Abstract

We present the results of measurements of the first five moments of the intensity fluctuations of stellar scintillation. Measurements were made using photon counting techniques. The moments were found to be consistent with a log normal model provided the normalized second moment of the intensity was less than ∼1.65. Above this, departure from log normal behavior occurred.

© 1980 Optical Society of America

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References

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  1. E. Jakeman, E. R. Pike, and P. N. Pusey, “Photon correlation study of stellar scintillation,” Nature 263, 215–216 (1976).
    [Crossref]
  2. R. S. Iyer and J. L. Bufton, “Aperture Averaging Effects in Stellar Scintillation,” Opt. Commun. 22, 377–381 (1977).
    [Crossref]
  3. G. Parry, J. G. Walker, and R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
    [Crossref]
  4. E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
    [Crossref]
  5. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  6. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation, translated from the Russian(National Technical Information Service, Springfield, Va., 1971).
  7. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [Crossref]
  8. D. Korff, “Analysis of a method for obtaining near-diffraction-limited information in the presence of atmospheric turbulence,” J. Opt. Soc. Am. 63, 971–980 (1973).
    [Crossref]
  9. A. T. Young, “Saturation of scintillation,” J. Opt. Soc. Am. 60, 1495–1500 (1970).
    [Crossref]
  10. A. Rocca, F. Roddier, and J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
    [Crossref]
  11. C. Roddier and J. Vernin, “Relative contribution of upper and lower atmosphere to integrated refractive-index profiles,” Appl. Opt. 16, 2250–2252 (1977).
    [Crossref]
  12. D. L. Fried, G. E. Mevers, and M. P. Keister, “Measurements of laser-beam scintillation in the atmosphere,” J. Opt. Soc. Am. 57, 787–797 (1967).
    [Crossref]
  13. R. S. Lawrence and J. W. Strohbehn, “A survey of clean-air propagation effects relevant to optical communications,”Proc. IEEE 58, 1523–1545 (1970).
    [Crossref]
  14. R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669–1691 (1975).
    [Crossref]
  15. A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
    [Crossref]
  16. Laser Beam Propagation in the Atmosphere, edited by J. W. Strohbehn, (Springer-Verlag, New York, 1978).
    [Crossref]
  17. G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
    [Crossref]
  18. G. Parry and P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
    [Crossref]
  19. Photon Correlation and Light Beating Spectroscopy, edited by E. R. Pike and H. Z. Cummins, (Plenum, New York, 1974).
  20. P. N. Pusey, in Photon Correlation Spectroscopy and Velocimetry, edited by H. Z. Cummins and E. R. Pike (Plenum, New York, 1977).
  21. E. Jakeman and P. N. Pusey, “A Model for Non-Rayleigh Sea Echo,” IEEE Trans.Antennas Propag. 24, 806–814 (1976).
    [Crossref]
  22. E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
    [Crossref]
  23. L. S. Taylor and C. J. Infosino, “Diffraction theory of optical scintillations due to turbulent layers,” J. Opt. Soc. Am. 65, 78–84 (1975).
    [Crossref]
  24. J. W. Strohbehn, Ting-i Wang, and J. P. Speck, “On the Probability Distribution of Line-of-sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
    [Crossref]

1979 (2)

G. Parry, J. G. Walker, and R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

G. Parry and P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[Crossref]

1978 (2)

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
[Crossref]

1977 (3)

R. S. Iyer and J. L. Bufton, “Aperture Averaging Effects in Stellar Scintillation,” Opt. Commun. 22, 377–381 (1977).
[Crossref]

C. Roddier and J. Vernin, “Relative contribution of upper and lower atmosphere to integrated refractive-index profiles,” Appl. Opt. 16, 2250–2252 (1977).
[Crossref]

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
[Crossref]

1976 (2)

E. Jakeman, E. R. Pike, and P. N. Pusey, “Photon correlation study of stellar scintillation,” Nature 263, 215–216 (1976).
[Crossref]

E. Jakeman and P. N. Pusey, “A Model for Non-Rayleigh Sea Echo,” IEEE Trans.Antennas Propag. 24, 806–814 (1976).
[Crossref]

1975 (4)

L. S. Taylor and C. J. Infosino, “Diffraction theory of optical scintillations due to turbulent layers,” J. Opt. Soc. Am. 65, 78–84 (1975).
[Crossref]

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, “On the Probability Distribution of Line-of-sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[Crossref]

R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669–1691 (1975).
[Crossref]

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
[Crossref]

1974 (1)

1973 (1)

1970 (2)

A. T. Young, “Saturation of scintillation,” J. Opt. Soc. Am. 60, 1495–1500 (1970).
[Crossref]

R. S. Lawrence and J. W. Strohbehn, “A survey of clean-air propagation effects relevant to optical communications,”Proc. IEEE 58, 1523–1545 (1970).
[Crossref]

1967 (1)

1966 (1)

Bufton, J. L.

R. S. Iyer and J. L. Bufton, “Aperture Averaging Effects in Stellar Scintillation,” Opt. Commun. 22, 377–381 (1977).
[Crossref]

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
[Crossref]

Cummins, H. Z.

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

Fante, R. L.

R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669–1691 (1975).
[Crossref]

Fried, D. L.

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
[Crossref]

Infosino, C. J.

Iyer, R. S.

R. S. Iyer and J. L. Bufton, “Aperture Averaging Effects in Stellar Scintillation,” Opt. Commun. 22, 377–381 (1977).
[Crossref]

Jakeman, E.

E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
[Crossref]

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
[Crossref]

E. Jakeman, E. R. Pike, and P. N. Pusey, “Photon correlation study of stellar scintillation,” Nature 263, 215–216 (1976).
[Crossref]

E. Jakeman and P. N. Pusey, “A Model for Non-Rayleigh Sea Echo,” IEEE Trans.Antennas Propag. 24, 806–814 (1976).
[Crossref]

Keister, M. P.

Korff, D.

Lawrence, R. S.

R. S. Lawrence and J. W. Strohbehn, “A survey of clean-air propagation effects relevant to optical communications,”Proc. IEEE 58, 1523–1545 (1970).
[Crossref]

McWhirter, J. G.

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
[Crossref]

Mevers, G. E.

Parry, G.

G. Parry and P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[Crossref]

G. Parry, J. G. Walker, and R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
[Crossref]

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
[Crossref]

Pike, E. R.

E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
[Crossref]

E. Jakeman, E. R. Pike, and P. N. Pusey, “Photon correlation study of stellar scintillation,” Nature 263, 215–216 (1976).
[Crossref]

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

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
[Crossref]

Pusey, P. N.

G. Parry and P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[Crossref]

E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
[Crossref]

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
[Crossref]

E. Jakeman, E. R. Pike, and P. N. Pusey, “Photon correlation study of stellar scintillation,” Nature 263, 215–216 (1976).
[Crossref]

E. Jakeman and P. N. Pusey, “A Model for Non-Rayleigh Sea Echo,” IEEE Trans.Antennas Propag. 24, 806–814 (1976).
[Crossref]

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

Rocca, A.

Roddier, C.

C. Roddier and J. Vernin, “Relative contribution of upper and lower atmosphere to integrated refractive-index profiles,” Appl. Opt. 16, 2250–2252 (1977).
[Crossref]

Roddier, F.

Scaddan, R. J.

G. Parry, J. G. Walker, and R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
[Crossref]

Speck, J. P.

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, “On the Probability Distribution of Line-of-sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[Crossref]

Strohbehn, J. W.

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, “On the Probability Distribution of Line-of-sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[Crossref]

R. S. Lawrence and J. W. Strohbehn, “A survey of clean-air propagation effects relevant to optical communications,”Proc. IEEE 58, 1523–1545 (1970).
[Crossref]

Tatarski, V. I.

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

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation, translated from the Russian(National Technical Information Service, Springfield, Va., 1971).

Taylor, L. S.

Vernin, J.

C. Roddier and J. Vernin, “Relative contribution of upper and lower atmosphere to integrated refractive-index profiles,” Appl. Opt. 16, 2250–2252 (1977).
[Crossref]

A. Rocca, F. Roddier, and J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
[Crossref]

Walker, J. G.

G. Parry, J. G. Walker, and R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

Wang, Ting-i

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, “On the Probability Distribution of Line-of-sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[Crossref]

Young, A. T.

Appl. Opt. (1)

C. Roddier and J. Vernin, “Relative contribution of upper and lower atmosphere to integrated refractive-index profiles,” Appl. Opt. 16, 2250–2252 (1977).
[Crossref]

Contemp. Phys. (1)

E. Jakeman, G. Parry, E. R. Pike, and P. N. Pusey, “The Twinkling of Stars,” Contemp. Phys. 19, 127–145 (1978).
[Crossref]

IEEE Trans.Antennas Propag. (1)

E. Jakeman and P. N. Pusey, “A Model for Non-Rayleigh Sea Echo,” IEEE Trans.Antennas Propag. 24, 806–814 (1976).
[Crossref]

J. Opt. Soc. Am. (7)

Nature (1)

E. Jakeman, E. R. Pike, and P. N. Pusey, “Photon correlation study of stellar scintillation,” Nature 263, 215–216 (1976).
[Crossref]

Opt. Acta (1)

G. Parry, J. G. Walker, and R. J. Scaddan, “On the statistics of stellar speckle patterns and pupil plane scintillation,” Opt. Acta 26, 563–574 (1979).
[Crossref]

Opt. Commun. (2)

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, “Focusing by a Random Phase Screen,” Opt. Commun. 22, 195–201 (1977).
[Crossref]

R. S. Iyer and J. L. Bufton, “Aperture Averaging Effects in Stellar Scintillation,” Opt. Commun. 22, 377–381 (1977).
[Crossref]

Phys. Rev. Lett. (1)

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

Proc. IEEE (3)

R. S. Lawrence and J. W. Strohbehn, “A survey of clean-air propagation effects relevant to optical communications,”Proc. IEEE 58, 1523–1545 (1970).
[Crossref]

R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669–1691 (1975).
[Crossref]

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, and V. I. Shishov, “Laser Irradiance Propagation in Turbulent Media,” Proc. IEEE 63, 790–871 (1975).
[Crossref]

Radio Sci. (1)

J. W. Strohbehn, Ting-i Wang, and J. P. Speck, “On the Probability Distribution of Line-of-sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[Crossref]

Other (5)

Laser Beam Propagation in the Atmosphere, edited by J. W. Strohbehn, (Springer-Verlag, New York, 1978).
[Crossref]

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

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

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

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation, translated from the Russian(National Technical Information Service, Springfield, Va., 1971).

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Figures (1)

FIG. 1
FIG. 1

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 lines (long dashes) indicate the moments expected from log normally distributed intensity fluctuations and apply to all values of 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 data points shown represent averages over 4–8 points and the error bars indicate the standard deviations in the measured values of both higher moments and second moment. The data point with a normalized second moment of 2.89 is taken from Ref. 1.

Equations (3)

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

n ( n 1 ) ( n m + 1 ) n m = I m I m ,
I m I m = m ! Γ ( m + y ) y m Γ ( y ) ,
I m I m = I 2 m ( m 1 ) / 2 I 2 .