Abstract

The characteristic size of a collimated Gaussian beam propagating through 1–13 km atmospheric paths is investigated by simulating phase screens using the fast Fourier transform method. Taking a threshold into account, a method to derive a modified centroid and corresponding characteristic radii of the short-term spots is proposed. Effective radius, robust radius, sharpness radius, and maximum radius are analyzed by probability statistics. Furthermore, several parameters representing the energy content of the spots within each radius and the energy duty cycle of the maximum radius are studied. The study shows that, when the modified centroid is taken as a center, the effective radius is more suitable for application after a long propagation path, while the maximum radius is more effective for a short distance. However, when all effective subspots of a short-term image are investigated, the maximum radius is usually utilized, and the energy duty cycle represents the effect probability.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  7. Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).
    [CrossRef]
  8. H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).
    [CrossRef]
  9. X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).
    [CrossRef]
  10. H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
    [CrossRef]
  11. J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
    [CrossRef]
  12. H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
    [CrossRef]
  13. B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
    [CrossRef]
  14. Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
    [CrossRef]
  15. H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).
    [CrossRef]
  16. X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).
    [CrossRef]
  17. X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).
    [CrossRef]
  18. X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).
    [CrossRef]
  19. Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
    [CrossRef]
  20. P. Zhou, X. L. Wang, Y. X. Ma, H. T. Ma, X. J. Xu, and Z. J. Liu, “Propagation property of a nonuniformly polarized beam array in turbulent atmosphere,” Appl. Opt. 50, 1234–1239 (2011).
    [CrossRef]
  21. X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
    [CrossRef]
  22. G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
    [CrossRef]
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    [CrossRef]
  26. A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39, 5426–5445 (2000).
    [CrossRef]
  27. X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).
  28. V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
    [CrossRef]
  29. R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

2012 (1)

2011 (6)

Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).
[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).
[CrossRef]

P. Zhou, X. L. Wang, Y. X. Ma, H. T. Ma, X. J. Xu, and Z. J. Liu, “Propagation property of a nonuniformly polarized beam array in turbulent atmosphere,” Appl. Opt. 50, 1234–1239 (2011).
[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

2010 (3)

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
[CrossRef]

X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).
[CrossRef]

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

2009 (1)

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).
[CrossRef]

2008 (6)

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).
[CrossRef]

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).
[CrossRef]

M. H. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008).
[CrossRef]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

2007 (2)

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).
[CrossRef]

2006 (1)

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

2005 (1)

2002 (1)

R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

2000 (2)

1988 (1)

1981 (1)

1973 (1)

Alavinejad, M.

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).
[CrossRef]

Altay, S.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

Baykal, Y.

Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).
[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).
[CrossRef]

Baykal, Y. K.

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

Belmonte, A.

Cai, Y.

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
[CrossRef]

Cai, Y. J.

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
[CrossRef]

Chen, B. S.

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Chen, R. P.

Chen, X. W.

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).
[CrossRef]

Chen, Y.

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
[CrossRef]

Chen, Z. Y.

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Chu, X. X.

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[CrossRef]

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).
[CrossRef]

X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).
[CrossRef]

Cui, Z. F.

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).
[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).
[CrossRef]

Feng, X. X.

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).
[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[CrossRef]

Flatté, S. M.

Frehlich, R.

Ghafary, B.

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).
[CrossRef]

Hardalaç, F.

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

Huang, Y. B.

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

Ji, X. L.

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).
[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).
[CrossRef]

Kashani, F. D.

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).
[CrossRef]

Khmelertov, S. S.

Knepp, D. L.

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” in Proceedings of IEEE Conference (IEEE, 1983), pp. 722–737.

Konyaev, P. A.

Li, W. H.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Liu, Z. J.

Lü, B.

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).
[CrossRef]

Lukin, V. P.

Ma, H. T.

Ma, Y. X.

Mahdieh, M. H.

M. H. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008).
[CrossRef]

Martin, J. M.

Pokasov, V. V.

Pu, J. X.

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Qian, X. M.

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

Qiao, C. H.

X. X. Chu, C. H. Qiao, X. X. Feng, and R. P. Chen, “Propagation of Gaussian–Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50, 3871–3878 (2011).
[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[CrossRef]

Qu, J.

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
[CrossRef]

Rao, R. Z.

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

Ren, J. H.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Sennikov, V. A.

Shi, J. P.

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

Wang, X. L.

Wu, G. H.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Xiao, X.

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).
[CrossRef]

Xu, X. J.

Zhang, J. Y.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Zhang, X. L.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Zhao, T. G.

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Zhong, Y. L.

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
[CrossRef]

Zhou, P.

Zhu, W. Y.

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

Acta Photonica Sinica (1)

X. M. Qian, W. Y. Zhu, Y. B. Huang, and R. Z. Rao, “Selection of computing parameters in numerical simulation of laser beam propagation in turbulent atmosphere,” Acta Photonica Sinica 37, 1986–1991 (2008) (in Chinese).

Appl. Opt. (9)

Appl. Phys. B (2)

H. T. Eyyuboğlu, Y. K. Baykal, and X. L. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Propagation of laser array beams in a turbulent atmosphere,” Appl. Phys. B 88, 467–475 (2007).
[CrossRef]

Chin. J. Lasers (1)

R. Z. Rao, “Pattern characteristics of collimated laser beam in a turbulent atmosphere: I. Characteristic radii,” Chin. J. Lasers 29, 889–894 (2002) (in Chinese).

Opt. Commun. (5)

X. X. Chu, “Beam spreading of truncated Gaussian beams in Kolmogorov turbulence,” Opt. Commun. 283, 3408–3414 (2010).
[CrossRef]

M. H. Mahdieh, “Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor,” Opt. Commun. 281, 3395–3402 (2008).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence,” Opt. Commun. 278, 17–22 (2007).
[CrossRef]

J. Qu, Y. L. Zhong, Z. F. Cui, and Y. J. Cai, “Elegant Laguerre–Gaussian beam in a turbulent atmosphere,” Opt. Commun. 283, 2772–2781 (2010).
[CrossRef]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264, 25–34 (2006).
[CrossRef]

Opt. Laser Technol. (8)

B. S. Chen, Z. Y. Chen, and J. X. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40, 820–827 (2008).
[CrossRef]

Y. L. Zhong, Z. F. Cui, J. P. Shi, and J. Qu, “Propagation properties of partially coherent Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 43, 741–747 (2011).
[CrossRef]

X. Xiao, X. L. Ji, and B. Lü, “The influence of turbulence on propagation properties of partially coherent sinh-Gaussian beams and their beam quality in the far field,” Opt. Laser Technol. 40, 129–136 (2008).
[CrossRef]

X. L. Ji and X. W. Chen, “Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence,” Opt. Laser Technol. 41, 165–171 (2009).
[CrossRef]

Y. Baykal, “Intensity correlations of general type beam in weakly turbulent atmosphere,” Opt. Laser Technol. 43, 1237–1242 (2011).
[CrossRef]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel–Gaussian beams in turbulence,” Opt. Laser Technol. 40, 343–351 (2008).
[CrossRef]

X. X. Chu, C. H. Qiao, and X. X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[CrossRef]

G. H. Wu, T. G. Zhao, J. H. Ren, J. Y. Zhang, X. L. Zhang, and W. H. Li, “Beam propagation factor of partially coherent Hermite–Gaussian beams through non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1225–1228 (2011).
[CrossRef]

Opt. Lasers Eng. (1)

M. Alavinejad, B. Ghafary, and F. D. Kashani, “Analysis of the propagation of flat-topped beam with various beam orders through turbulent atmosphere,” Opt. Lasers Eng. 46, 1–5 (2008).
[CrossRef]

Other (2)

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

D. L. Knepp, “Multiple phase-screen calculation of the temporal behavior of stochastic waves,” in Proceedings of IEEE Conference (IEEE, 1983), pp. 722–737.

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Figures (4)

Fig. 1.
Fig. 1.

Typical laser beam contour (initially collimated Gaussian laser beam with λ=1.064μm and beam radius ω0=25mm) propagating through turbulent atmosphere with a moderate level of refractive index structure parameter Cn2=1e14 at a distance of (a) 1, (b) 5, (c) 10, and (d) 13 km.

Fig. 2.
Fig. 2.

Average intensity contour of 900 random short-term spot images by numerical simulation (initially collimated Gaussian laser beam with λ=1.064μm and beam radius ω0=25mm) at a distance of (a) 1, (b) 5, (c) 10, and (d) 13 km.

Fig. 3.
Fig. 3.

Typical results of the spot centroid (asterisk), effective radius (thinner solid circle), robust radius (dashed circle) and sharpness radius (thicker solid circle) at a distance of (a) 1, (b) 5, (c) 10, and (d) 13 km (initially collimated Gaussian laser beam with λ=1.064μm and beam radius ω0=25mm, Cn2=1e14).

Fig. 4.
Fig. 4.

Medians of ηeff (circles), ηrbt (squares), ηshp (diamonds), and η (triangles) versus the propagation distance from 1 to 13 km.

Tables (4)

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Table 1. Numerical Descriptive Statistics of Effective Radius Taking the Modified Centroid as the Center for Different Propagation Distances of 1–13 km

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Table 2. Numerical Descriptive Statistics of Robust Radius Taking the Modified Centroid as the Center for Different Propagation Distances of 1–13 km

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Table 3. Numerical Descriptive Statistics of Sharpness Radius Taking the Modified Centroid as the Center for Different Propagation Distances of 1–13 km

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Table 4. Numerical Descriptive Statistics of Maximum Radius Taking the Modified Centroid as the Center for Different Propagation Distances of 1–13 km

Equations (15)

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2ikψz+2ψ+2k2nψ=0,
ψ(r,zi)=f1{f[ψ(r,zi1)exp(iS)]exp(iκx2+κy22kΔz)},
{xc=xI(x,y)dxdyI(x,y)dxdyyc=yI(x,y)dxdyI(x,y)dxdy,
{xc=i=1mj=1ni×I(i,j)i=1mj=1nI(i,j),yc=i=1mj=1nj×I(i,j)i=1mj=1nI(i,j).
ωeff2=r2I(x,y)dxdyI(x,y)dxdy,
ωrbt=rI(x,y)dxdyI(x,y)dxdy.
ωshp2=r2I2(x,y)dxdyI2(x,y)dxdy.
{xc=SxI(x,y)dxdySI(x,y)dxdy,yc=SyI(x,y)dxdySI(x,y)dxdy.
ωeff2=Sr2I(x,y)dxdySI(x,y)dxdy,
ωrbt=SrI(x,y)dxdySI(x,y)dxdy,
ωshp2=Sr2I2(x,y)dxdySI2(x,y)dxdy.
η=S0/Smax,
SK=1ni=1n(ωiω¯)3(1ni=1n(ωiω¯)2)3.
BK=1ni=1n(ωiω¯)4(1ni=1n(ωiω¯)2)2.
ηeff=S1/S0,ηrbt=S2/S0,ηshp=S3/S0,

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