Abstract

Experimental results are described of measurements of irradiance fluctuations of laser radiation through atmospheric turbulence. Simultaneous measurements of irradiance fluctuations, inner scale, and structure parameter were made in conditions of homogeneous turbulence during a number of summer days, from very early in the morning, before sunrise, until approximately noon. During the measurements the turbulence strength varied continuously, spanning very low as well as intermediate and very high levels. We used the data collected in selected intervals, during which turbulence was stationary, to obtain plots of irradiance variance versus the structure parameter for fixed ranges of values of the inner scale. The results clearly show the effect of the inner scale. For a given value of the structure parameter larger inner scales result in larger values of irradiance variance in the regime of strong scintillation.

© 1993 Optical Society of America

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References

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  1. A. M. Obukhov, “Structure of the temperature field in turbulent flow,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).
  2. V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, 1971)(in Russian); English translation, The Effect of the Turbulent Atmosphere on Wave Propagation (Ketter, Jerusalem, 1971).
  3. R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
    [CrossRef]
  4. G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
    [CrossRef] [PubMed]
  5. E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
    [CrossRef]
  6. R. J. Hill, G. R. Ochs, “Inner-scale dependence of scintillation variances measured in weak scintillation,” J. Opt. Soc. Am. A 9, 1406–1411 (1992).
    [CrossRef]
  7. I. G. Yakushkin, “Asymptotic calculations of intensity fluctuations in a turbulent medium for long paths,” Radiophys. Quantum Electron. 18, 1224–1229 (1975).
    [CrossRef]
  8. I. G. Yakushkin, “Strong intensity fluctuations in the field of a light beam in a turbulent atmosphere,” Radiophys. Quantum Electron. 19, 270–276 (1976).
    [CrossRef]
  9. R. L. Fante, “Inner-scale size effect on the scintillation of light in the turbulent atmosphere,”J. Opt. Soc. Am. 73, 277–279 (1983).
    [CrossRef]
  10. I. G. Yakushkin, “Intensity fluctuations during small-angle scattering of wave fields (review),” Radiophys. Quantum Electron. 28, 365–389 (1985).
    [CrossRef]
  11. R. G. Frehlich, “Intensity covariance of a point source in a random medium with a Kolmogorov spectrum and an inner scale of turbulence,”J. Opt. Soc. Am. 4, 360–366 (1987).
    [CrossRef]
  12. M. J. Beran, A. M. Whitman, “Effect of the turbulence inner scale on scintillation in the atmosphere,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 2–10 (1989).
    [CrossRef]
  13. A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation from a point source,” J. Opt. Soc. Am. A 5, 735–737 (1988).
    [CrossRef]
  14. J. M. Martin, S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990).
    [CrossRef]
  15. R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,”J. Opt. Soc. Am. 68, 892–899 (1978).
    [CrossRef]
  16. R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale, and surface fluxes,” Waves Random Media 2, 179–201 (1992).
    [CrossRef]
  17. J. H. Churnside, R. J. Hill, G. Conforti, A. Consortini, “Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere,” Appl. Opt. 28, 4126–4132 (1989).
    [CrossRef] [PubMed]
  18. G. R. Ochs, W. D. Cartwright, D. D. Russell, “Optical Cn2instrument model II,”NOAA Tech. Memo. ERL WPL-51 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161; order number WPL51:PB 80-209000.)
  19. G. R. Ochs, W. D. Cartwright, “A crosswind measurement module for the model II optical Cn2instrument,”NOAA Tech. Memo. ERL WPL-53 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (A vailable from the National Technical Information Service, 5285 Port Royal Rd., Spring-field, Va. 22161; order number WPL53:PB 80-217607.)
  20. G. R. Ochs, J. K. Holler, J. J. Wilson, “An optical inner-scale meter,” NOAA Tech. Memo. ERL WPL-183 (NOAA Environmental Research Laboratories, Boulder, Colo., 1990). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161.)
  21. R. J. Hill, “Comparison of scintillation methods for measuring the inner scale of turbulence,” Appl. Opt. 27, 2187–2193 (1988).
    [CrossRef] [PubMed]
  22. A. Consortini, G. Conforti, “Detector saturation effect on higher order moments of intensity fluctuations in atmospheric laser propagation measurements,” J. Opt. Soc. Am. A 1, 1075–1077 (1984).
    [CrossRef]
  23. A. Consortini, E. Briccolani, G. Conforti, “Strong scintillation statistics deterioration due to detector saturation,” J. Opt. Soc. Am. A 3, 101–107 (1986).
    [CrossRef]
  24. A. Consortini, R. J. Hill, “Reduction of the moments of intensity fluctuations caused by amplifier saturation for both the K and the log-normally modulated exponential probability densities,” Opt. Lett. 12, 304–306 (1987).
    [CrossRef] [PubMed]
  25. J. H. Churnside, R. J. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence,” J. Opt. Soc. Am. A 4, 727–733 (1987).
    [CrossRef]
  26. N. Ben-Yoseph, E. Goldner, “Sample size influence on optical scintillation analysis. 1: Analytical treatment of the higher order irradiance moments,” Appl. Opt. 27, 2167–2171 (1988).
    [CrossRef]
  27. E. Goldner, N. Ben-Yoseph, “Sample size influence on optical scintillation analysis. 2: Simulation approach,” Appl. Opt. 27, 2172–2177 (1988).
    [CrossRef] [PubMed]
  28. R. G. Frehlich, J. H. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
    [CrossRef]
  29. R. J. Hill, J. H. Churnside, “Observational challenges of strong scintillations of irradiance,” J. Opt. Soc. Am. A 5, 445–447 (1988).
    [CrossRef]
  30. G. Parry, “Measurement of atmospheric turbulence-induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
    [CrossRef]
  31. R. L. Philips, L. C. Andrews, “Measured statistics of laser-light scattering in atmospheric turbulence,”J. Opt. Soc. Am. 71, 1440–1445 (1981).
    [CrossRef]
  32. M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978).
    [CrossRef]
  33. R. J. Hill, S. F. Clifford, “Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra,”J. Opt. Soc. Am. 71, 675–686 (1981).
    [CrossRef]
  34. W. A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillation in the atmosphere,”J. Opt. Soc. Am. 72, 1042–1048 (1982).
    [CrossRef]
  35. J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of plane-wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  36. S. M. Flatté, G.-Y. Wang, J. Martin, “Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment,” J. Opt. Soc. Am. A 10, 2363–2370 (1993).
    [CrossRef]

1993 (1)

1992 (2)

R. J. Hill, G. R. Ochs, “Inner-scale dependence of scintillation variances measured in weak scintillation,” J. Opt. Soc. Am. A 9, 1406–1411 (1992).
[CrossRef]

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale, and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[CrossRef]

1990 (1)

1989 (2)

J. H. Churnside, R. J. Hill, G. Conforti, A. Consortini, “Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere,” Appl. Opt. 28, 4126–4132 (1989).
[CrossRef] [PubMed]

R. G. Frehlich, J. H. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

1988 (7)

1987 (3)

1986 (1)

1985 (2)

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
[CrossRef] [PubMed]

I. G. Yakushkin, “Intensity fluctuations during small-angle scattering of wave fields (review),” Radiophys. Quantum Electron. 28, 365–389 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (1)

1981 (3)

1978 (2)

1976 (1)

I. G. Yakushkin, “Strong intensity fluctuations in the field of a light beam in a turbulent atmosphere,” Radiophys. Quantum Electron. 19, 270–276 (1976).
[CrossRef]

1975 (1)

I. G. Yakushkin, “Asymptotic calculations of intensity fluctuations in a turbulent medium for long paths,” Radiophys. Quantum Electron. 18, 1224–1229 (1975).
[CrossRef]

1949 (1)

A. M. Obukhov, “Structure of the temperature field in turbulent flow,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).

Andrews, L. C.

Azar, Z.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
[CrossRef]

Azoulay, E.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
[CrossRef]

Ben-Yoseph, N.

Beran, M. J.

A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation from a point source,” J. Opt. Soc. Am. A 5, 735–737 (1988).
[CrossRef]

M. J. Beran, A. M. Whitman, “Effect of the turbulence inner scale on scintillation in the atmosphere,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 2–10 (1989).
[CrossRef]

Briccolani, E.

Cartwright, W. D.

G. R. Ochs, W. D. Cartwright, “A crosswind measurement module for the model II optical Cn2instrument,”NOAA Tech. Memo. ERL WPL-53 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (A vailable from the National Technical Information Service, 5285 Port Royal Rd., Spring-field, Va. 22161; order number WPL53:PB 80-217607.)

G. R. Ochs, W. D. Cartwright, D. D. Russell, “Optical Cn2instrument model II,”NOAA Tech. Memo. ERL WPL-51 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161; order number WPL51:PB 80-209000.)

Churnside, J. H.

Clifford, S. F.

Coles, W. A.

Conforti, G.

Consortini, A.

Fante, R. L.

Flatté, S. M.

Frehlich, R. G.

R. G. Frehlich, J. H. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

R. G. Frehlich, “Intensity covariance of a point source in a random medium with a Kolmogorov spectrum and an inner scale of turbulence,”J. Opt. Soc. Am. 4, 360–366 (1987).
[CrossRef]

W. A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillation in the atmosphere,”J. Opt. Soc. Am. 72, 1042–1048 (1982).
[CrossRef]

Goldner, E.

Gracheva, M. E.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

Gurvich, A. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

Hill, R. J.

R. J. Hill, G. R. Ochs, “Inner-scale dependence of scintillation variances measured in weak scintillation,” J. Opt. Soc. Am. A 9, 1406–1411 (1992).
[CrossRef]

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale, and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[CrossRef]

J. H. Churnside, R. J. Hill, G. Conforti, A. Consortini, “Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere,” Appl. Opt. 28, 4126–4132 (1989).
[CrossRef] [PubMed]

R. J. Hill, “Comparison of scintillation methods for measuring the inner scale of turbulence,” Appl. Opt. 27, 2187–2193 (1988).
[CrossRef] [PubMed]

R. J. Hill, J. H. Churnside, “Observational challenges of strong scintillations of irradiance,” J. Opt. Soc. Am. A 5, 445–447 (1988).
[CrossRef]

J. H. Churnside, R. J. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence,” J. Opt. Soc. Am. A 4, 727–733 (1987).
[CrossRef]

A. Consortini, R. J. Hill, “Reduction of the moments of intensity fluctuations caused by amplifier saturation for both the K and the log-normally modulated exponential probability densities,” Opt. Lett. 12, 304–306 (1987).
[CrossRef] [PubMed]

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
[CrossRef] [PubMed]

R. J. Hill, S. F. Clifford, “Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra,”J. Opt. Soc. Am. 71, 675–686 (1981).
[CrossRef]

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[CrossRef]

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,”J. Opt. Soc. Am. 68, 892–899 (1978).
[CrossRef]

Holler, J. K.

G. R. Ochs, J. K. Holler, J. J. Wilson, “An optical inner-scale meter,” NOAA Tech. Memo. ERL WPL-183 (NOAA Environmental Research Laboratories, Boulder, Colo., 1990). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161.)

Jetter, A.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
[CrossRef]

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

Kohnle, A.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
[CrossRef]

Martin, J.

Martin, J. M.

Obukhov, A. M.

A. M. Obukhov, “Structure of the temperature field in turbulent flow,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).

Ochs, G. R.

R. J. Hill, G. R. Ochs, “Inner-scale dependence of scintillation variances measured in weak scintillation,” J. Opt. Soc. Am. A 9, 1406–1411 (1992).
[CrossRef]

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
[CrossRef] [PubMed]

G. R. Ochs, W. D. Cartwright, D. D. Russell, “Optical Cn2instrument model II,”NOAA Tech. Memo. ERL WPL-51 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161; order number WPL51:PB 80-209000.)

G. R. Ochs, W. D. Cartwright, “A crosswind measurement module for the model II optical Cn2instrument,”NOAA Tech. Memo. ERL WPL-53 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (A vailable from the National Technical Information Service, 5285 Port Royal Rd., Spring-field, Va. 22161; order number WPL53:PB 80-217607.)

G. R. Ochs, J. K. Holler, J. J. Wilson, “An optical inner-scale meter,” NOAA Tech. Memo. ERL WPL-183 (NOAA Environmental Research Laboratories, Boulder, Colo., 1990). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161.)

Parry, G.

G. Parry, “Measurement of atmospheric turbulence-induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

Philips, R. L.

Pokasov, V. L. V.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

Russell, D. D.

G. R. Ochs, W. D. Cartwright, D. D. Russell, “Optical Cn2instrument model II,”NOAA Tech. Memo. ERL WPL-51 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161; order number WPL51:PB 80-209000.)

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, 1971)(in Russian); English translation, The Effect of the Turbulent Atmosphere on Wave Propagation (Ketter, Jerusalem, 1971).

Thiermann, V.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
[CrossRef]

Wang, G.-Y.

Whitman, A. M.

A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation from a point source,” J. Opt. Soc. Am. A 5, 735–737 (1988).
[CrossRef]

M. J. Beran, A. M. Whitman, “Effect of the turbulence inner scale on scintillation in the atmosphere,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 2–10 (1989).
[CrossRef]

Wilson, J. J.

G. R. Ochs, J. K. Holler, J. J. Wilson, “An optical inner-scale meter,” NOAA Tech. Memo. ERL WPL-183 (NOAA Environmental Research Laboratories, Boulder, Colo., 1990). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161.)

Yakushkin, I. G.

I. G. Yakushkin, “Intensity fluctuations during small-angle scattering of wave fields (review),” Radiophys. Quantum Electron. 28, 365–389 (1985).
[CrossRef]

I. G. Yakushkin, “Strong intensity fluctuations in the field of a light beam in a turbulent atmosphere,” Radiophys. Quantum Electron. 19, 270–276 (1976).
[CrossRef]

I. G. Yakushkin, “Asymptotic calculations of intensity fluctuations in a turbulent medium for long paths,” Radiophys. Quantum Electron. 18, 1224–1229 (1975).
[CrossRef]

Appl. Opt. (6)

Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. (1)

A. M. Obukhov, “Structure of the temperature field in turbulent flow,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).

J. Fluid Mech. (1)

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[CrossRef]

J. Mod. Opt. (1)

R. G. Frehlich, J. H. Churnside, “Statistical properties of estimates of the moments of laser scintillation,” J. Mod. Opt. 36, 1645–1659 (1989).
[CrossRef]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (8)

J. Phys. D (1)

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurement of the inner scale of turbulence,”J. Phys. D 21, S41–S44 (1988).
[CrossRef]

Opt. Acta (1)

G. Parry, “Measurement of atmospheric turbulence-induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

Opt. Lett. (1)

Radiophys. Quantum Electron. (3)

I. G. Yakushkin, “Asymptotic calculations of intensity fluctuations in a turbulent medium for long paths,” Radiophys. Quantum Electron. 18, 1224–1229 (1975).
[CrossRef]

I. G. Yakushkin, “Strong intensity fluctuations in the field of a light beam in a turbulent atmosphere,” Radiophys. Quantum Electron. 19, 270–276 (1976).
[CrossRef]

I. G. Yakushkin, “Intensity fluctuations during small-angle scattering of wave fields (review),” Radiophys. Quantum Electron. 28, 365–389 (1985).
[CrossRef]

Waves Random Media (1)

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale, and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[CrossRef]

Other (6)

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, 1971)(in Russian); English translation, The Effect of the Turbulent Atmosphere on Wave Propagation (Ketter, Jerusalem, 1971).

M. J. Beran, A. M. Whitman, “Effect of the turbulence inner scale on scintillation in the atmosphere,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 2–10 (1989).
[CrossRef]

G. R. Ochs, W. D. Cartwright, D. D. Russell, “Optical Cn2instrument model II,”NOAA Tech. Memo. ERL WPL-51 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161; order number WPL51:PB 80-209000.)

G. R. Ochs, W. D. Cartwright, “A crosswind measurement module for the model II optical Cn2instrument,”NOAA Tech. Memo. ERL WPL-53 (NOAA Environmental Research Laboratories, Boulder, Colo., 1979). (A vailable from the National Technical Information Service, 5285 Port Royal Rd., Spring-field, Va. 22161; order number WPL53:PB 80-217607.)

G. R. Ochs, J. K. Holler, J. J. Wilson, “An optical inner-scale meter,” NOAA Tech. Memo. ERL WPL-183 (NOAA Environmental Research Laboratories, Boulder, Colo., 1990). (Available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, Va. 22161.)

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Figures (6)

Fig. 1
Fig. 1

Some typical results plotted versus time: (a)σI2, one point for each cycle, measured on August 15, (b) Cn2 sampled at the end of every cycle on August 19, (c) l0 sampled at every cycle on September 2. The dashed lines in (c) delimit the tested range of the inner-scale apparatus.

Fig. 2
Fig. 2

Some results of a day (August 18) with some clouds, showing that the behavior of l0 is generally opposite to the behavior of Cn2 and that σI2 depends on both: (a) σI2, (b) Cn2, (c) l0.

Fig. 3
Fig. 3

σI2 measured on August 15 plotted versus β0. Circles denote data before the minimum of Fig. 1(a), and plusses denote data after the minimum of Fig. 1(a). Arrows give the direction of time corresponding to the circles and the plusses.

Fig. 4
Fig. 4

σI2 measured on August 15, 18, and 19 and September 2 plotted versus β0. All the data were used. The three error bars are discussed in Appendix A.

Fig. 5
Fig. 5

σI2 from selected stationary intervals of the same days as in Fig. 4 (except August 15) plotted versus β0.

Fig. 6
Fig. 6

σI2 plotted versus β0 for the intervals of the inner scale shown in the upper right-hand corner of each graph. All the data were used. Selected data of Fig. 5 are plotted as circles, August 15 data are plotted as triangles, and other data are plotted as plusses.

Equations (10)

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

S = I + B .
I = S - B ,
I 2 - I 2 = ( S 2 - S 2 ) - ( B 2 - B 2 ) ,
σ I 2 = ( I 2 - I 2 ) / I 2 .
α = I sat / I ,
β 0 2 = 0.496 C n 2 k 7 / 6 L 11 / 6 ,
ρ 0 = { 1.44 ( C n 2 k 2 L ) - 3 / 5 = 0.945 β 0 - 6 / 5 ( L / k ) 1 / 2 for ρ 0 l 0 , 1.27 ( k 2 L C n 2 l 0 - 1 / 3 ) - 1 / 2 = 0.849 β 0 - 1 l 0 1 / 6 [ ( L / k ) 1 / 2 ] 5 / 6 for ρ 0 l 0 .
1.34 k 2 L C n 2 l 0 5 / 3 = β 0 2 [ l 0 / ( L / k ) 1 / 2 ] 5 / 3 0.496 .
β 0 l 0 5 / 6 5.4 ,
ρ 0 8 mm / β 0 ;

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