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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8433–8443

Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence

Bindang Xue, Linyan Cui, Wenfang Xue, Xiangzhi Bai, and Fugen Zhou  »View Author Affiliations

Optics Express, Vol. 19, Issue 9, pp. 8433-8443 (2011)

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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.

© 2011 OSA

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: January 14, 2011
Revised Manuscript: March 27, 2011
Manuscript Accepted: April 2, 2011
Published: April 18, 2011

Bindang Xue, Linyan Cui, Wenfang Xue, Xiangzhi Bai, and Fugen Zhou, "Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence," Opt. Express 19, 8433-8443 (2011)

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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).

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