Abstract

Experimental results are presented for the statistics of 0.6328-μm laser irradiance fluctuations for multiple-pass propagation through a laboratory-simulated atmospheric turbulence of strength Cn2=2.476×1011m2/3 and the smallest scale size l0 = 2.74 mm. The coefficients of variation γ0, skewness γ1, and excess γ2 of irradiance fluctuations are plotted as a function of path length. From the plots of γ2 vs γ1 for various values of σ12(=1.23k7/6Cn2L11/6) in different regions within the turbulence, the following forms of the probability distribution functions for the irradiance fluctuations are considered: lognormal, Rice-Nakagami, m distribution, gamma (and exponential), and K distribution. We have also demonstrated the characteristic feature of −8/3 power law behavior of power spectrum and the shift of Tatarski's peak frequency in the case of strong turbulence.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
    [CrossRef]
  2. R. L. Fante, Proc. IEEE 63, 1669 (1975).
    [CrossRef]
  3. J. W. Strobehn, Ed., Laser Beam Propagation in the Atmosphere (Springer, Berlin, 1978).
    [CrossRef]
  4. A. Ishimaru, Proc. IEEE 65, 1030 (1977).
    [CrossRef]
  5. V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
    [CrossRef]
  6. M. S. Belenkii, V. V. Boronoev, N. Ts. Gomboev, V. L. Mironov, Opt. Lett. 5, 67 (1980).
    [CrossRef]
  7. J. Carl Leader, J. Opt. Soc. Am. 71, 542 (1981).
    [CrossRef]
  8. R. J. Hill, S. F. Clifford, J. Opt. Soc. Am. 71, 675 (1981).
    [CrossRef]
  9. D. Bensimon, A. Englander, S. Shtrikman, M. Slatkine, D. Treves, Appl. Opt. 20, 947 (1981).
    [CrossRef] [PubMed]
  10. L. R. Bissonnette, Appl. Opt. 16, 2242 (1977).
    [CrossRef] [PubMed]
  11. R. S. Rohde, R. G. Buser, Appl. Opt. 18, 698 (1979).
    [CrossRef] [PubMed]
  12. L. R. Bissonnette, P. L. Wizinowich, Appl. Opt. 18, 1590 (1979).
    [CrossRef] [PubMed]
  13. R. A. Elliott, J. R. Kerr, P. A. Pincus, Appl. Opt. 18, 3315 (1979).
    [CrossRef] [PubMed]
  14. H. Gamo, A. K. Majumdar, Appl. Opt. 17, 3755 (1978).
    [CrossRef] [PubMed]
  15. A. K. Majumdar, H. Gamo, “Characterization of an Atmospheric Turbulence Chamber by Laser Irradiance Fluctuations Measurements,” submitted to Appl. Opt. (1981).
  16. G. Bourgois, C. Cheynet, Astron. Astrophys. 21, 25 (1972).
  17. G. Bourgois, Astron. Astrophys. 21, 33 (1972).
  18. D. L. Knepp, G. C. Valley, Radio Sci. 13, 59 (1979);D. L. Knepp, G. C. Valley, J. Geophys. Res. 81, 4723 (1976).
    [CrossRef]
  19. P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
    [CrossRef]
  20. A. K. Majumdar, J. Opt. Soc. Am. 69, 199 (1979).
    [CrossRef]
  21. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, TT-68-50464 (National Science Foundation, Washington, D.C., distributed by NTIS, Springfield, Va., 1971).
  22. H. T. Yura, J. Opt. Soc. Am. 64, 357 (1974).
    [CrossRef]
  23. Ref. 14.
  24. S. S. Khmelevtsov, Appl. Opt. 12, 2421 (1973).
    [CrossRef] [PubMed]
  25. M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer, Berlin, 1978).
  26. G. Parry, P. N. Pusey, J. Opt. Soc. Am. 69, 796 (1979).
    [CrossRef]
  27. E. Jakeman, P. N. Pusey, Phys. Rev. Lett. 40, 546 (1978).
    [CrossRef]
  28. S. F. Clifford, R. J. Hill, J. Opt. Soc. Am. 71, 112 (1981).
    [CrossRef]
  29. J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
    [CrossRef]
  30. E. Brookner, IEEE Trans. Commun. COM-18, 396 (1970).
    [CrossRef]
  31. J. Aitchison, J. A. C. Brown, The Log-Normal Distribution, (Cambridge U.P., London, 1957).
  32. R. L. Mitchell, J. Opt. Soc. Am. 58, 1267 (1968).
    [CrossRef]
  33. P. Beckmann, Probability in Communication Engineering (Harcourt, Brace, Jovanovich, New York, 1967).
  34. M. Nakagami, in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, Ed.(Pergamon, New York, 1960).

1981 (4)

1980 (1)

1979 (8)

G. Parry, P. N. Pusey, J. Opt. Soc. Am. 69, 796 (1979).
[CrossRef]

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

R. S. Rohde, R. G. Buser, Appl. Opt. 18, 698 (1979).
[CrossRef] [PubMed]

L. R. Bissonnette, P. L. Wizinowich, Appl. Opt. 18, 1590 (1979).
[CrossRef] [PubMed]

R. A. Elliott, J. R. Kerr, P. A. Pincus, Appl. Opt. 18, 3315 (1979).
[CrossRef] [PubMed]

D. L. Knepp, G. C. Valley, Radio Sci. 13, 59 (1979);D. L. Knepp, G. C. Valley, J. Geophys. Res. 81, 4723 (1976).
[CrossRef]

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

A. K. Majumdar, J. Opt. Soc. Am. 69, 199 (1979).
[CrossRef]

1978 (2)

H. Gamo, A. K. Majumdar, Appl. Opt. 17, 3755 (1978).
[CrossRef] [PubMed]

E. Jakeman, P. N. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[CrossRef]

1977 (2)

1975 (2)

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
[CrossRef]

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

1974 (1)

1973 (1)

1972 (2)

G. Bourgois, C. Cheynet, Astron. Astrophys. 21, 25 (1972).

G. Bourgois, Astron. Astrophys. 21, 33 (1972).

1970 (1)

E. Brookner, IEEE Trans. Commun. COM-18, 396 (1970).
[CrossRef]

1968 (2)

Aitchison, J.

J. Aitchison, J. A. C. Brown, The Log-Normal Distribution, (Cambridge U.P., London, 1957).

Beckmann, P.

P. Beckmann, Probability in Communication Engineering (Harcourt, Brace, Jovanovich, New York, 1967).

Belenkii, M. S.

Bensimon, D.

Bissonnette, L. R.

Boronoev, V. V.

Bourgois, G.

G. Bourgois, C. Cheynet, Astron. Astrophys. 21, 25 (1972).

G. Bourgois, Astron. Astrophys. 21, 33 (1972).

Brookner, E.

E. Brookner, IEEE Trans. Commun. COM-18, 396 (1970).
[CrossRef]

Brown, J. A. C.

J. Aitchison, J. A. C. Brown, The Log-Normal Distribution, (Cambridge U.P., London, 1957).

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
[CrossRef]

Buser, R. G.

Carl Leader, J.

Cheynet, C.

G. Bourgois, C. Cheynet, Astron. Astrophys. 21, 25 (1972).

Ciolli, P.

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

Clifford, S. F.

Consortini, A.

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

Elepov, B. S.

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

Elliott, R. A.

Englander, A.

Fante, R. L.

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

Gamo, H.

H. Gamo, A. K. Majumdar, Appl. Opt. 17, 3755 (1978).
[CrossRef] [PubMed]

A. K. Majumdar, H. Gamo, “Characterization of an Atmospheric Turbulence Chamber by Laser Irradiance Fluctuations Measurements,” submitted to Appl. Opt. (1981).

Gochelashviby, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
[CrossRef]

Gomboev, N. Ts.

Gracheva, M. E.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer, Berlin, 1978).

Gurvich, A. S.

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer, Berlin, 1978).

Hill, R. J.

Ishimaru, A.

A. Ishimaru, Proc. IEEE 65, 1030 (1977).
[CrossRef]

Jakeman, E.

E. Jakeman, P. N. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[CrossRef]

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer, Berlin, 1978).

Kerr, J. R.

Khmelevtsov, S. S.

Knepp, D. L.

D. L. Knepp, G. C. Valley, Radio Sci. 13, 59 (1979);D. L. Knepp, G. C. Valley, J. Geophys. Res. 81, 4723 (1976).
[CrossRef]

Majumdar, A. K.

A. K. Majumdar, J. Opt. Soc. Am. 69, 199 (1979).
[CrossRef]

H. Gamo, A. K. Majumdar, Appl. Opt. 17, 3755 (1978).
[CrossRef] [PubMed]

A. K. Majumdar, H. Gamo, “Characterization of an Atmospheric Turbulence Chamber by Laser Irradiance Fluctuations Measurements,” submitted to Appl. Opt. (1981).

Mironov, V. L.

Mitchell, R. L.

Nakagami, M.

M. Nakagami, in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, Ed.(Pergamon, New York, 1960).

Pandolfini, P.

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

Parry, G.

Pasqualetti, F.

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

Pincus, P. A.

Pokasov, V. V.

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer, Berlin, 1978).

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
[CrossRef]

Pusey, P. N.

G. Parry, P. N. Pusey, J. Opt. Soc. Am. 69, 796 (1979).
[CrossRef]

E. Jakeman, P. N. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[CrossRef]

Rohde, R. S.

Ronchi, L.

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

Sabelfeld, K. K.

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
[CrossRef]

Shtrikman, S.

Slatkine, M.

Strohbehn, J. W.

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, TT-68-50464 (National Science Foundation, Washington, D.C., distributed by NTIS, Springfield, Va., 1971).

Treves, D.

Valley, G. C.

D. L. Knepp, G. C. Valley, Radio Sci. 13, 59 (1979);D. L. Knepp, G. C. Valley, J. Geophys. Res. 81, 4723 (1976).
[CrossRef]

Vanni, R.

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

Wizinowich, P. L.

Yura, H. T.

Appl. Opt. (7)

Astron. Astrophys. (2)

G. Bourgois, C. Cheynet, Astron. Astrophys. 21, 25 (1972).

G. Bourgois, Astron. Astrophys. 21, 33 (1972).

IEEE Trans. Commun. (1)

E. Brookner, IEEE Trans. Commun. COM-18, 396 (1970).
[CrossRef]

J. Opt. Soc. Am. (7)

Opt. Acta (2)

P. Ciolli, A. Consortini, P. Pandolfini, F. Pasqualetti, L. Ronchi, R. Vanni, Opt. Acta 26, 253 (1979).
[CrossRef]

V. I. Tatarskii, A. S. Gurvich, B. S. Elepov, V. V. Pokasov, K. K. Sabelfeld, Opt. Acta 26, 531 (1979).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

E. Jakeman, P. N. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[CrossRef]

Proc. IEEE (4)

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
[CrossRef]

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashviby, V. I. Shishov, Proc. IEEE 63, 790 (1975).
[CrossRef]

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

A. Ishimaru, Proc. IEEE 65, 1030 (1977).
[CrossRef]

Radio Sci. (1)

D. L. Knepp, G. C. Valley, Radio Sci. 13, 59 (1979);D. L. Knepp, G. C. Valley, J. Geophys. Res. 81, 4723 (1976).
[CrossRef]

Other (8)

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, TT-68-50464 (National Science Foundation, Washington, D.C., distributed by NTIS, Springfield, Va., 1971).

J. W. Strobehn, Ed., Laser Beam Propagation in the Atmosphere (Springer, Berlin, 1978).
[CrossRef]

A. K. Majumdar, H. Gamo, “Characterization of an Atmospheric Turbulence Chamber by Laser Irradiance Fluctuations Measurements,” submitted to Appl. Opt. (1981).

Ref. 14.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer, Berlin, 1978).

P. Beckmann, Probability in Communication Engineering (Harcourt, Brace, Jovanovich, New York, 1967).

M. Nakagami, in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, Ed.(Pergamon, New York, 1960).

J. Aitchison, J. A. C. Brown, The Log-Normal Distribution, (Cambridge U.P., London, 1957).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic diagram of experimental setup for multipass experiment.

Fig. 2
Fig. 2

Statistical data acquisition system used for measuring the histograms, higher-order moments, and power spectra.

Fig. 3
Fig. 3

Normalized histograms for different laser paths. The numbers 1,2 … denote the number of paths.

Fig. 4
Fig. 4

Coefficients of variation γ0, skewness γ1, and excess γ2 as a function of increasing path length.

Fig. 5
Fig. 5

Variations of the excess coefficient γ2, with the skewness coefficient γ1 for different paths. The numbers in brackets denote the number of paths.

Fig. 6
Fig. 6

Histograms of irradiance fluctuations for path = 7 and path = 9.

Fig. 7
Fig. 7

Normalized power spectra for various paths.

Tables (1)

Tables Icon

Table I Hiqher-Order Cumulants

Equations (25)

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

γ 0 = σ / m ,
γ 1 = μ 3 / σ 3 ,
γ 2 = μ 4 / σ 4 3 ,
Γ n = χ n [ χ 2 ] n ,
U ( f ) = f W ( f ) / 0 W ( f ) d f .
Γ n = χ n [ χ 2 ] n
Γ n ( exp ) Γ n ( K distr . )
Γ n ( exp ) Γ n ( lognormal )
Γ n ( exp ) Γ n ( K distr . )
Γ n ( exp ) Γ n ( lognormal )
p ( I ) = 1 / 2 π σ ¯ I exp [ ( ln I λ ) 2 / 2 σ ¯ 2 ] ,
γ 0 = q ,
γ 1 = 3 q + q 3 ,
γ 2 = 16 q 2 + 15 q 4 + 6 q 6 + q 8 ,
q = [ exp ( σ ¯ 2 ) 1 ] 1 / 2 .
p ( I ) = ( 1 / σ 2 ) exp [ ( I + I c ) / σ 2 ] I 0 [ 2 ( I I c ) 1 / 2 / σ 2 ] .
γ 0 = 2 ( β + 1 / 2 ) 1 / 2 ( β + 1 ) 1 ,
γ 1 = 3 / 2 ( β + 1 / 3 ) ( β + 1 / 2 ) 3 / 2 ,
γ 2 = 6 ( β + 1 / 4 ) ( β + 1 / 2 ) 2 .
p ( I ) = 1 / β α Γ ( α ) I α 1 exp ( I / β ) ,
γ 0 = α 1 , γ 1 = 2 α 1 / 2 , γ 2 = 6 α 1 .
p ( I ) = m m I m 1 / Γ ( m ) ( I ¯ ) m exp ( m I / I ¯ ) ,
γ 0 = m 1 / 2 , γ 1 = 2 m 1 / 2 , γ 2 = 6 m 1 .
p ( I ) = 2 Γ ( y ) ( y I ) ( y + 1 ) / 2 I . ( y 1 ) / 2 K y 1 ( 2 I y / I ) .
γ 0 = ( 1 + 2 y ) 1 / 2 , γ 1 = 2 ( y 2 + 6 y + 6 ) y 1 / 2 ( 2 + y ) 3 / 2 , γ 2 = ( 6 y 3 + 72 y 2 + 204 y + 144 ) ( y 3 + 4 y 2 + 4 y ) .

Metrics