Abstract

Features of optical wave fluctuations while propagating through a randomly inhomogeneous turbulent medium with a finite outer scale are considered, including conditions when areas with dominating influence of one large-scale coherent structure are observed in the atmosphere, for which the spectrum of atmospheric turbulence can differ significantly from the Kolmogorov model spectrum. Using an approximate model of the spectrum for coherent turbulence, described earlier in our works, the variance of jitter of an optical image is calculated (under the applicability condition for the smooth perturbation method). The comparison of these equations with known similar equations for Kolmogorov turbulence has shown that the variance of fluctuations is significantly weaker in coherent turbulence than in the Kolmogorov theory under similar conditions. This means that phase fluctuations of optical radiation decrease significantly in coherent turbulence. The importance of this conclusion is noted for interpretation of the results of optical sounding of atmospheric turbulence.

© 2014 Optical Society of America

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  1. V. P. Lukin and V. V. Pokasov, “Phase fluctuations of an optical wave which propagates in a turbulent atmosphere,” Radiophys. Quantum Electron. 16, 1335–1337 (1973).
    [Crossref]
  2. G. M. B. Bouricius and S. F. Clifford, “Experimental study of atmospheric ally induced phase fluctuations in an optical signal,” J. Opt. Soc. Am. 60, 1484–1489 (1970).
    [Crossref]
  3. A. Consortini, L. Ronchi, and E. Moroder, “Role of the outer scale of turbulence in atmospheric degradation of optical images,” J. Opt. Soc. Am. 63, 1246–1248 (1973).
    [Crossref]
  4. V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).
  5. V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
    [Crossref]
  6. A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Nauka, 1967), Vol. 1.
  7. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).
  8. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.
  9. E. M. Dewan and N. Grossbard, “The inertial range “outer scale” and optical turbulence,” Environ. Fluid Mech. 7, 383–396 (2007).
  10. V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).
  11. A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in Turbulent Atmosphere (Nauka, 1976) [in Russian].
  12. A. I. Kon, V. L. Mironov, and V. V. Nosov, “Fluctuations of the centers of gravity of light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 17, 1147–1155 (1974).
    [Crossref]
  13. V. L. Mironov, V. V. Nosov, and B. N. Chen, “Quivering of optical images of laser sources in a turbulent atmosphere,” Radiophys. Quantum Electron. 23, 319–325 (1980).
    [Crossref]
  14. V. P. Lukin, “Intercomparison of models of the atmospheric turbulence spectrum,” Atmos. Ocean. Opt. 6, 628–631 (1993).
  15. V. V. Voitsekhovich, “Optical scale of turbulence: comparison of different models,” J. Opt. Soc. Am. A 12, 1346–1353 (1995).
    [Crossref]
  16. J. Borgnino, “Estimation of the spatial coherence outer scale relevant to long baseline interferometry,” Appl. Opt. 29, 1863–1865 (1990).
    [Crossref]
  17. V. P. Lukin, B. V. Fortes, and E. V. Nosov, “The efficient outer scale of atmospheric turbulence,” Atmos. Oceanic Opt. 10, 100–106 (1997).
  18. S. P. Darchiya, V. I. Ivanov, and P. G. Kovadlo, “Results of seeing researches at SibIZMIR SB AS USSR in 1971–1976,” in New Equipment in Astronomy (Nauka, Leningrad, 1979), p. 154.
  19. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).
  20. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.
  21. A. Ziad, M. Schock, G. A. Chanan, M. Troy, R. Dekany, B. F. Lane, J. Borgnino, and F. Martin, “Comparison of measurements of the outer scale of turbulence by three different techniques,” Appl. Opt. 43, 2316–2324 (2004).
    [Crossref]
  22. V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

2011 (1)

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

2010 (1)

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

2008 (1)

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

2007 (1)

E. M. Dewan and N. Grossbard, “The inertial range “outer scale” and optical turbulence,” Environ. Fluid Mech. 7, 383–396 (2007).

2005 (1)

V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).

2004 (1)

1997 (1)

V. P. Lukin, B. V. Fortes, and E. V. Nosov, “The efficient outer scale of atmospheric turbulence,” Atmos. Oceanic Opt. 10, 100–106 (1997).

1995 (1)

1993 (1)

V. P. Lukin, “Intercomparison of models of the atmospheric turbulence spectrum,” Atmos. Ocean. Opt. 6, 628–631 (1993).

1990 (1)

1981 (1)

1980 (1)

V. L. Mironov, V. V. Nosov, and B. N. Chen, “Quivering of optical images of laser sources in a turbulent atmosphere,” Radiophys. Quantum Electron. 23, 319–325 (1980).
[Crossref]

1977 (1)

V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).

1974 (1)

A. I. Kon, V. L. Mironov, and V. V. Nosov, “Fluctuations of the centers of gravity of light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 17, 1147–1155 (1974).
[Crossref]

1973 (2)

A. Consortini, L. Ronchi, and E. Moroder, “Role of the outer scale of turbulence in atmospheric degradation of optical images,” J. Opt. Soc. Am. 63, 1246–1248 (1973).
[Crossref]

V. P. Lukin and V. V. Pokasov, “Phase fluctuations of an optical wave which propagates in a turbulent atmosphere,” Radiophys. Quantum Electron. 16, 1335–1337 (1973).
[Crossref]

1970 (1)

Borgnino, J.

Bouricius, G. M. B.

Chanan, G. A.

Chen, B. N.

V. L. Mironov, V. V. Nosov, and B. N. Chen, “Quivering of optical images of laser sources in a turbulent atmosphere,” Radiophys. Quantum Electron. 23, 319–325 (1980).
[Crossref]

Clifford, S. F.

Consortini, A.

Darchiya, S. P.

S. P. Darchiya, V. I. Ivanov, and P. G. Kovadlo, “Results of seeing researches at SibIZMIR SB AS USSR in 1971–1976,” in New Equipment in Astronomy (Nauka, Leningrad, 1979), p. 154.

Dekany, R.

Dewan, E. M.

E. M. Dewan and N. Grossbard, “The inertial range “outer scale” and optical turbulence,” Environ. Fluid Mech. 7, 383–396 (2007).

Emaleev, O. N.

V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).

Fortes, B. V.

V. P. Lukin, B. V. Fortes, and E. V. Nosov, “The efficient outer scale of atmospheric turbulence,” Atmos. Oceanic Opt. 10, 100–106 (1997).

Grigor’ev, V. M.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

Grossbard, N.

E. M. Dewan and N. Grossbard, “The inertial range “outer scale” and optical turbulence,” Environ. Fluid Mech. 7, 383–396 (2007).

Gurvich, A. S.

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in Turbulent Atmosphere (Nauka, 1976) [in Russian].

Ivanov, V. I.

S. P. Darchiya, V. I. Ivanov, and P. G. Kovadlo, “Results of seeing researches at SibIZMIR SB AS USSR in 1971–1976,” in New Equipment in Astronomy (Nauka, Leningrad, 1979), p. 154.

Khmelevtsov, S. S.

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in Turbulent Atmosphere (Nauka, 1976) [in Russian].

Kon, A. I.

A. I. Kon, V. L. Mironov, and V. V. Nosov, “Fluctuations of the centers of gravity of light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 17, 1147–1155 (1974).
[Crossref]

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in Turbulent Atmosphere (Nauka, 1976) [in Russian].

Kovadlo, P. G.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

S. P. Darchiya, V. I. Ivanov, and P. G. Kovadlo, “Results of seeing researches at SibIZMIR SB AS USSR in 1971–1976,” in New Equipment in Astronomy (Nauka, Leningrad, 1979), p. 154.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

Lane, B. F.

Lukin, V. P.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).

V. P. Lukin, B. V. Fortes, and E. V. Nosov, “The efficient outer scale of atmospheric turbulence,” Atmos. Oceanic Opt. 10, 100–106 (1997).

V. P. Lukin, “Intercomparison of models of the atmospheric turbulence spectrum,” Atmos. Ocean. Opt. 6, 628–631 (1993).

V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
[Crossref]

V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).

V. P. Lukin and V. V. Pokasov, “Phase fluctuations of an optical wave which propagates in a turbulent atmosphere,” Radiophys. Quantum Electron. 16, 1335–1337 (1973).
[Crossref]

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

Martin, F.

Mironov, V. L.

V. L. Mironov, V. V. Nosov, and B. N. Chen, “Quivering of optical images of laser sources in a turbulent atmosphere,” Radiophys. Quantum Electron. 23, 319–325 (1980).
[Crossref]

A. I. Kon, V. L. Mironov, and V. V. Nosov, “Fluctuations of the centers of gravity of light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 17, 1147–1155 (1974).
[Crossref]

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in Turbulent Atmosphere (Nauka, 1976) [in Russian].

Monin, A. S.

A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Nauka, 1967), Vol. 1.

Moroder, E.

Nosov, E. V.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).

V. P. Lukin, B. V. Fortes, and E. V. Nosov, “The efficient outer scale of atmospheric turbulence,” Atmos. Oceanic Opt. 10, 100–106 (1997).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

Nosov, V. V.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).

V. L. Mironov, V. V. Nosov, and B. N. Chen, “Quivering of optical images of laser sources in a turbulent atmosphere,” Radiophys. Quantum Electron. 23, 319–325 (1980).
[Crossref]

A. I. Kon, V. L. Mironov, and V. V. Nosov, “Fluctuations of the centers of gravity of light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 17, 1147–1155 (1974).
[Crossref]

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

Pokasov, V. V.

V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
[Crossref]

V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).

V. P. Lukin and V. V. Pokasov, “Phase fluctuations of an optical wave which propagates in a turbulent atmosphere,” Radiophys. Quantum Electron. 16, 1335–1337 (1973).
[Crossref]

Ronchi, L.

Schock, M.

Time, N. S.

V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).

Torgaev, A. V.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

Troy, M.

Turovtseva, L. S.

V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).

Voitsekhovich, V. V.

Yaglom, A. M.

A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Nauka, 1967), Vol. 1.

Ziad, A.

Appl. Opt. (3)

Atmos. Ocean. Opt. (3)

V. P. Lukin, “Intercomparison of models of the atmospheric turbulence spectrum,” Atmos. Ocean. Opt. 6, 628–631 (1993).

V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18, 756–772 (2005).

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Astroclimate of specialized rooms at the large solar vacuum telescope. Part 2,” Atmos. Ocean. Opt. 21, 180–190 (2008).

Atmos. Oceanic Opt. (1)

V. P. Lukin, B. V. Fortes, and E. V. Nosov, “The efficient outer scale of atmospheric turbulence,” Atmos. Oceanic Opt. 10, 100–106 (1997).

Environ. Fluid Mech. (1)

E. M. Dewan and N. Grossbard, “The inertial range “outer scale” and optical turbulence,” Environ. Fluid Mech. 7, 383–396 (2007).

Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana (1)

V. P. Lukin, V. V. Pokasov, N. S. Time, and L. S. Turovtseva, “Retrieval of the pulsation spectrum of the refraction index in the atmosphere from optical measurements,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 90–94 (1977).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Optika atmosfery i okeana (1)

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Recomendations for the selection of sites for the ground-based astronomical telescopes,” Optika atmosfery i okeana 23, 1099–1110 (2010).

Radiophys. Quantum Electron. (3)

A. I. Kon, V. L. Mironov, and V. V. Nosov, “Fluctuations of the centers of gravity of light beams in a turbulent atmosphere,” Radiophys. Quantum Electron. 17, 1147–1155 (1974).
[Crossref]

V. L. Mironov, V. V. Nosov, and B. N. Chen, “Quivering of optical images of laser sources in a turbulent atmosphere,” Radiophys. Quantum Electron. 23, 319–325 (1980).
[Crossref]

V. P. Lukin and V. V. Pokasov, “Phase fluctuations of an optical wave which propagates in a turbulent atmosphere,” Radiophys. Quantum Electron. 16, 1335–1337 (1973).
[Crossref]

Vestn. MSTU “STANKIN” (1)

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent atmospheric turbulence,” Vestn. MSTU “STANKIN” 10, 56–65 (2011).

Other (5)

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Effect of weakening of light fluctuations in coherent turbulence,” in Proceedings of the XVII International Symposium on Atmospheric and Ocean Optics. Atmospheric Physics (Publishing House of Institute of Atmospheric Optics SB RAS, 2011), pp. B117–B120.

V. V. Nosov, V. M. Grigor’ev, P. G. Kovadlo, V. P. Lukin, E. V. Nosov, and A. V. Torgaev, “Coherent structures in the turbulent atmosphere,” in Mathematical Models of Non-Linear Phenomena, Processes and Systems: From Molecular Scale to Planetary Atmosphere, A. Nadykto and L. Uvarova, eds. (Nova Science, 2010), Part 20, pp. 120–152.

A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Nauka, 1967), Vol. 1.

A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in Turbulent Atmosphere (Nauka, 1976) [in Russian].

S. P. Darchiya, V. I. Ivanov, and P. G. Kovadlo, “Results of seeing researches at SibIZMIR SB AS USSR in 1971–1976,” in New Equipment in Astronomy (Nauka, Leningrad, 1979), p. 154.

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Figures (4)

Fig. 1.
Fig. 1.

Kolmogorov turbulence is the result of mixing of different coherent structures. WT, smoothed spectra; DT, structure functions of temperature fluctuations; curve 1, summer daytime measurements in mountains (at a height of 2032 m); curve 2, wind transfer of a frozen spatial pattern of flows inside the BSVT through one point.

Fig. 2.
Fig. 2.

Standard deviation of astronomical image jitter of the solar limb as a function of the diameter of telescope input aperture 2at Sayan Solar observatory measurements.

Fig. 3.
Fig. 3.

Jitter of astronomical images. Comparison of the conventional incoherent theory with the coherent theory and experiments [19,20].

Fig. 4.
Fig. 4.

Process of generation of Kolmogorov turbulence spectrum of four spectra with the outer scales of 60, 30, 15, and 7.5 m.

Equations (26)

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ρFpl=FkS(ρ⃗1)d2ρ1.
S(ρ⃗1)=i0Xdξ1d2n(κ⃗1,Xξ1)κ⃗1exp(iκ⃗1ρ⃗1),
(ρFpl)2=F22d2ρ1d2ρ20Xdξ10Xdξ2(κ⃗1κ⃗2)exp(iκ⃗1ρ⃗1)exp(iκ⃗2ρ⃗2)×d2n(κ⃗1,Xξ1)d2n(κ⃗2,Xξ2).
(ρFpl)2=2π2F20Xdξd2κκ2Φn(κ⃗,ξ)exp(κ2R2/2).
Φn(κ⃗,ξ)=0.033Cn2(ξ)κ11/3{1exp(κ2/κ02)}exp(κ2/κm2).
(ρFpl)2=2π2F20.033Γ(1/6)0XdξCn2(ξ)[R/1321/6κ01/3].
(ρFpl)/F2=(φFpl)23.23R1/30dξCn2(ξ)[1(κ02R2/2)1/6].
(κ0*)1=[0dξCn2(ξ)κ01/3/0dξCn2(ξ)]3.
r0(k20dξCn2(ξ))3/5,
(φFpl)23.23R1/3r05/3k2[121/6(κ0*R)1/3].
Φn(κ⃗,ξ)=0.033Cn2(ξ)(κ2+κ02)11/6exp(κ2/κm2),
0dκκ3exp(κ2R2/2)(κ2+κ02)11/6=12[Γ(16)Γ(116)κ01/3F11(2,76;κ02R2/2)+Γ(16)(R02/2)1/6F11(116,56;κ02R2/2)].
0dκκ3exp(κ2R2/2)(κ2+κ02)11/6Γ(16)25/6R01/3185κ01/3.
Φncoh(κ⃗,ξ)=0.033(Cn2(ξ))coh(κ2+κ02)7/3exp(κ2/κm2).
0dκκ3exp(κ2R2/2)(κ2+κ02)7/3=12[Γ(1/3)Γ(7/3)κ02/3F11(2,2/3;κ02R2/2)+Γ(1/3)(R02/2)1/3F11(7/3,4/3;κ02R2/2)].
(φFpl)2=2π20.0330dξ(Cn2(ξ))coh[Γ(13)Γ(73)κ02/33Γ(23)(R2/2)1/3].
(φFçä)2=2π20.033Γ(13)Γ(73)0dξ(Cn2(ξ))cohκ02/3[13Γ(2/3)(R2/2)1/3]1.460dξ(Cn2(ξ))cohκ02/3[13Γ(2/3)(R2/2)1/3].
0dκκΦnccoh(κ)=0dκκΦn(κ).
0dκκΦn(κ)=0.033Cn22[Γ(5/6)Γ(11/6)κ05/3F11(1,1/6;κ02/κm2)+Γ(5/6)κm5/3F11(11/6,11/6;κ02/κm2)].
0dκκΦn(κ)350.033Cn2(ξ)κ05/3.
0dκκΦncoh(κ)=0.033(N˜n2)coh2[Γ(4/3)Γ(7/3)κ08/3F11(1,1/3;κ02/κm2)+Γ(4/3)κm8/3F11(7/3,7/3;κ02/κm2)].
0dκκΦncoh(κ)380.033(N˜n2)cohκ08/3.
(N˜n2)coh=85κ0N˜n2.
(φFpl)2coh=2π20.0330dξCn2(ξ)[Γ(1/3)Γ(7/3)κ01/33Γ(23)κ0(R2/2)1/3].
(φFçä)2coh=165π20.033Γ(1/3)Γ(7/3)0dξCn2(ξ)κ01/3.
(φFpl)2coh(φFpl)2kolmog(κ0*R)1/3.

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