Abstract

Experimental results are presented which suggest that the probability distribution of fluctuations in the intensity of laser light propagating through atmospheric turbulence are reasonably well described by K distributions in the intermediate range of propagation path lengths, L ≃ 600 m, β0≃1–2, where the mean square fluctuation 〈I2〉 /〈I2 can be as high as five.

© 1979 Optical Society of America

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References

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  1. F. Davidson and A. Gonzalez-del-Valle, J. Opt. Soc. Am. 65, 655 (1975).
    [Crossref]
  2. G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
    [Crossref]
  3. J. W. Strohbehn, Ting-i Wang, and J. P. Speck, Radio Science 10, 59 (1975).
    [Crossref]
  4. E. Jakeman and P. N. Pusey, IEEE Trans. Antennas Propag. 24, 806 (1976).
    [Crossref]
  5. P. N. Pusey, in: Photon Correlation Spectroscopy and Velocimetry, edited by H. Z. Cummins and E. R. Pike (Plenum, New York, 1977).
  6. E. Jakeman and P. N. Pusey, Phys. Rev. Lett. 40, 546 (1978).
    [Crossref]
  7. For example, in Photon Correlation and Light Beating Spectroscopy, edited by H. Z. Cummins and E. R. Pike (Plenum, New York, 1974), p. 45.
  8. R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
    [Crossref]
  9. V. I. Tatarski, Wave Propagation in a Turbulent Medium, (McGraw-Hill, New York, 1961, Dover, New York, 1967).
  10. S. F. Clifford, G. R. Ochs, and R. S. Lawrence, J. Opt. Soc. Am. 64, 148 (1974).
    [Crossref]
  11. M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].
  12. A. S. Gurvich and V. I. Tatarski, Radio Science 10, 3 (1975).
    [Crossref]
  13. J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 63, 981 (1973).
    [Crossref]
  14. R. L. Fante, Proc. IEEE 63, 1669 (1975).
    [Crossref]
  15. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, Proc. IEEE,  63, 790 (1975).
    [Crossref]

1978 (1)

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

1977 (1)

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
[Crossref]

1976 (1)

E. Jakeman and P. N. Pusey, IEEE Trans. Antennas Propag. 24, 806 (1976).
[Crossref]

1975 (6)

F. Davidson and A. Gonzalez-del-Valle, J. Opt. Soc. Am. 65, 655 (1975).
[Crossref]

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, Radio Science 10, 59 (1975).
[Crossref]

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].

A. S. Gurvich and V. I. Tatarski, Radio Science 10, 3 (1975).
[Crossref]

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

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

1974 (1)

1973 (1)

1969 (1)

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[Crossref]

Alley, C. O.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[Crossref]

Bunkin, F. V.

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

Chang, R. F.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[Crossref]

Clifford, S. F.

Davidson, F.

Detenbeck, R. W.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[Crossref]

Dunphy, J. R.

Fante, R. L.

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

Gochelashvily, K. S.

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

Gonzalez-del-Valle, A.

Gracheva, M. E.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].

Gurvich, A. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].

A. S. Gurvich and V. I. Tatarski, Radio Science 10, 3 (1975).
[Crossref]

Jakeman, E.

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

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
[Crossref]

E. Jakeman and P. N. Pusey, IEEE Trans. Antennas Propag. 24, 806 (1976).
[Crossref]

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].

Kerr, J. R.

Korenman, V.

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[Crossref]

Lawrence, R. S.

McWhirter, J. G.

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
[Crossref]

Ochs, G. R.

Parry, G.

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
[Crossref]

Pokasov, V. V.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].

Prokhorov, A. M.

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

Pusey, P. N.

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

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
[Crossref]

E. Jakeman and P. N. Pusey, IEEE Trans. Antennas Propag. 24, 806 (1976).
[Crossref]

P. N. Pusey, in: Photon Correlation Spectroscopy and Velocimetry, edited by H. Z. Cummins and E. R. Pike (Plenum, New York, 1977).

Shishov, V. I.

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

Speck, J. P.

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, Radio Science 10, 59 (1975).
[Crossref]

Strohbehn, J. W.

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, Radio Science 10, 59 (1975).
[Crossref]

Tatarski, V. I.

A. S. Gurvich and V. I. Tatarski, Radio Science 10, 3 (1975).
[Crossref]

V. I. Tatarski, Wave Propagation in a Turbulent Medium, (McGraw-Hill, New York, 1961, Dover, New York, 1967).

Wang, Ting-i

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, Radio Science 10, 59 (1975).
[Crossref]

IEEE Trans. Antennas Propag. (1)

E. Jakeman and P. N. Pusey, IEEE Trans. Antennas Propag. 24, 806 (1976).
[Crossref]

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, Opt. Commun. 22, 195 (1977).
[Crossref]

Phys. Rev. (1)

R. F. Chang, V. Korenman, C. O. Alley, and R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[Crossref]

Phys. Rev. Lett. (1)

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

Proc. IEEE (2)

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

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

Radio Science (2)

A. S. Gurvich and V. I. Tatarski, Radio Science 10, 3 (1975).
[Crossref]

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, Radio Science 10, 59 (1975).
[Crossref]

Sov. Phys. JETP (1)

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and V. V. Pokasov, Sov. Phys. JETP 40, 1011 (1975).[Zh. Eksp. Teor. Fiz. 67, 2035 (1974)].

Other (3)

P. N. Pusey, in: Photon Correlation Spectroscopy and Velocimetry, edited by H. Z. Cummins and E. R. Pike (Plenum, New York, 1977).

For example, in Photon Correlation and Light Beating Spectroscopy, edited by H. Z. Cummins and E. R. Pike (Plenum, New York, 1974), p. 45.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, (McGraw-Hill, New York, 1961, Dover, New York, 1967).

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Figures (2)

FIG. 1
FIG. 1

The measured normalized variance of intensity is plotted as a function of the parameter β 0 = ( 0.5 C n 2 k 7 / 6 L 11 / 6 ) 1 / 2. Data was obtained at L = 281m, 431m, and 645m on four days for C n 2 values in the range 1 × 10−13−5 × 10−13 m−2/3. The data points shown represent averages over 8–10 points and the error bars indicate the standard deviations in the measured values of both second moment and β0.

FIG. 2
FIG. 2

Measured values of the normalized third, fourth, and fifth moments are compared with the values expected from various model distributions, having the same normalized second moments as the experimental data. The long dashes indicate the moments expected from log-normally distributed intensity fluctuations and apply to all values of normalized second moment. The continuous lines indicate moments expected from K-distributed fluctuations and apply to values of the normalized second moment greater than 2. The shorter dashes indicate moments of the Rice distribution valid for normalized second moment less than 2. Conditions under which the data was obtained are given in the Fig. 1 caption and text. The abscissa 〈I2〉/〈I2 can be converted to β0 via the curve in Fig. 1.

Equations (7)

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σ 2 Δ I 2 / I 2 = I 2 / I 2 1
n [ m ] = n ( n 1 ) ( n m + 1 ) / n m .
σ 2 = exp ( 0.5 C n 2 k 7 / 6 L 11 / 6 ) 1
I P L N ( I ) = exp [ ( ln x y 1 / 2 ) 2 / 2 ln y ] x ( 2 π ln y ) 1 / 2 , n L N [ m ] = y m ( m 1 ) / 2 , x = I / I , y = 1 + σ 2 ;
I P R ( I ) = ( 1 y ) 1 exp [ x + y 1 y ] I 0 [ 2 ( x y ) 1 / 2 1 y ] , n R [ m ] = m ! L m [ ( y 1 1 ) 1 ] ( 1 y ) m , x = I / I , y = ( 1 σ 2 ) 1 / 2 / 4 ;
I P K ( I ) = 2 Γ ( y ) y ( y + 1 ) / 2 x ( y 1 ) / 2 K y 1 [ 2 ( x y ) 1 / 2 ] , n K [ m ] = m ! Γ ( m + y ) / y m Γ ( y ) , x = I / I , y = 2 / ( σ 2 1 ) ;
I m I m = P ( I ) [ 1 + Δ I I ] m d I , = 1 + m ( m 1 ) 2 σ 2 + 0 ( Δ I 3 I 3 ) ,