the atmospheric temperature field,” J. Atmos. Sci. 51, 237–248 (1994).
[CrossRef]

J. Exp. Theor. Phys. (1)

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996).

J. Geophys. Res. (1)

A. S. Gurvich and I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108(D5), article 4166, ACL 6-1–ACL 6-4 (2003).
[CrossRef]

J. Mod. Opt. (1)

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

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]

G. D. Boreman and C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 13, 517–522(1996).
[CrossRef]

W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
[CrossRef]

T. S. McKechnie, “Atmospheric turbulence and the resolution limits of large ground-based telescopes,” J. Opt. Soc. Am. A 9, 1937–1954 (1992).
[CrossRef]

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]

I. Toselli, B. Agrawal, and S. Restaino, “Light propagation through anisotropic turbulence,” J. Opt. Soc. Am. A 28, 483–488 (2011).
[CrossRef]

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]

R. Gudimetla, R. B. Holmes, C. Smith, and G. 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).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (13)

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low-frequency range,” Proc. SPIE 2471, 347 (1995).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6457, 64570T (2007).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[CrossRef]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc. SPIE 5987, 598702 (2005).
[CrossRef]

D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2110, 43–55 (1994).
[CrossRef]

V. P. Lukin, “Investigation of some peculiarities in the structure of large scale atmospheric turbulence,” Proc. SPIE 2200, 384–395 (1994).
[CrossRef]

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

M. S. Belen’kii, E. Cuellar, K. A. Hughes, and V. A. Rye, “Experimental study of spatial structure of turbulence at Maui Space Surveillance Site (MSSS),” Proc. SPIE 6304, 63040U (2006).
[CrossRef]

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]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50–51 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[CrossRef]

Other (6)

V. P. Lukin, “Investigation of the anisotropy of the atmospheric turbulence spectrum in the low frequency range,” in Geoscience and Remote Sensing Symposium, 1996. IGARSS ’96. Remote Sensing for a Sustainable Future (IEEE, 1996), pp. 22–24.

A. D. Wheelon, in Electromagnetic Scintillation I: Geometrical Optics (Cambridge University, 2001), Chaps. 2 and 4.

A. D. Wheelon, in Electromagnetic Scintillation II. Weak Scattering (Cambridge University, 2001), Chap. 3.

M. Vorontsov, G. W. Carhart, V. S. Rao 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. (Amostech, 2011).

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, 1994).

J. D. Schmidt, Numerical Simulation Of Optical Wave Propagation With Examples in MATLAB (SPIE, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Comparison of the wave optics simulation and the analytical log-amplitude correlation with anisotropy=1, generalized Rytov variance=0.1. Left, strong-turbulence axis; right, weak-turbulence axis. Range=100km, wavelength=0.737μm. Simulation results: solid curve, exponent α=19/6; dashed curve, α=22/6; dotted curve, α=23/6. Analytic results: circles, α=19/6; crosses, α=22/6; triangles, α=23/6.

Fig. 2.
Fig. 2.

Comparison of the wave optics simulation and the analytical log-amplitude correlation. Range=100km, wavelength=0.737μm, analytic Rytov variance=0.3, anisotropy ε=1.0. Left, strong-turbulence axis; right, weak-turbulence axis. Simulation results: solid curve, exponent α=19/6; dashed curve, α=22/6; dotted curve, α=23/6. Analytic results: circles, α=19/6; crosses, α=22/6; triangles, α=23/6.

Fig. 3.
Fig. 3.

Comparison of the wave optics simulation and the analytical log-amplitude correlation. Range=100km, wavelength=0.737μm, generalized Rytov variance=0.1, Kolmogorov exponent α=19/6. Left, strong-turbulence axis; right, weak-turbulence axis. Simulation results: solid line, ε=0; dashed line, ε=1; dotted line, ε=2. Analytic results: circles, ε=0; crosses, ε=1; triangles, ε=2.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ϕ(K)=A(α)β(a2Kx2+b2Ky2+Kz2)α/2.
ϕ(K)=A(α)β(ab)α/2(a2Kx2+b2Ky2)α/2.
ϕn(K)=A(α)βKα(1+ε2)α/4(1+ε2sin2(θK))α/2.
Bχ(ρ,θρ)=πk2LA(α)β(1+ε2)1/2d2KeiK·ρ{1kK2Lsin[K2Lk]}Kα(1+ε2sin2(θK))α/2=A(α)βπk2L(1+ε2)α/40dKKα+1{1kK2Lsin[K2Lk]}02πdθKeiKρcos(θKθρ)1(1+ε2sin2(θK))α/2.
Bχ(ρ,θρ)=0.5A(α)πk3α/2Lα/2β(1+ε2)α/4F(0,ε2)[Qm1Qm2aQm2b]m=0+(A(α)πk3α/2Lα/2β)(1+ε2)α/4m=1(1)mcos(2mθρ)F(m,ε2)[Qm1Qm2aQm2b].
Qm1=(k8Lρ2)α/212α/21πΓ[m/2α/4+1/2m/2α/4+1m/2+α/4m/2+α/4+1/23/2],
Qm2a=2α/21π(k8Lρ2)mΓ[m/2α/4+1/21/2m+1/2m+1α/4+1m/2]{F32(m/2α/4+1/2,m/2α/4;1/2,m+1/2,m+1;(k8Lρ2)2)},
Qm2b=2α/21π(k8Lρ2)m+1Γ[m/2α/4+11/2m+1m+3/2α/4+1/2m/2]{F32(m/2α/4+1,m/2α/4+1/2;3/2,m+1,m+3/2;(k8Lρ2)2)}.
s=m/2+n1withn1=0,1,2s=m/2+1/2+n2withn2=0,1,2s=α/41/2n3withn3=0.
σR2(α)=(A(α)/α)β2(1α/2)π5/2k(3α/2)Lα/2Γ[(2α)/4]/Γ[α/4].

Metrics