Abstract

A new atmospheric spectral model and expressions of irradiance scintillation index are derived theoretically for optical wave propagating through moderate-to-strong non-Kolmogorov turbulence. They are developed under Andrews’ assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave, and the geometrical optics approximation is adopted for mathematical development. A wide range of turbulence strength is considered instead of a limited range for weak turbulence. The atmospheric spectral model has a spectral power law value in the range of 3 to 4 instead of the standard power law value of 11/3. Numerical calculations are conducted to analyze the influences of spectral power law and turbulence strength.

© 2012 Optical Society of America

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  1. V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation,” (translated for NOAA by Israel Program for Scientific Translations, Jerusalem, 1971).
  2. R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2, 179–201 (1992).
    [CrossRef]
  3. A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
    [CrossRef]
  4. L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16, 1417–1429 (1999).
    [CrossRef]
  5. L. C. Andrews, “An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
    [CrossRef]
  6. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11, 2719–2726 (1994).
    [CrossRef]
  7. R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
    [CrossRef]
  8. L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
    [CrossRef]
  9. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  10. Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
    [CrossRef]
  11. D. T. Kyrazis, J. B. Wissler, 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]
  12. 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]
  13. 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]
  14. 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]
  15. T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
    [CrossRef]
  16. E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004).
    [CrossRef]
  17. 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]
  18. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. I and II.
  19. L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE, 1998).
  20. M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
    [CrossRef]
  21. J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
    [CrossRef]
  22. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [CrossRef]
  23. M. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
    [CrossRef]

2011 (1)

M. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[CrossRef]

2009 (1)

Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
[CrossRef]

2008 (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]

2007 (1)

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)

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
[CrossRef]

2004 (1)

2003 (1)

A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
[CrossRef]

2002 (1)

L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

1999 (1)

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 (1)

T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

1995 (1)

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

1994 (3)

W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11, 2719–2726 (1994).
[CrossRef]

M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
[CrossRef]

D. T. Kyrazis, J. B. Wissler, 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]

1992 (2)

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[CrossRef]

L. C. Andrews, “An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
[CrossRef]

1986 (1)

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Al-Habash, M. A.

Andrews, L. C.

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, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16, 1417–1429 (1999).
[CrossRef]

W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A 11, 2719–2726 (1994).
[CrossRef]

L. C. Andrews, “An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
[CrossRef]

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

L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE, 1998).

Baker, G. J.

M. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[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, 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]

Bishop, K. P.

D. T. Kyrazis, J. B. Wissler, 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]

Brown, J. M.

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]

Charnotskii, M.

M. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[CrossRef]

Charnotskii, M. I.

M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
[CrossRef]

Codona, J. L.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Consortini, A.

A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
[CrossRef]

Creamer, D. B.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[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]

Elperin, T.

T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

Ferrero, V.

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]

Flatte, S. M.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Frehlich, R. G.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Fugate, R. Q.

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]

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]

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

Hao, Y.

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
[CrossRef]

Henyey, F. S.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Hill, R. J.

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[CrossRef]

Hopen, C. Y.

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]

Innocenti, C.

A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. I and II.

Jian-ping, S.

Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
[CrossRef]

Jian-wei, F.

Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
[CrossRef]

Karis, S. J.

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. B. Wissler, 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]

Kleeorin, N.

T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

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]

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. B. Wissler, 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]

Miller, W. B.

Phillips, R. L.

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, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16, 1417–1429 (1999).
[CrossRef]

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

Ping Li, Z.

A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
[CrossRef]

Preble, A. J.

D. T. Kyrazis, J. B. Wissler, 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]

Ricklin, J. C.

Rogachevskii, I.

T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[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]

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]

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]

Song, X.

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (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]

Sun, Y. Y.

A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation,” (translated for NOAA by Israel Program for Scientific Translations, Jerusalem, 1971).

Toselli, I.

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]

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]

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. B.

D. T. Kyrazis, J. B. Wissler, 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]

Wu, J.

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
[CrossRef]

Wu, Z.

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
[CrossRef]

Xi-wen, Q.

Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
[CrossRef]

Yan, H.

Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
[CrossRef]

Yang, R.

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
[CrossRef]

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]

Appl. Opt. (1)

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]

Int. J. Infrared Millim. Waves (1)

R. Yang, X. Song, Z. Wu, Y. Hao, and J. Wu, “Analysis of inner-scale effect on atmosphere scintillation for infrared laser beam propagation on Earth-space paths,” Int. J. Infrared Millim. Waves 26, 467–481 (2005).
[CrossRef]

J. Mod. Opt. (1)

L. C. Andrews, “An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
[CrossRef]

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

Opt. Commun. (1)

A. Consortini, Y. Y. Sun, C. Innocenti, and Z. Ping Li, “Measuring inner scale of atmospheric turbulence by angle of arrival and scintillation,” Opt. Commun. 216, 19–23 (2003).
[CrossRef]

Phys. Rev. E (1)

T. Elperin, N. Kleeorin, and I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

Proc. SPIE (8)

L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE 4489, 23–34 (2002).
[CrossRef]

Q. Xi-wen, S. Jian-ping, F. Jian-wei, and H. Yan, “Irradiance scintillation on laser beam propagation in the near ground turbulent atmosphere,” Proc. SPIE 7382, 73824O (2009).
[CrossRef]

D. T. Kyrazis, J. B. Wissler, 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]

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]

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]

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]

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

M. Charnotskii and G. J. Baker, “Practical calculation of the beam scintillation index based on the rigorous asymptotic propagation theory,” Proc. SPIE 8038, 803804 (2011).
[CrossRef]

Radio Sci. (1)

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21, 929–948 (1986).
[CrossRef]

Waves Random Media (2)

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[CrossRef]

M. I. Charnotskii, “Asymptotic analysis of finite-beam scintillation in a turbulent medium,” Waves Random Media 4, 243–273 (1994).
[CrossRef]

Other (4)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. I and II.

L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE, 1998).

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

V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation,” (translated for NOAA by Israel Program for Scientific Translations, Jerusalem, 1971).

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Figures (4)

Fig. 1.
Fig. 1.

Irradiance scintillation index versus strength of turbulence with different α. (a) plane wave, (b) spherical wave.

Fig. 2.
Fig. 2.

Comparisons among weak turbulence, strong turbulence, and moderate-to-strong turbulence with specific α=3.2. (a) plane wave, (b) spherical wave.

Fig. 3.
Fig. 3.

Comparisons among weak turbulence, strong turbulence, and moderate-to-strong turbulence with specific α=3.4. (a) plane wave, (b) spherical wave.

Fig. 4.
Fig. 4.

Comparisons among weak turbulence, strong turbulence, and moderate-to-strong turbulence with specific α=11/3. (a) plane wave, (b) spherical wave.

Equations (49)

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Φn1(κ,α)=Φn(κ,α)G(κ,α),(2π/L0κ2π/l0,3<α<4),
Φn(κ,α)=A(α)·C^n2·κα,(2π/L0κ2π/l0,3<α<4),
A(α)=Γ(α1)4π2sin[(α3)π2].
G(κ,α)=GX(κ,α)+GY(κ,α).
GX(κ,α)=exp[κ2κX2(α)],GY(κ,α)=κα[κ2+κY2(α)]α/2.
1κX2(α)=c1(α)Lk+c2(α)[Lkρ0(α)]2,κY2(α)=c3(α)kL+c4(α)·1ρ02(α),
σI2=I2I21=X2Y21=[1+σX2][1+σY2]1=σX2+σY2+σX2·σY2,
σX2=exp[σlnX2]1,σY2=exp[σlnY2]1,
σI2=exp[σlnI2]1=exp[σlnX2+σlnY2]1.
σI2σlnX2+σlnY2,σI21.
σR(pl)2(α)=8π2k20L0κΦn(κ,α)[1cos(κ2zk)]dκdz,
σR(sp)2(α)=8π2k20L0κΦn(κ,α)[1cos(κ2z(1z/L)k)]dκdz,
Γ(x)=0κx1·eκdκ.
σR(pl)2(α)=β1(α)·A(α)C^n2π2k3α/2Lα/2,
σR(sp)2(α)=β2(α)·A(α)C^n2π2k3α/2Lα/2,
β1(α)=4·Γ(α2)·sin(πα4),
β2(α)=4·Γ(1α2)·sin(πα4)·Γ2(α/2)Γ(α)
σI_S2(α)=1+8π2L3·010κ5Φn(κ,α)·w2(ε,ε)exp{01Ds[Lκkw(τ,ε)]dτ}dκdε,
w(τ,ε)={τ(1Θ˜ε),τ<εε(1Θ˜τ),τ>ε.
Ds(ρ,α)=4π2A(α)C^n2k2L·[Γ(1α/2)Γ(α/2)·(ρ24)α21].
F12(A,B;C;Z)=Γ(C)Γ(B)·Γ(CB)01tB1·(1t)CB1·(1tZ)Adt.
σI_S(pl)2(α)=1+r1(α)·I1(α)·σR(pl)4(α4)α2(α),σI_S(sp)2(α)=1+r2(α)·I2(α)·σR(sp)4(α4)α2(α),
r1(α)=1α2·[2](3α)(α10)α2·[Γ(1α/2)Γ(α/2)]α6α2·Γ(6αα2)·[β1(α)]82αα2,
I1(α)=1α3F12(6αα2,α3;α2;α2α1),
r2(α)=1α2·[2](3α)(α10)α2·[Γ(1α/2)Γ(α/2)]α6α2·Γ(6αα2)·[β2(α)]82αα2,
I2(α)=(α1)6αα2·Γ2(α3)Γ(2α6).
σI(pl)2(α)=exp[σlnX(pl)2(α)+σlnY(pl)2(α)]1,
σlnX(pl)2(α)=8π2k20L0κ·Φn(κ,α)·GX(κ,α)·[1cos(κ2zk)]dκdz,
σlnY(pl)2(α)=8π2k20L0κ·Φn(κ,α)·GY(κ,α)·[1cos(κ2zk)]dκdz.
σlnX(pl)2(α)=2Γ(3α/2)3β1(α)·ηX(pl)3α2(α)·σR(pl)2(α).
σlnY(pl)2(α)=8(α2)β1(α)·ηY(pl)1α2(α)·σR(pl)2(α).
{exp[σlnX(pl)2(α)+σlnY(pl)2(α)]1σlnX(pl)2(α)+σlnY(pl)2(α)σR(pl)2(α),(σR(pl)2(α)1)exp[σlnX(pl)2(α)+σlnY(pl)2(α)]1σI_S(pl)2(α),(σR(pl)2(α)1),
{ηX(pl)(α)1c1(pl)(α),ηY(pl)(α)c3(pl)(α),(σR(pl)21)ηX(pl)(α)k·ρ0(pl)2(α)L·c2(pl)(α),ηY(pl)(α)L·c4(pl)(α)k·ρ0(pl)2(α),(σR(pl)21),
ρ0(pl)(α)=[ρ1(α)]1α2·[π2A(α)C^n2k2L]1α2,ρ1(α)=Γ(α/2)Γ(1α/2)·23α.
c1(pl)(α)=[2Γ(3α/2)3β1(α)×0.49]26α,c2(pl)(α)=[3β1(α)·r1(α)·I1(α)4Γ(3α/2)]2α6·[ρ1(α)·β1(α)]2α2,c3(pl)(α)=[0.51×(α2)·β1(α)8]22α,c4(pl)(α)=[(α2)·ln28·ρ1(α)]22α.
ηX(pl)(α)=[3β1(α)×0.492Γ(3α/2)]26α[1+fX(pl)(α)·σR(pl)4α2(α)],
ηY(pl)(α)=[0.51×(α2)·β1(α)8]22α·[1+fY(pl)(α)·σR(pl)4α2(α)],
fX(pl)(α)=[r1(α)·I1(α)2×0.49]2α6,fY(pl)(α)=(ln20.51)22α.
σI(pl)2(α)=exp[0.49σR(pl)2(α)[1+fX(pl)(α)·σR(pl)4α2(α)]3α2+0.51σR(pl)2(α)[1+fY(pl)(α)·σR(pl)4α2(α)]α21]1.
σI(sp)2(α)=exp[σlnX(sp)2(α)+σlnY(sp)2(α)]1.
σlnX(sp)2(α)=8π2k20L0κ·Φn(κ,α)·GX(κ,α)·[1cos(κ2z(1z/L)k)]dκdz,
σlnY(sp)2(α)=8π2k20L0κ·Φn(κ,α)·GY(κ,α)·[1cos(κ2z(1z/L)k)]dκdz.
ρ0(sp)(α)=[ρ2(α)]1α2·[π2A(α)C^n2k2L]1α2,ρ2(α)=Γ(α/2)(α1)Γ(1α/2)·23α,
c1(sp)(α)=[2Γ(3α/2)30β2(α)×0.49]26α,c2(sp)(α)=[30β2(α)·r2(α)·I2(α)4Γ(3α/2)]2α6·[ρ2(α)·β2(α)]2α2,c3(sp)(α)=[0.51×(α2)·β2(α)8]22α,c4(sp)(α)=[(α2)·ln28·ρ2(α)]22α.
σlnX(sp)2(α)=2Γ(3α/2)30β2(α)·ηX(sp)3α2(α)·σR(sp)2(α),σlnY(sp)2(α)=8(α2)β2(α)·ηY(sp)1α2(α)·σR(sp)2(α),
ηX(sp)(α)=LκX(sp)2(α)k=[30β2(α)×0.492Γ(3α/2)]26α1+fX(sp)(α)·[σR(sp)2(α)]2α2,
ηY(sp)(α)=LκY(sp)2(α)k=[0.51×(α2)·β2(α)8]22α·[1+fY(sp)(α)·σR(sp)4α2(α)],
fX(sp)(α)=[r2(α)·I2(α)2×0.49]2α6,fY(sp)(α)=(ln20.51)22α.
σI(sp)2(α)=exp[0.49σR(sp)2(α)[1+fX(sp)(α)·σR(sp)4α2(α)]3α2+0.51σR(sp)2(α)[1+fY(sp)(α)·σR(sp)4α2(α)]α21]1.

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