Abstract

Interest in the higher-order moments of irradiance scintillation draws attention to extremely large excursions of irradiance. Observation of such excursions has many experimental difficulties involving receiver dynamic range, aperture size, and bandwidth as well as sufficiency of number of samples, surface reflections (mirages), and source divergence. We discuss these difficulties as well as techniques to mitigate them. Visual biases exist in graphical presentations of moments and probability-density functions; we make suggestions for effective graphical interpretation of data. We recommend measuring both the refractive-index structure parameter and the inner scale of turbulence simultaneously with irradiance statistics.

© 1988 Optical Society of America

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  1. A. K. Majumdar, “Higher-order statistics of laser-irradiance fluctuations due to turbulence,” J. Opt. Soc. Am. A 1, 1067–1074 (1984).
    [CrossRef]
  2. A. Consortini, G. Conforti, “Detector saturation effect on higher-order moments of intensity fluctuations in atmospheric laser propagation mesurement,” J. Opt. Soc. Am A 1, 1075–1077 (1984).
    [CrossRef]
  3. A. Consortini, E. Briccolani, G. Conforti, “Strong-scintillation statistics deteriorated due to detector saturation,” J. Opt. Soc. Am. A 3, 101–107 (1986).
    [CrossRef]
  4. 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]
  5. 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]
  6. G. Parry, “Measurement of atmospheric turbulence-induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
    [CrossRef]
  7. E. Azoulay, Z. Azar, M. Tur, “Aperture-averaged statistics of laser intensity fluctuations in strong turbulence,” in Digest of the International Conference on Optical and Millimeter-Wave Propagation and Scattering in the Atmosphere (University of Florence, Florence, Italy, 1986), pp. 211–214.
  8. R. J. Hill, J. H. Churnside, “Measured statistics of laser beam scintillation in strong refractive turbulence relevant to eye safety,” Health Phys. 53, 639–647 (1987).
    [CrossRef] [PubMed]
  9. F. V. Bunkin, K. S. Gochelashvili, “Random spatial overshoots of the field-strength when a wave travels through a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 697–702 (1969) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 875–881 (1969)].
    [CrossRef]
  10. G. R. Ochs, S. F. Clifford, R. B. Fritz, “Observations of spherical-wave covariance in strong refractive-index turbulence,” J. Opt. Soc. Am. A 3 (13), P100–P101 (1986).
  11. 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]
  12. R. L. Phillips, L. C. Andrews, “Measured statistics of laserlight scattering in atmospheric turbulence,” J. Opt. Soc. Am. 71, 1440–1445 (1981).
    [CrossRef]
  13. K. S. Gochelashvili, V. G. Pevgov, V. I. Shishov, “Saturation of fluctuations of the intensity of laser radiation at large distances in a turbulent atmosphere (Fraunhofer zone of transmitter),” Sov. J. Quantum Electron. 4, 632–637 (1974) [Kvantovaya Elektron. (Moscow) 1, 1156–1165 (1974)].
    [CrossRef]
  14. R. L. Fante, “Inner-scale size effect on the scintillations of light in the turbulent atmosphere,” J. Opt. Soc. Am. 73, 277–281 (1983).
    [CrossRef]
  15. V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation radius of the inhomogeneities,” Sov. Phys. JETP 48, 27–31 (1978) [Zh. Eksp. Teor. Fiz. 75, 56–65 (1978)].
  16. R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
    [CrossRef]
  17. A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensities in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 1020–1031 (1977)].
    [CrossRef]
  18. R. A. Elliott, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3322 (1979).
    [CrossRef] [PubMed]
  19. T.-i Wang, G. R. Ochs, S. F. Clifford, “A saturation resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978).
    [CrossRef]
  20. G. R. Ochs, W. D. Cartwright, “Optical system model IV for space-averaging wind and Cn2 measurements,” NOAA Tech. Memo. ERL WPL-52 (National Technical Information Service, Springfield, Va., 1980; revised 1985).
  21. G. R. Ochs, R. J. Hill, “A study of factors influencing the calibration of optical Cn2 meters,” NOAA Tech. Memo. ERL WPL-106 (National Technical Information Service, Springfield, Va., 1982).
  22. G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2430–2432 (1985).
    [CrossRef] [PubMed]

1987

1986

G. R. Ochs, S. F. Clifford, R. B. Fritz, “Observations of spherical-wave covariance in strong refractive-index turbulence,” J. Opt. Soc. Am. A 3 (13), P100–P101 (1986).

A. Consortini, E. Briccolani, G. Conforti, “Strong-scintillation statistics deteriorated due to detector saturation,” J. Opt. Soc. Am. A 3, 101–107 (1986).
[CrossRef]

1985

1984

A. K. Majumdar, “Higher-order statistics of laser-irradiance fluctuations due to turbulence,” J. Opt. Soc. Am. A 1, 1067–1074 (1984).
[CrossRef]

A. Consortini, G. Conforti, “Detector saturation effect on higher-order moments of intensity fluctuations in atmospheric laser propagation mesurement,” J. Opt. Soc. Am A 1, 1075–1077 (1984).
[CrossRef]

1983

1982

1981

R. L. Phillips, L. C. Andrews, “Measured statistics of laserlight scattering in atmospheric turbulence,” J. Opt. Soc. Am. 71, 1440–1445 (1981).
[CrossRef]

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

1979

1978

T.-i Wang, G. R. Ochs, S. F. Clifford, “A saturation resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978).
[CrossRef]

V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation radius of the inhomogeneities,” Sov. Phys. JETP 48, 27–31 (1978) [Zh. Eksp. Teor. Fiz. 75, 56–65 (1978)].

1977

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensities in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 1020–1031 (1977)].
[CrossRef]

1974

K. S. Gochelashvili, V. G. Pevgov, V. I. Shishov, “Saturation of fluctuations of the intensity of laser radiation at large distances in a turbulent atmosphere (Fraunhofer zone of transmitter),” Sov. J. Quantum Electron. 4, 632–637 (1974) [Kvantovaya Elektron. (Moscow) 1, 1156–1165 (1974)].
[CrossRef]

1969

F. V. Bunkin, K. S. Gochelashvili, “Random spatial overshoots of the field-strength when a wave travels through a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 697–702 (1969) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 875–881 (1969)].
[CrossRef]

Andrews, L. C.

Azar, Z.

E. Azoulay, Z. Azar, M. Tur, “Aperture-averaged statistics of laser intensity fluctuations in strong turbulence,” in Digest of the International Conference on Optical and Millimeter-Wave Propagation and Scattering in the Atmosphere (University of Florence, Florence, Italy, 1986), pp. 211–214.

Azoulay, E.

E. Azoulay, Z. Azar, M. Tur, “Aperture-averaged statistics of laser intensity fluctuations in strong turbulence,” in Digest of the International Conference on Optical and Millimeter-Wave Propagation and Scattering in the Atmosphere (University of Florence, Florence, Italy, 1986), pp. 211–214.

Briccolani, E.

Bunkin, F. V.

F. V. Bunkin, K. S. Gochelashvili, “Random spatial overshoots of the field-strength when a wave travels through a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 697–702 (1969) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 875–881 (1969)].
[CrossRef]

Cartwright, W. D.

G. R. Ochs, W. D. Cartwright, “Optical system model IV for space-averaging wind and Cn2 measurements,” NOAA Tech. Memo. ERL WPL-52 (National Technical Information Service, Springfield, Va., 1980; revised 1985).

Churnside, J. H.

R. J. Hill, J. H. Churnside, “Measured statistics of laser beam scintillation in strong refractive turbulence relevant to eye safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

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]

Clifford, S. F.

G. R. Ochs, S. F. Clifford, R. B. Fritz, “Observations of spherical-wave covariance in strong refractive-index turbulence,” J. Opt. Soc. Am. A 3 (13), P100–P101 (1986).

T.-i Wang, G. R. Ochs, S. F. Clifford, “A saturation resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978).
[CrossRef]

Coles, W. A.

Conforti, G.

A. Consortini, E. Briccolani, G. Conforti, “Strong-scintillation statistics deteriorated due to detector saturation,” J. Opt. Soc. Am. A 3, 101–107 (1986).
[CrossRef]

A. Consortini, G. Conforti, “Detector saturation effect on higher-order moments of intensity fluctuations in atmospheric laser propagation mesurement,” J. Opt. Soc. Am A 1, 1075–1077 (1984).
[CrossRef]

Consortini, A.

Dashen, R.

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

Elliott, R. A.

Fante, R. L.

Frehlich, R. G.

Fritz, R. B.

G. R. Ochs, S. F. Clifford, R. B. Fritz, “Observations of spherical-wave covariance in strong refractive-index turbulence,” J. Opt. Soc. Am. A 3 (13), P100–P101 (1986).

Gochelashvili, K. S.

K. S. Gochelashvili, V. G. Pevgov, V. I. Shishov, “Saturation of fluctuations of the intensity of laser radiation at large distances in a turbulent atmosphere (Fraunhofer zone of transmitter),” Sov. J. Quantum Electron. 4, 632–637 (1974) [Kvantovaya Elektron. (Moscow) 1, 1156–1165 (1974)].
[CrossRef]

F. V. Bunkin, K. S. Gochelashvili, “Random spatial overshoots of the field-strength when a wave travels through a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 697–702 (1969) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 875–881 (1969)].
[CrossRef]

Gurvich, A. S.

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensities in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 1020–1031 (1977)].
[CrossRef]

Hill, R. J.

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensities in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 1020–1031 (1977)].
[CrossRef]

Kerr, J. R.

Majumdar, A. K.

Martvel, F. E.

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensities in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 1020–1031 (1977)].
[CrossRef]

Ochs, G. R.

G. R. Ochs, S. F. Clifford, R. B. Fritz, “Observations of spherical-wave covariance in strong refractive-index turbulence,” J. Opt. Soc. Am. A 3 (13), P100–P101 (1986).

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

T.-i Wang, G. R. Ochs, S. F. Clifford, “A saturation resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978).
[CrossRef]

G. R. Ochs, W. D. Cartwright, “Optical system model IV for space-averaging wind and Cn2 measurements,” NOAA Tech. Memo. ERL WPL-52 (National Technical Information Service, Springfield, Va., 1980; revised 1985).

G. R. Ochs, R. J. Hill, “A study of factors influencing the calibration of optical Cn2 meters,” NOAA Tech. Memo. ERL WPL-106 (National Technical Information Service, Springfield, Va., 1982).

Parry, G.

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

Pevgov, V. G.

K. S. Gochelashvili, V. G. Pevgov, V. I. Shishov, “Saturation of fluctuations of the intensity of laser radiation at large distances in a turbulent atmosphere (Fraunhofer zone of transmitter),” Sov. J. Quantum Electron. 4, 632–637 (1974) [Kvantovaya Elektron. (Moscow) 1, 1156–1165 (1974)].
[CrossRef]

Phillips, R. L.

Pincus, P. A.

Shishov, V. I.

K. S. Gochelashvili, V. G. Pevgov, V. I. Shishov, “Saturation of fluctuations of the intensity of laser radiation at large distances in a turbulent atmosphere (Fraunhofer zone of transmitter),” Sov. J. Quantum Electron. 4, 632–637 (1974) [Kvantovaya Elektron. (Moscow) 1, 1156–1165 (1974)].
[CrossRef]

Tur, M.

E. Azoulay, Z. Azar, M. Tur, “Aperture-averaged statistics of laser intensity fluctuations in strong turbulence,” in Digest of the International Conference on Optical and Millimeter-Wave Propagation and Scattering in the Atmosphere (University of Florence, Florence, Italy, 1986), pp. 211–214.

Wang, T.-i

Zavorotnyi, V. U.

V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation radius of the inhomogeneities,” Sov. Phys. JETP 48, 27–31 (1978) [Zh. Eksp. Teor. Fiz. 75, 56–65 (1978)].

Appl. Opt.

Health Phys.

R. J. Hill, J. H. Churnside, “Measured statistics of laser beam scintillation in strong refractive turbulence relevant to eye safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

J. Math. Phys.

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

J. Opt. Soc. Am A

A. Consortini, G. Conforti, “Detector saturation effect on higher-order moments of intensity fluctuations in atmospheric laser propagation mesurement,” J. Opt. Soc. Am A 1, 1075–1077 (1984).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

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

Opt. Lett.

Radiophys. Quantum Electron.

F. V. Bunkin, K. S. Gochelashvili, “Random spatial overshoots of the field-strength when a wave travels through a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 697–702 (1969) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 875–881 (1969)].
[CrossRef]

A. S. Gurvich, M. A. Kallistratova, F. E. Martvel, “An investigation of strong fluctuations of light intensities in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977) [Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20, 1020–1031 (1977)].
[CrossRef]

Sov. J. Quantum Electron.

K. S. Gochelashvili, V. G. Pevgov, V. I. Shishov, “Saturation of fluctuations of the intensity of laser radiation at large distances in a turbulent atmosphere (Fraunhofer zone of transmitter),” Sov. J. Quantum Electron. 4, 632–637 (1974) [Kvantovaya Elektron. (Moscow) 1, 1156–1165 (1974)].
[CrossRef]

Sov. Phys. JETP

V. U. Zavorotnyi, “Strong fluctuations of electromagnetic waves in a random medium with finite longitudinal correlation radius of the inhomogeneities,” Sov. Phys. JETP 48, 27–31 (1978) [Zh. Eksp. Teor. Fiz. 75, 56–65 (1978)].

Other

E. Azoulay, Z. Azar, M. Tur, “Aperture-averaged statistics of laser intensity fluctuations in strong turbulence,” in Digest of the International Conference on Optical and Millimeter-Wave Propagation and Scattering in the Atmosphere (University of Florence, Florence, Italy, 1986), pp. 211–214.

G. R. Ochs, W. D. Cartwright, “Optical system model IV for space-averaging wind and Cn2 measurements,” NOAA Tech. Memo. ERL WPL-52 (National Technical Information Service, Springfield, Va., 1980; revised 1985).

G. R. Ochs, R. J. Hill, “A study of factors influencing the calibration of optical Cn2 meters,” NOAA Tech. Memo. ERL WPL-106 (National Technical Information Service, Springfield, Va., 1982).

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