Abstract

A new generalized modified atmospheric spectral model is derived theoretically for wave propagating through non-Kolmogorov turbulence, which has been reported recently by increasing experimental evidence and theoretical investigation. The generalized, modified atmospheric spectrum considers finite turbulence inner and outer scales and has a spectral power law value in the range of 3 to 5 instead of the standard power law value of 11/3. When the inner scale and outer scale are set to zero and infinity, respectively, this spectral model is reduced to the classical non-Kolmogorov spectrum.

© 2011 Optical Society of America

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  1. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1971).
  2. 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]
  3. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47, 2414–2429(2008).
    [CrossRef] [PubMed]
  4. K. Kazaura, K. Omae, T. Suzuki, and M. Matsumoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14, 4958–4968 (2006).
    [CrossRef] [PubMed]
  5. V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation” (translated for NOAA by Israel Program for Scientific Translations, Jerusalem, 1971).
  6. R. J. Hill and S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).
    [CrossRef]
  7. J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
    [CrossRef]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996). http://adsabs.harvard.edu//abs/1996JETP...83..192M.
  14. 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]
  15. E. Golbraikh and N. S. Kopeika, “Behavior of structure function of refraction coefficients in different turbulent fields,” Appl. Opt. 43, 6151–6156 (2004).
    [CrossRef] [PubMed]
  16. A. Zilberman and N. S. Kopeika, “Slant-path generalized atmospheric MTF,” in Proceedings of IEEE 25th Convention of Electrical and Electronics Engineers (IEEE, 2008), pp. 217–221.
    [CrossRef]
  17. N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
    [CrossRef]
  18. W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express 18, 5763–5775 (2010).
    [CrossRef] [PubMed]
  19. 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 (2007).
    [CrossRef]
  20. 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, 21269–21283 (2010).
    [CrossRef] [PubMed]
  21. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [CrossRef]
  22. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Freespace optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47, 026003(2008).
    [CrossRef]
  23. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47, 6385–6391 (2008).
    [CrossRef] [PubMed]
  24. L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE, 1998).

2010 (3)

2008 (5)

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

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47, 6385–6391 (2008).
[CrossRef] [PubMed]

A. Zilberman and N. S. Kopeika, “Slant-path generalized atmospheric MTF,” in Proceedings of IEEE 25th Convention of Electrical and Electronics Engineers (IEEE, 2008), pp. 217–221.
[CrossRef]

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]

J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47, 2414–2429(2008).
[CrossRef] [PubMed]

2007 (1)

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 (2007).
[CrossRef]

2006 (2)

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]

K. Kazaura, K. Omae, T. Suzuki, and M. Matsumoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14, 4958–4968 (2006).
[CrossRef] [PubMed]

2004 (1)

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]

1998 (1)

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

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 (2)

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996). http://adsabs.harvard.edu//abs/1996JETP...83..192M.

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 (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)

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]

1990 (1)

J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
[CrossRef]

1978 (1)

1971 (2)

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1971).

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

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Freespace 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, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (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, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE, 1998).

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]

Anguita, J. A.

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]

Cao, X.-G.

Chkhetiani, O. G.

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996). http://adsabs.harvard.edu//abs/1996JETP...83..192M.

Churnside, J. H.

J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
[CrossRef]

Clifford, S. F.

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]

Cui, L.-Y.

Dong, J.-K.

Du, W.

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, “Freespace 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, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (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.

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47, 6385–6391 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Hill, R. J.

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]

Jiang, Y.

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]

Kazaura, K.

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.

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

A. Zilberman and N. S. Kopeika, “Slant-path generalized atmospheric MTF,” in Proceedings of IEEE 25th Convention of Electrical and Electronics Engineers (IEEE, 2008), pp. 217–221.
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47, 6385–6391 (2008).
[CrossRef] [PubMed]

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] [PubMed]

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]

Lumley, J. L.

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1971).

Ma, J.

Matsumoto, M.

Moiseev, S. S.

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996). http://adsabs.harvard.edu//abs/1996JETP...83..192M.

Neifeld, M. A.

Omae, K.

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Freespace 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, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (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]

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]

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]

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]

Suzuki, T.

Tan, L.

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).

Tennekes, H.

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1971).

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Freespace 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, “Angle of arrival fluctuations for free space laser beam propagation through non-Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[CrossRef]

Vasic, B. V.

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]

Wang, J.-N.

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]

Xue, B.-D.

Zilberman, A.

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[CrossRef]

A. Zilberman and N. S. Kopeika, “Slant-path generalized atmospheric MTF,” in Proceedings of IEEE 25th Convention of Electrical and Electronics Engineers (IEEE, 2008), pp. 217–221.
[CrossRef]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47, 6385–6391 (2008).
[CrossRef] [PubMed]

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. (3)

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]

J. Exp. Theor. Phys. (1)

S. S. Moiseev and O. G. Chkhetiani, “Helical scaling in turbulence,” J. Exp. Theor. Phys. 83, 192–198 (1996). http://adsabs.harvard.edu//abs/1996JETP...83..192M.

J. Mod. Opt. (2)

J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
[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]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

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

Opt. Express (3)

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 (7)

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 (2007).
[CrossRef]

N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE 7588, 758808 (2010).
[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]

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]

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

Other (4)

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

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1971).

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

A. Zilberman and N. S. Kopeika, “Slant-path generalized atmospheric MTF,” in Proceedings of IEEE 25th Convention of Electrical and Electronics Engineers (IEEE, 2008), pp. 217–221.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

A ( α ) and c ( α ) as functions of α. (a)  A ( α ) ; (b)  c ( α ) .

Fig. 2
Fig. 2

Scaled generalized modified atmospheric spectrum as a function of spatial wave number with a logarithmic scale ( L 0 = 2 m , l 0 = 1 mm ).

Tables (1)

Tables Icon

Table 1 List of Some Atmospheric Turbulence Spectra a

Equations (25)

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

Φ n ( κ ) = 0.033 C n 2 κ 11 / 3 [ 1 exp ( κ 2 κ 0 2 ) ] [ 1 + a 1 · ( κ κ l ) b 1 · ( κ κ l ) 7 / 6 ] exp ( κ 2 κ l 2 ) ( 0 k < ) ,
Φ n ( κ , α ) = A ( α ) · C ^ n 2 · F ( k , l 0 , L 0 , α ) ( 0 κ < , 3 < α < 5 ) ,
Φ n ( κ , α , l 0 , L 0 ) = A ^ ( α ) · C ^ n 2 · F ( k , l 0 , L 0 , α ) = 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 ) ] [ 1 + a 1 · ( κ κ l ) b 1 · ( κ κ l ) 7 / 6 ] exp ( κ 2 κ l 2 ) ,
D n ( R ) = 8 π 0 κ 2 · Φ n ( k ) · ( 1 sin κ R κ R ) d κ .
D n ( R , α ) = 8 π 0 κ 2 · Φ n ( k , α ) · ( 1 sin κ R κ R ) d κ .
D n ( R , α ) = 8 π 0 κ 2 α · A ^ ( α ) · C ^ n 2 · [ 1 + a 1 · ( κ κ l ) b 1 · ( κ κ l ) 7 / 6 ] exp ( κ 2 κ l 2 ) · ( 1 sin κ R κ R ) d κ
1 sin κ R κ R = n = 1 ( 1 ) n 1 ( 2 n + 1 ) ! κ 2 n R 2 n ,
D n 1 ( R , α ) = 8 π · A ^ ( α ) · C ^ n 2 · n = 1 ( 1 ) n 1 ( 2 n + 1 ) ! R 2 n 0 κ 2 α + 2 n [ 1 + a 1 · ( κ κ l ) b 1 · ( κ κ l ) 7 / 6 ] exp ( κ 2 κ l 2 ) d κ .
Γ ( x ) = 0 κ x 1 · e κ d κ ( κ > 0 , x > 0 ) , F 1 1 ( a ; b ; z ) = n = 0 ( a ) n · z n ( b ) n · n ! ,
( a ) n = Γ ( a + n ) Γ ( a ) = a ( a + 1 ) ( a + n 1 ) .
D n ( R , α ) = 4 π A ^ ( α ) C ^ n 2 κ l 3 α { Γ ( α 2 + 3 2 ) [ 1 F 1 1 ( α 2 + 3 2 ; 3 2 ; R 2 κ l 2 4 ) ] + a 1 · Γ ( α 2 + 2 ) [ 1 F 1 1 ( α 2 + 2 ; 3 2 ; R 2 κ l 2 4 ) ] b 1 · Γ ( α 2 + 25 12 ) [ 1 F 1 1 ( α 2 + 25 12 ; 3 2 ; R 2 κ l 2 4 ) ] } .
D n ( R , α ) = { C ^ n 2 l 0 α 5 R 2 , 0 R l 0 C ^ n 2 R α 3 , l 0 R L 0 .
F 1 1 ( a ; b ; x ) Γ ( b ) Γ ( b a ) x a ( x 1 ) .
D n ( R , α ) 4 π A ^ ( α ) C ^ n 2 Γ ( α 2 + 3 2 ) Γ ( 3 / 2 ) Γ ( α / 2 ) ( 1 2 ) α 3 ( R ) α 3 ( l 0 R L 0 ) .
Γ ( α + 1 ) = α Γ ( α ) , Γ ( 1 α ) Γ ( α ) = π sin ( π α ) , Γ ( α ) Γ ( α + 1 / 2 ) = 2 1 2 α π Γ ( 2 α ) .
A ^ ( α ) = Γ ( α 1 ) 4 π 2 sin [ ( α 3 ) π 2 ] ,
F 1 1 ( a ; b ; x ) n = 0 1 ( a ) n · z n ( b ) n · n ! = 1 + a b x ( x 1 ) .
D n ( R , α ) π A ^ ( α ) C ^ n 2 κ l 5 α R 2 · [ Γ ( α 2 + 3 2 ) ( 3 α 3 ) + a 1 · Γ ( α 2 + 2 ) ( 4 α 3 ) b 1 · Γ ( α 2 + 25 12 ) ( 25 6 α 18 ) ] ( 0 R l 0 ) .
c ( α ) = { π A ^ ( α ) [ Γ ( α 2 + 3 2 ) ( 3 α 3 ) + a 1 · Γ ( α 2 + 2 ) ( 4 α 3 ) b 1 · Γ ( α 2 + 25 12 ) ( 25 6 α 18 ) ] } 1 α 5 .
Φ n ( κ , α , l 0 , L 0 ) = A ^ ( α ) · C ^ n 2 · κ α ( 0 κ < , 3 < α < 5 ) ,
Φ n ( κ , α , l 0 , L 0 ) Φ n ( κ , α , l 0 , L 0 ) = f ( κ , l 0 , L 0 , α ) ,
Φ n ( κ ) = 0.033 C n 2 κ 11 / 3 { exp ( 1.29 κ 2 l 0 2 ) + 1.45 exp [ 0.97 ( ln κ l 0 0.452 ) 2 ] } ( 0 k < ) ,
d d κ { κ 14 / 3 [ ( 13.9 κ η ) 3.8 + 1 ] 0.175 d d κ Φ n ( κ ) } = 14.1 κ 4 η 4 / 3 Φ n ( κ ) .
d d κ H ( κ ) d d κ Φ T ( κ ) = 2 D κ 4 Φ T ( κ ) ,

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