Abstract

Based on the generalized exponential spectrum for non-Kolmogorov atmospheric turbulence, theoretical expressions of the angle-of-arrival (AOA) variance are derived for plane and spherical optical waves propagating through weak turbulence. Without particular assumption, the new expressions relate the AOA variance to the receiver aperture, finite turbulence inner and outer scales, and the optical wavelength.

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References

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  1. R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves in Random and Complex Media 2, 179–201 (1992). http://dx.doi.org/10.1088/0959-7174/2/3/001 .
  2. M. J. Vilcheck, A. E. Reed, and H. R. Burris, “Multiple methods for measuring atmospheric turbulence,” Proc. SPIE 4821, 300–309 (2002).
    [CrossRef]
  3. H. T. Eyyuboglu and Y. Baykal, “Analysis of laser multimode content on the angle-of-arrival fluctuations in free-space optics access systems,” Opt. Eng. 44(5), 056002 (2005).
    [CrossRef]
  4. E. Masciadri, J. Vernin, and P. Bougeault, “3D mapping of optical turbulence using an atmospheric numerical model. I. A useful tool for the ground-based astronomy,” Astron. Astrophys. Suppl. Ser. 137(1), 185–202 (1999).
    [CrossRef]
  5. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (trans. for NOAA by Israel Program for Scientific Translations, Jerusalem, 1971).
  6. A. D. Wheelon, Electromagnetic Scintillation. I. Geometrical Optics (Cambridge U. Press, 2001).
  7. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, Bellingham, 2005).
  8. D. H. Tofsted, “Outer-scale effects on beam-wander and angle-of-arrival variances,” Appl. Opt. 31(27), 5865–5870 (1992).
    [CrossRef] [PubMed]
  9. H. T. Eyyuboğlu and Y. Baykal, “Angle-of-arrival fluctuations for general-type beams,” Opt. Eng. 46(9), 096001 (2007).
    [CrossRef]
  10. R. Conan, J. Borgnino, A. Ziad, and F. Martin, “Analytical solution for the covariance and for the decorrelation time of the angle of arrival of a wave front corrugated by atmospheric turbulence,” J. Opt. Soc. Am. A 17(10), 1807–1818 (2000).
    [CrossRef]
  11. Y. Cheon and A. Muschinski, “Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence,” J. Opt. Soc. Am. A 24(2), 415–422 (2007).
    [CrossRef]
  12. 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]
  13. 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]
  14. 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, 63040U-12 (2006).
    [CrossRef]
  15. 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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
    [CrossRef]
  16. A. S. Gurvich and M. S. Belen’kii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12(11), 2517–2522 (1995).
    [CrossRef]
  17. M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20(12), 1359–1361 (1995).
    [CrossRef] [PubMed]
  18. 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, 65510E-12 (2007).
    [CrossRef]
  19. W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
    [CrossRef]
  20. L. Tan, W. Du, and J. Ma, “Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence,” J. Russ. Laser Res. 30(6), 552–559 (2009).
    [CrossRef]
  21. L. Y. Cui, B. D. Xue, X. G. Cao, J. K. Dong, and J. N. Wang, “Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(20), 21269–21283 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-20-21269 .
    [CrossRef] [PubMed]
  22. C. Ho, and A. Wheelon, “Power Spectrum of Atmospheric Scintillation for the Deep Space Network Goldstone Ka-band Downlink,” Jet Propulsion Laboratory, California (2004). http://ipnpr.jpl.nasa.gov/progress_report/42-158/158F.pdf
  23. W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(6), 5763–5775 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-6-5763 .
    [CrossRef] [PubMed]
  24. L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1998).

2010 (2)

2009 (2)

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

L. Tan, W. Du, and J. Ma, “Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence,” J. Russ. Laser Res. 30(6), 552–559 (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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[CrossRef]

2007 (3)

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, 65510E-12 (2007).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Angle-of-arrival fluctuations for general-type beams,” Opt. Eng. 46(9), 096001 (2007).
[CrossRef]

Y. Cheon and A. Muschinski, “Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence,” J. Opt. Soc. Am. A 24(2), 415–422 (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, 63040U-12 (2006).
[CrossRef]

2005 (1)

H. T. Eyyuboglu and Y. Baykal, “Analysis of laser multimode content on the angle-of-arrival fluctuations in free-space optics access systems,” Opt. Eng. 44(5), 056002 (2005).
[CrossRef]

2002 (1)

M. J. Vilcheck, A. E. Reed, and H. R. Burris, “Multiple methods for measuring atmospheric turbulence,” Proc. SPIE 4821, 300–309 (2002).
[CrossRef]

2000 (1)

1999 (1)

E. Masciadri, J. Vernin, and P. Bougeault, “3D mapping of optical turbulence using an atmospheric numerical model. I. A useful tool for the ground-based astronomy,” Astron. Astrophys. Suppl. Ser. 137(1), 185–202 (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]

1995 (2)

1994 (1)

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 (1)

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, 65510E-12 (2007).
[CrossRef]

Baykal, Y.

H. T. Eyyuboğlu and Y. Baykal, “Angle-of-arrival fluctuations for general-type beams,” Opt. Eng. 46(9), 096001 (2007).
[CrossRef]

H. T. Eyyuboglu and Y. Baykal, “Analysis of laser multimode content on the angle-of-arrival fluctuations in free-space optics access systems,” Opt. Eng. 44(5), 056002 (2005).
[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, 63040U-12 (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]

A. S. Gurvich and M. S. Belen’kii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12(11), 2517–2522 (1995).
[CrossRef]

M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20(12), 1359–1361 (1995).
[CrossRef] [PubMed]

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]

Borgnino, J.

Bougeault, P.

E. Masciadri, J. Vernin, and P. Bougeault, “3D mapping of optical turbulence using an atmospheric numerical model. I. A useful tool for the ground-based astronomy,” Astron. Astrophys. Suppl. Ser. 137(1), 185–202 (1999).
[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]

Burris, H. R.

M. J. Vilcheck, A. E. Reed, and H. R. Burris, “Multiple methods for measuring atmospheric turbulence,” Proc. SPIE 4821, 300–309 (2002).
[CrossRef]

Cao, X. G.

Cheon, Y.

Conan, R.

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, 63040U-12 (2006).
[CrossRef]

Cui, L. Y.

Dong, J. K.

Du, W.

W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(6), 5763–5775 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-6-5763 .
[CrossRef] [PubMed]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

L. Tan, W. Du, and J. Ma, “Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence,” J. Russ. Laser Res. 30(6), 552–559 (2009).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu and Y. Baykal, “Angle-of-arrival fluctuations for general-type beams,” Opt. Eng. 46(9), 096001 (2007).
[CrossRef]

H. T. Eyyuboglu and Y. Baykal, “Analysis of laser multimode content on the angle-of-arrival fluctuations in free-space optics access systems,” Opt. Eng. 44(5), 056002 (2005).
[CrossRef]

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, 65510E-12 (2007).
[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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[CrossRef]

Gurvich, A. S.

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, 63040U-12 (2006).
[CrossRef]

Jiang, Y.

W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(6), 5763–5775 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-6-5763 .
[CrossRef] [PubMed]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (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]

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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[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 trubulence,” Atmos. Res. 88(1), 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]

Ma, J.

W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(6), 5763–5775 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-6-5763 .
[CrossRef] [PubMed]

L. Tan, W. Du, and J. Ma, “Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence,” J. Russ. Laser Res. 30(6), 552–559 (2009).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

Martin, F.

Masciadri, E.

E. Masciadri, J. Vernin, and P. Bougeault, “3D mapping of optical turbulence using an atmospheric numerical model. I. A useful tool for the ground-based astronomy,” Astron. Astrophys. Suppl. Ser. 137(1), 185–202 (1999).
[CrossRef]

Muschinski, A.

Phillips, R. L.

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, 65510E-12 (2007).
[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]

Reed, A. E.

M. J. Vilcheck, A. E. Reed, and H. R. Burris, “Multiple methods for measuring atmospheric turbulence,” Proc. SPIE 4821, 300–309 (2002).
[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, 63040U-12 (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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[CrossRef]

Tan, L.

W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(6), 5763–5775 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-6-5763 .
[CrossRef] [PubMed]

L. Tan, W. Du, and J. Ma, “Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence,” J. Russ. Laser Res. 30(6), 552–559 (2009).
[CrossRef]

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

Tofsted, D. H.

Toselli, I.

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, 65510E-12 (2007).
[CrossRef]

Vernin, J.

E. Masciadri, J. Vernin, and P. Bougeault, “3D mapping of optical turbulence using an atmospheric numerical model. I. A useful tool for the ground-based astronomy,” Astron. Astrophys. Suppl. Ser. 137(1), 185–202 (1999).
[CrossRef]

Vilcheck, M. J.

M. J. Vilcheck, A. E. Reed, and H. R. Burris, “Multiple methods for measuring atmospheric turbulence,” Proc. SPIE 4821, 300–309 (2002).
[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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[CrossRef]

Wang, J. N.

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]

Xie, W.

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

Xue, B. D.

Yu, S.

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

Ziad, A.

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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. Suppl. Ser. (1)

E. Masciadri, J. Vernin, and P. Bougeault, “3D mapping of optical turbulence using an atmospheric numerical model. I. A useful tool for the ground-based astronomy,” Astron. Astrophys. Suppl. Ser. 137(1), 185–202 (1999).
[CrossRef]

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 trubulence,” Atmos. Res. 88(1), 66–77 (2008).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Russ. Laser Res. (1)

L. Tan, W. Du, and J. Ma, “Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence,” J. Russ. Laser Res. 30(6), 552–559 (2009).
[CrossRef]

Opt. Commun. (1)

W. Du, S. Yu, L. Tan, J. Ma, Y. Jiang, and W. Xie, “Angle-of-arrival fluctuations for wave propagation through non-Kolmolgorov turbulence,” Opt. Commun. 282(5), 705–708 (2009).
[CrossRef]

Opt. Eng. (2)

H. T. Eyyuboglu and Y. Baykal, “Analysis of laser multimode content on the angle-of-arrival fluctuations in free-space optics access systems,” Opt. Eng. 44(5), 056002 (2005).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Angle-of-arrival fluctuations for general-type beams,” Opt. Eng. 46(9), 096001 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (5)

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, 65510E-12 (2007).
[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, 63040U-12 (2006).
[CrossRef]

M. J. Vilcheck, A. E. Reed, and H. R. Burris, “Multiple methods for measuring atmospheric turbulence,” Proc. SPIE 4821, 300–309 (2002).
[CrossRef]

Other (6)

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves in Random and Complex Media 2, 179–201 (1992). http://dx.doi.org/10.1088/0959-7174/2/3/001 .

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (trans. for NOAA by Israel Program for Scientific Translations, Jerusalem, 1971).

A. D. Wheelon, Electromagnetic Scintillation. I. Geometrical Optics (Cambridge U. Press, 2001).

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

L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1998).

C. Ho, and A. Wheelon, “Power Spectrum of Atmospheric Scintillation for the Deep Space Network Goldstone Ka-band Downlink,” Jet Propulsion Laboratory, California (2004). http://ipnpr.jpl.nasa.gov/progress_report/42-158/158F.pdf

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Figures (5)

Fig. 1
Fig. 1

β ( α ) as a function of α.

Fig. 2
Fig. 2

Variance of AOA fluctuations as a function of α with different wavelength values. (a): plane wave. (b): spherical wave.

Fig. 3
Fig. 3

Variance of AOA fluctuations as a function of α with different inner scale values.(a): plane wave. (b): spherical wave.

Fig. 4
Fig. 4

Variance of AOA fluctuations as a function of α with different outer scale values. (a): plane wave. (b): spherical wave.

Fig. 5
Fig. 5

Variance of AOA fluctuations as a function of α with different Dvalues. (a): plane wave. (b): spherical wave.

Equations (29)

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

Φ n ( κ , α , l 0 , L 0 ) = A ( α ) C n 2 κ α f ( k , l 0 , L 0 , α ) ( 0 κ < , 3 < α < 5 ) ,
f ( κ , l 0 , L 0 , α ) = [ 1 exp ( κ 2 / κ 0 2 ) ] exp ( κ 2 / κ l 2 ) .
A ( α ) = Γ ( α 1 ) 4 π 2 sin [ ( α 3 ) π 2 ] , c ( α ) = { π A ( α ) [ Γ ( α 2 + 3 2 ) ( 3 α 3 ) } 1 α 5 .
Φ n ( κ , α ) = A ( α ) C n 2 κ α ( 0 κ < , 3 < α < 5 ) .
σ 2 = π 2 L 0 d κ 0 1 d ξ κ 3 Φ n ( κ ) h ( κ , ξ ) ,
h p l ( κ ) = [ 1 + k κ 2 L sin ( κ 2 L k ) ] A ( a κ ) ,
h s p ( κ ) = [ 1 + cos ( κ 2 ξ ( 1 ξ ) L k ) ] ξ 2 A ( a κ ξ ) ,
A ( x ) = [ 2 J 1 ( x ) x ] 2 ,
A ( x ) exp [ ( β x ) 2 ] .
β ( α ) = 1 2 { Γ ( α 1 ) [ Γ ( α / 2 ) ] 2 + Γ ( 1 + α / 2 ) } 1 / ( α 4 ) , ( 3 < α < 4 ) .
σ ( p l ) 2 = π 2 L 0 d κ 0 1 d ξ κ 3 Φ n ( κ ) [ 1 + k L κ 2 sin ( L κ 2 k ) ] exp [ β 2 D 2 κ 2 4 ] ,
σ ( p l ) 2 ( α , λ , D , l 0 , L 0 ) = π 2 L 0 d κ 0 1 d ξ κ 3 Φ n ( κ , α , l 0 , L 0 ) [ 1 + k L κ 2 sin ( L κ 2 k ) ] exp [ β 2 D 2 κ 2 4 ] ,
f ( κ , l 0 , L 0 , α ) = f 1 ( κ , l 0 , L 0 , α ) + f 2 ( κ , l 0 , L 0 , α ) , f 1 ( κ , l 0 , L 0 , α ) = exp ( κ 2 / k l 2 ) , f 2 ( κ , l 0 , L 0 , α ) = exp [ κ 2 ( 1 / k 0 2 + 1 / k l 2 ) ] .
Γ ( x ) = 0 κ x 1 e κ d κ ,
0 κ μ 1 exp ( a κ ) sin ( b κ ) d κ = Γ ( μ ) ( a 2 + b 2 ) μ / 2 sin [ μ tan 1 ( b a ) ] ,
σ ( p l ) 2 ( α , λ , D , l 0 , L 0 ) = π 2 A ( α ) C n 2 L [ g 1 ( A 11 , B 11 , C 11 ) g 1 ( A 21 , B 21 , C 21 ) ] ,
g 1 ( A i j , B i j , C i j ) = 1 2 Γ ( A i j + 1 2 ) B i j A i j + 1 2 + 1 2 C i j Γ ( A i j 1 2 ) ( B i j 2 + C i j 2 ) A i j 1 4 sin [ A i j 1 2 tan 1 ( C i j B i j ) ] ,
σ ( s p ) 2 = π 2 L 0 d κ 0 1 d ξ κ 3 Φ n ( κ ) [ 1 + cos ( κ 2 ξ ( 1 ξ ) L k ) ] ξ 2 exp [ β 2 D 2 κ 2 ξ 2 4 ] ,
σ ( s p ) 2 ( α , λ , D , l 0 , L 0 ) = π 2 L 0 0 1 κ 3 Φ n ( κ , α , l 0 , L 0 ) [ 1 + cos ( κ 2 ξ ( 1 ξ ) L k ) ] ξ 2 exp [ ( β D κ ξ ) 2 4 ] d κ d ξ .
F 2 1 ( A , B ; C ; Z ) = Γ ( C ) Γ ( B ) Γ ( C B ) 0 1 t B 1 ( 1 t ) C B 1 ( 1 t Z ) A d t .
σ s p 2 ( α , λ , D , l 0 , L 0 ) = π 2 A ( α ) C n 2 L [ g 2 ( A 11 , B 11 , C 11 ) g 2 ( A 21 , B 21 , C 21 ) ] .
g 2 ( A i j , B i j , C i j ) = 1 2 Γ ( A i j + 1 2 ) { 1 3 B i j A i j + 1 2 F 2 1 ( A i j + 1 2 , 3 2 ; 5 2 ; b 2 B i j ) + Re { 0 1 ξ 2 [ B i j + b 2 ξ 2 + i C i j ξ ( 1 ξ ) ] A i j + 1 2 d ξ } } .
B 11 = 1 k l 2 , B 21 = 1 k l 2 + 1 k 0 2 , b 2 = β 2 D 2 4 .
Re { 0 1 ξ 2 [ B 11 + b 2 ξ 2 + i C 11 ξ ( 1 ξ ) ] A 11 + 1 2 d ξ } Re { 0 1 ξ 2 [ b 2 ξ 2 + i C 11 ξ ( 1 ξ ) ] A 11 + 1 2 d ξ } = Re [ ( i C 11 ) A 11 + 1 2 2 5 A 11 F 2 1 ( A 11 + 1 2 , 5 A 11 2 ; 7 A 11 2 ; 1 + i b 2 C 11 ) ] ,
Re { 0 1 ξ 2 [ B 21 + b 2 ξ 2 + i C 21 ξ ( 1 ξ ) ] A 21 + 1 2 d ξ } 0 1 ξ 2 [ B 21 + b 2 ξ 2 ] A 21 + 1 2 d ξ = 1 3 B 21 A i j + 1 2 F 2 1 ( A 21 + 1 2 , 3 2 ; 5 2 ; b 2 B 21 ) .
σ s p 2 ( α , λ , D , l 0 , L 0 ) = π 2 A ( α ) C n 2 L [ g 2 ( A 11 , B 11 , C 11 ) g 2 ( A 21 , B 21 , C 21 ) ] ,
g 2 ( A 11 , B 11 , C 11 ) = 1 2 Γ ( A 11 + 1 2 ) { 1 3 B 11 A 11 + 1 2 F 2 1 ( A 11 + 1 2 , 1 2 ; 3 2 ; b 2 B 11 ) Re [ ( i C 11 ) A 11 + 1 2 2 5 A 11 F 2 1 ( A 11 + 1 2 , 5 A 11 2 ; 7 A 11 2 ; 1 + i b 2 C 11 ) ] } ,
g 2 ( A 21 , B 21 , C 21 ) = 1 3 Γ ( A 21 + 1 2 ) B 21 A 21 + 1 2 F 2 1 ( A 21 + 1 2 , 1 2 ; 3 2 ; b 2 B 21 ) .
C n 2 = 1 × 10 14 m 3 α   ,   L = 1000 m

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