Abstract

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς2α.

© 2011 Optical Society of America

Full Article  |  PDF Article

Corrections

Italo Toselli, Brij Agrawal, and Sergio Restaino, "Light propagation through anisotropic turbulence: erratum," J. Opt. Soc. Am. A 30, 2415-2415 (2013)
https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-30-11-2415

References

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  1. I. Toselli, L. C. Andrews, and R. L. Phillips, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
    [Crossref]
  2. D. Dayton, B. Pierson, and B. Spielbusch, “Atmospheric structure function measurements with a Shack-Hartmann wave front sensor,” Opt. Lett. 17, 1737-1739 (1992).
    [Crossref]
  3. A. Tunik, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
    [Crossref]
  4. M. S. Be1enkii, S. J. Karis, J. M. Brown II, 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]
  5. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181-196 (1995).
    [Crossref]
  6. D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
    [Crossref]
  7. C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
    [Crossref]
  8. L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
    [Crossref]
  9. L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
    [Crossref]
  10. M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
    [Crossref]
  11. F. S. Vetelino, K. Grayshan, and C. Y. Young, “Inferring path average Cn2 values in the marine environment,” J. Opt. Soc. Am. A 24, 3198-3206 (2007).
    [Crossref]
  12. 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]
  13. M. S. Belen'kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20, 1359-1361 (1995).
    [Crossref]
  14. M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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]
  15. 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]
  16. M. S. Belen'kii, S. J. Karis, and C. L. Osmon, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50-51(1999).
    [Crossref]
  17. R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6-16(1995).
    [Crossref]
  18. L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
    [Crossref]
  19. A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularitie,” Waves Rand. Compl. Media 4, 297-305 (1994).
    [Crossref]
  20. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
  21. A. S. Gurvich and A. I. Kon, “The backscattering from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 6, 107-118 (1992).
    [Crossref]
  22. A. S. Gurvich and A. I. Kon, “Aspect sensitivity of radar returns from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 7, 1343-1353 (1993).
    [Crossref]
  23. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
    [Crossref]
  24. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
    [Crossref]

2009 (2)

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
[Crossref]

2008 (1)

I. Toselli, L. C. Andrews, and R. L. Phillips, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
[Crossref]

2007 (4)

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

A. Tunik, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
[Crossref]

F. S. Vetelino, K. Grayshan, and C. Y. Young, “Inferring path average Cn2 values in the marine environment,” J. Opt. Soc. Am. A 24, 3198-3206 (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (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)

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

2004 (1)

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

1999 (3)

M. S. Belen'kii, S. J. Karis, and C. L. Osmon, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50-51(1999).
[Crossref]

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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]

1997 (1)

M. S. Be1enkii, S. J. Karis, J. M. Brown II, 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]

1995 (4)

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

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

1994 (2)

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularitie,” Waves Rand. Compl. Media 4, 297-305 (1994).
[Crossref]

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

1993 (1)

A. S. Gurvich and A. I. Kon, “Aspect sensitivity of radar returns from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 7, 1343-1353 (1993).
[Crossref]

1992 (2)

D. Dayton, B. Pierson, and B. Spielbusch, “Atmospheric structure function measurements with a Shack-Hartmann wave front sensor,” Opt. Lett. 17, 1737-1739 (1992).
[Crossref]

A. S. Gurvich and A. I. Kon, “The backscattering from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 6, 107-118 (1992).
[Crossref]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
[Crossref]

I. Toselli, L. C. Andrews, and R. L. Phillips, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Barchers, J. D.

M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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]

Be1enkii, M. S.

M. S. Be1enkii, S. J. Karis, J. M. Brown II, 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]

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, S. J. Karis, and C. L. Osmon, “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 II, 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]

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]

Bishop, K. P.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

Black, D. G.

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

Brown, J. M.

M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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. Be1enkii, S. J. Karis, J. M. Brown II, 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]

Burris, H. R.

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Chang, M.

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[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]

Dayton, D.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Font, C. O.

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

Fugate, R. Q.

M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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. Be1enkii, S. J. Karis, J. M. Brown II, 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]

Gilbreath, G. C.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Grayshan, K.

Gurvich, A. S.

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. S. Gurvich and A. I. Kon, “Aspect sensitivity of radar returns from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 7, 1343-1353 (1993).
[Crossref]

A. S. Gurvich and A. I. Kon, “The backscattering from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 6, 107-118 (1992).
[Crossref]

Hotten, L. J.

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

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]

J., W.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Jones, B. A.

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

Karis, S. J.

M. S. Belen'kii, S. J. Karis, and C. L. Osmon, “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 II, 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. Be1enkii, S. J. Karis, J. M. Brown II, 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. D. B.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

Kon, A. I.

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularitie,” Waves Rand. Compl. Media 4, 297-305 (1994).
[Crossref]

A. S. Gurvich and A. I. Kon, “Aspect sensitivity of radar returns from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 7, 1343-1353 (1993).
[Crossref]

A. S. Gurvich and A. I. Kon, “The backscattering from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 6, 107-118 (1992).
[Crossref]

Kyrazis, D. T.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

Lane, J.

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

Luna, Y.

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

Mahon, R.

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Moore, C. I.

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Osmon, C. L.

M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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, and C. L. Osmon, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50-51(1999).
[Crossref]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
[Crossref]

I. Toselli, L. C. Andrews, and R. L. Phillips, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Pierson, B.

Preble, A. J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

Rabinovich, W.

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

Rabinovich, W. S.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Restaino, S.

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

Roggemann, L. C.

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

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]

Roura, E.

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

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]

Santiago, F.

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

Spielbusch, B.

Stell, M.

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

Stell, M. F.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

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]

Suite, M.

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

Suite, M. R.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Swingen, L. A.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
[Crossref]

I. Toselli, L. C. Andrews, and R. L. Phillips, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Tunik, A.

A. Tunik, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
[Crossref]

Vetelino, F. S.

Wasiczko, L.

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

Wasiczko, L. M.

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

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]

Wissler, J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

Young, C. Y.

IEEE Trans. Antennas Propag. (1)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov turbulence,” IEEE Trans. Antennas Propag. 57, 1783-1788 (2009).
[Crossref]

J. Electromagn. Waves Appl. (2)

A. S. Gurvich and A. I. Kon, “The backscattering from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 6, 107-118 (1992).
[Crossref]

A. S. Gurvich and A. I. Kon, “Aspect sensitivity of radar returns from anisotropic turbulent irregularities,” J. Electromagn. Waves Appl. 7, 1343-1353 (1993).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

I. Toselli, L. C. Andrews, and R. L. Phillips, “Free space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (14)

M. S. Belen'kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown II, 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, 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, S. J. Karis, and C. L. Osmon, “Experimental evidence of the effects of non-Kolmogorov turbulence and anisotropy of turbulence,” Proc. SPIE 3749, 50-51(1999).
[Crossref]

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

L. J. Hotten, L. C. Roggemann, B. A. Jones, J. Lane, and D. G. Black, “High bandwidth atmospheric turbulence data collection platform,” Proc. SPIE 3866, 23-32 (1999).
[Crossref]

A. Tunik, “Analysis of free-space laser signal intensity over a 2.33 km optical path,” Proc. SPIE 6708, 670802 (2007).
[Crossref]

M. S. Be1enkii, S. J. Karis, J. M. Brown II, 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]

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

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43-55(1994).
[Crossref]

C. I. Moore, H. R. Burris, W. S. Rabinovich, L. Wasiczko, M. R. Suite, L. A. Swingen, R. Mahon, M. F. Stell, G. C. Gilbreath, and W. J. Scharpf, “Overview of NRL's maritime laser communication test facility,” Proc. SPIE 5892, 589206 (2005).
[Crossref]

L. M. Wasiczko, C. I. Moore, H. R. Burris, M. Suite, M. Stell, and W. Rabinovich, “Studies of atmospheric propagation in the maritime environment at NRL,” Proc. SPIE 6551, 65510F (2007).
[Crossref]

L. M. Wasiczko, R. Mahon, C. I. Moore, H. R. Burris, M. Suite, and W. Rabinovich, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[Crossref]

M. Chang, C. O. Font, F. Santiago, Y. Luna, E. Roura, and S. Restaino, “Marine environment optical propagation measurements,” Proc. SPIE 5550, 40-46 (2004).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Waves Rand. Compl. Media (1)

A. I. Kon, “Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularitie,” Waves Rand. Compl. Media 4, 297-305 (1994).
[Crossref]

Other (1)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

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Figures (6)

Fig. 1
Fig. 1

Long-term beam spread as a function of alpha for a horizontal path.

Fig. 2
Fig. 2

Propagation geometry for a laser beam originating at distance L to the left of a thin Gaussian lens.

Fig. 3
Fig. 3

Scintillation index for the plane wave as a function of alpha for several anisotropic coefficient values.

Fig. 4
Fig. 4

Scintillation index for the spherical wave as a function of alpha for several anisotropic coefficient values.

Fig. 5
Fig. 5

Scintillation index for the Gaussian beam as a function of alpha for several anisotropic coefficient values.

Fig. 6
Fig. 6

Anisotropic factor as a function of alpha for several zeta values.

Equations (15)

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D n ( r ) = β · C n 2 · ( Δ x 2 + Δ y 2 ς + Δ z 2 ) γ 2 ,
Φ n ( κ , α ) = A ( α ) · C ˜ n 2 · ς 2 · [ κ z 2 + ς ( κ x 2 + κ y 2 ) ] α 2 ,
A ( α ) = 1 4 π 2 Γ ( α 1 ) cos ( α π 2 ) , 3 < α < 4 ,
W e 2 = W L T 2 ( α ) = W 2 · [ 1 + T ( α ) ] ,
T ( α ) = 4 π 2 k 2 L · ( 0 1 0 κ · ϕ n ( α , κ ) d κ d ξ 0 1 0 κ · ϕ n ( α , κ ) exp ( Λ L κ 2 ξ 2 k ) d κ d ξ ) = 0.25 · α α 1 · [ sin ( α · π 4 ) ] 1 · σ ˜ R 2 ( α ) · Λ α 2 1 · ς 2 α = T ( α ) isotropic · ς 2 α ,
σ ˜ R 2 ( α ) = 8 π 2 · A ( α ) · 1 α · Γ ( 1 α 2 ) · sin ( α · π 4 ) · C ˜ n 2 · k 3 α 2 · L α 2 .
σ I 2 = I 2 I 2 1 ,
σ I _ plane 2 ( α , D G ) = 8 π 2 · k 2 · L · Re { 0 1 0 κ · Φ n ( κ , α ) · exp ( D G 2 · κ 2 16 ) · [ 1 exp ( j L · κ 2 · ξ k ) ] d κ d ξ } = 8 π 2 · A ( α ) · C ˜ n 2 · k 3 α 2 · L α 2 · Γ ( 1 α 2 ) · 1 α · ς 2 α · { α 2 · ( k · D G 2 16 · L ) α 2 1 [ ( k · D G 2 16 · L ) 2 + 1 ] α 4 · sin [ α 2 · arctg ( 16 · L k · D G 2 ) ] } = σ ˜ R 2 ( α ) · [ sin ( α · π 4 ) ] 1 · ς 2 α · { α 2 · ( k · D G 2 16 · L ) α 2 1 [ ( k · D G 2 16 · L ) 2 + 1 ] α 4 · sin [ α 2 · arctg ( 16 · L k · D G 2 ) ] } = σ I _ plane 2 ( α , D G ) isotropic · ς 2 α .
L = 50000 m ; C ˜ n 2 = 7 · 10 18 m α + 3 ; λ = 1.55 μm ; D G = 0.1 m .
σ I _ spherical 2 ( α , D G ) = 8 π 2 · k 2 · L · Re { 0 1 0 κ · Φ n ( κ , α ) · exp ( D G 2 · κ 2 · ξ 2 16 ) · [ 1 exp ( j L · κ 2 · ξ · ( 1 ξ ) k ) ] d κ d ξ } = 4 π 2 · k 2 · L · A ( α ) · C ˜ n 2 · ( 16 D G 2 ) 1 α 2 · Γ ( 1 α 2 ) · ς 2 α · { 1 α 1 Re { ( j 16 L k D G 2 ) α 2 1 · 2 α · F 1 2 ( 1 α 2 , α 2 ; 1 + α 2 ; 1 + j k D G 2 16 L ) } } = σ I _ spherical 2 ( α , D G ) isotropic · ς 2 α ,
F 1 2 ( a , b ; c ; z ) = 0 ( a ) n · ( b ) n ( c ) n · z n n ! , | z | < ,
( a ) n = Γ ( a + n ) Γ ( a ) .
at the transmitter   ( z = 0 ) :   Θ 0 = 1 L F 0 , Λ 0 = 2 L k W 0 2 ,
at the Gaussian lens   ( z = L ) :   Θ 1 = Θ 0 Θ 0 2 + Λ 0 2 , Λ 1 = Λ 0 Θ 0 2 + Λ 0 2 .
σ I _ Gaussian 2 ( α , D G ) = 4 π 2 · k 3 α 2 · L · × Re 0 1 0 κ · Φ n ( κ , α ) · exp { L · κ 2 k ( Λ 1 + Ω G ) · [ ( 1 Θ ¯ 1 ξ ) 2 + Λ 1 Ω G ξ 2 ] } · { 1 exp [ j L κ 2 k ( Ω G Λ 1 Λ 1 + Ω G ) ξ ( 1 Θ ¯ 1 ξ ) ] } d κ d ξ = 4 π 2 · k 2 · L · A ( α ) · C ˜ n 2 · Γ ( 1 α 2 ) · [ k L · ( Λ 1 + Ω G ) ] 1 α 2 · ς 2 α · { 0 1 [ ( 1 Θ ¯ 1 · ξ ) 2 + Λ 1 Ω G ξ 2 ] α 2 1 d ξ Re 0 1 [ ( 1 Θ ¯ 1 · ξ ) 2 + Λ 1 Ω G ξ 2 + j ( Ω G Λ 1 ) · ξ ( 1 Θ ¯ 1 · ξ ) ] α 2 1 d ξ } = σ I _ Gaussian 2 ( α , D G ) isotropic · ς 2 α .

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