Abstract

Numerical simulation of propagation through atmospheric turbulence of an initially spherical wave is used to calculate irradiance variance σI2, variance of log irradiance σlnI2, and mean of log irradiance 〈ln I〉 for 13 values of l 0/RF (i.e., of turbulence inner scale l 0 normalized by Fresnel scale RF) and 10 values of Rytov variance σRytov2, which is the irradiance variance, including the inner-scale effect, predicted by perturbation methods; l 0/RF was varied from 0 to 2.5 and σRytov2 from 0.06 to 5.0. The irradiance probability distribution function (PDF) and, hence, σI2, σlnI2, and 〈ln I〉 are shown to depend on only two dimensionless parameters, such as l 0/RF and σRytov2. Thus the effects of the onset of strong scintillation on the three statistics are characterized completely. Excellent agreement is obtained with previous simulations that calculated σI2. We find that σI2, σlnI2, and 〈ln I〉 are larger than their weak-scintillation asymptotes (namely, σRytov2,σRytov2, and σRytov2/2, respectively) for the onset of strong scintillation for all l 0/RF. An exception is that for the largest l 0/RF, the onset of strong scintillation causes σlnI2 to decrease relative to its weak-scintillation limit, σRytov2. We determine the efficacy of each of the three statistics for measurement of l 0, taking into account the relative difficulties of measuring each statistic. We find that measuring σI2 is most advantageous, although it is not the most sensitive to l 0 of the three statistics. All three statistics and, hence, the PDF become insensitive to l 0 for roughly 1<β02<3 (where β02 is σRytov2 for l 0 = 0); this is a condition for which retrieval of l 0 is problematic.

© 1996 Optical Society of America

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1995 (1)

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

1994 (3)

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

S. M. Flatté, C. Bracher, G. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994).
[CrossRef]

R. G. Frehlich, “The effects of global intermittency on wave propagation in random media,” Appl. Opt. 33, 5764–5769 (1994).
[CrossRef] [PubMed]

1993 (2)

1992 (5)

V. Thiermann, H. Grassl, “The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation,” Boundary-Layer Meteorol. 58, 367–389 (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]

R. Frehlich, “Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer,” J. Atmos. Sci. 49, 1494–1509 (1992).
[CrossRef]

J. Gozani, “Wave propagation in an intermittent quasi-homogeneous turbulent medium,” Opt. Lett. 17, 559–561 (1992).
[CrossRef] [PubMed]

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]

1991 (2)

A. Consortini, K. A. O’Donnell, “Beam wandering of thin parallel beams through atmospheric turbulence,” Waves Random Media 3, S11–S28 (1991).
[CrossRef]

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite-size source scintillations in a random medium,” Waves Random Media 1, 223–243 (1991).
[CrossRef]

1990 (4)

R. G. Frehlich, G. R. Ochs, “Effects of saturation on the optical scintillometer,” Appl. Opt. 29, 548–553 (1990).
[CrossRef] [PubMed]

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]

R. G. Frehlich, “Variance of focal-plane centroids,” J. Opt. Soc. Am. A 7, 2119–2140 (1990).
[CrossRef]

A. Consortini, Y. Y. Sun, L. Z. Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

1989 (3)

L. Mahrt, “Intermittency of atmospheric turbulence,” J. Atmos. Sci. 46, 79–95 (1989).
[CrossRef]

J.H. Churnside, R.G. Frehlich, “Experimental evaluation of log-normally modulated Rician and IK models of optical scintillation in the atmosphere,” J. Opt. Soc. Am. A 6, 1760–1766 (1989).
[CrossRef]

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)

N. Ben-Yosef, 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] [PubMed]

E. Goldner, N. Ben-Yosef, “Sample size influence on optical scintillation analysis. 2: Simulation approach,” Appl. Opt. 27, 2172–2177 (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]

R. G. Frehlich, “Estimation of the parameters of the atmospheric turbulence spectrum using measurements of the spatial intensity covariance,” Appl. Opt. 27, 2194–2198 (1988).
[CrossRef] [PubMed]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
[CrossRef] [PubMed]

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurements of the inner scale of turbulence,” J. Phys. D 21, 541–544 (1988).
[CrossRef]

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

1987 (4)

1986 (1)

1985 (2)

V. I. Tatarskii, V. U. Zavorotnyi, “Wave propagation in random media with fluctuating turbulent parameters,” J. Opt. Soc. Am. A 2, 2069–2076 (1985).
[CrossRef]

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

1984 (1)

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]

1982 (4)

R. J. Hill, “Theory of measuring the path-averaged inner scale of turbulence by spatial filtering of optical scintillation,” Appl. Opt. 21, 1201–1211 (1982).
[CrossRef] [PubMed]

W.A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillations in the atmosphere,” J. Opt. Soc. Am. 72, 1041–1048 (1982).
[CrossRef]

M. Tur, “Numerical solutions for the fourth moment of a plane wave propagating in a random medium,” J. Opt. Soc. Am. 72, 1683–1691 (1982).
[CrossRef]

R. J. Hill, “Theory of saturation of optical scintillation by strong turbulence: plane-wave variance and covariance and spherical-wave covariance,” J. Opt. Soc. Am. 72, 212–221 (1982).
[CrossRef]

1981 (3)

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, 675–685 (1981).
[CrossRef]

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

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

1980 (1)

A. Consortini, P. Pandolfini, C. Romanelli, R. Vanni, “Turbulence investigation of small scale by angle-of-arrival fluctuations of a laser beam,” Opt. Acta 27, 1221–1228 (1980).
[CrossRef]

1979 (2)

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

R. A. Elliot, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3323 (1979).
[CrossRef]

1978 (6)

R. J. Hill, “Optical propagation in turbulent water,” J. Opt. Soc. Am. 68, 1067–1072 (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]

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

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

R. J. Hill, G. R. Ochs, “Fine calibration of large-aperture optical scintillometers and an optical estimate of the inner scale of turbulence,” Appl. Opt. 17, 3608–3612 (1978).
[CrossRef] [PubMed]

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

1977 (2)

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

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).[Sov. Phys. JETP 46, 252–260 (1977)].

1976 (2)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

V. P. Lukin, V. L. Mironov, V. V. Pokasov, S. S. Khmelevtsov, “Optical phase measurements of refractive-index fluctuations,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 12, 550–553 (1976).[Izv. Akad. Sci. USSR Atmos. Oceanic Phys. 12, 333–335 (1976)].

1975 (3)

A. S. Gurvich, V. I. Tatarskii, “Coherence and intensity fluctuations of light in the turbulent atmosphere,” Radio Sci. 10, 3–14 (1975).
[CrossRef]

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

I. G. Yakushkin, “Asymptotic calculations of field-intensity fluctuations in a turbulent medium for long paths,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 18, 1660–1666 (1975).[Radiophys. Quantum Electron. 18, 1224–1229 (1975)].

1974 (4)

K. S. Gochelashvily, 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 transmitter2,” Kvant. Elektron. 1, 1156–1165 (1974).[Sov. J. Quantum Electron. 4, 632–637 (1974)].

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
[CrossRef]

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, “Similarity relations for strong fluctuations of light in a turbulent medium,” Zh. Eksp. Teor. Fiz. 67, 2035–2046 (1974).[Sov. Phys. JETP 40, 1011–1016 (1974)].

A. Consortini, L. Ronchi, “Laser propagation through atmospheric turbulence,” Alta Freq. 10, 769–772 (1974).

1972 (2)

P. M. Livingston, “Proposed method of inner scale measurement in a turbulent atmosphere,” Appl. Opt. 11, 684–687 (1972).
[CrossRef] [PubMed]

N. S. Time, “Estimation of the turbulence spectrum in the dissipation range from measurements of laser light fluctuations,” Atmos. Oceanic Phys. 8, 48–49 (1972).

1971 (2)

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence-function spectra,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 734–738 (1971).[Radiophys. Quantum Electron. 14, 580–583 (1971)].

V. I. Klyatskin, V. I. Tatarskii, “A new method of successive approximations in the problem of the propagation of waves in a medium having random large-scale inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 1400–1415 (1971).[Radiophys. Quantum Electron. 14, 1100–1111 (1971)].

1970 (4)

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

V. I. Klyatskin, V. I. Tatarskii, “The parabolic equation approximation for propagation of waves in a medium with random inhomogeneities,” Zh. Eksp. Teor. Fiz. 58, 624–634 (1970).[Sov. Phys. JETP 31, 335–339 (1970)].

J. W. Strohbehn, “The feasibility of laser experiments for measuring the permittivity spectrum of the turbulent atmosphere,” J. Geophys. Res. 75, 1067–1076 (1970).
[CrossRef]

D. A. Gray, A. T. Waterman, “Measurement of fine-scale atmospheric structure using an optical propagation technique,” J. Geophys. Res. 75, 1077–1083 (1970).
[CrossRef]

1969 (2)

V. I. Tatarskii, “Light propagation in a medium with random refractive index inhomogeneities in the Markov random process approximation,” Zh. Eksp. Teor. Fiz. 56, 2106–2117 (1969).[Sov. Phys. JETP 29, 1133–1138 (1969)].

V. I. Klyatskin, “Applicability of the approximation of a Markov random process in problems relating to the propagation of light in a medium with random inhomogeneities,” Zh. Eksp. Teor. Fiz. 57, 952–958 (1969).[Sov. Phys. JETP 30, 520–523 (1970)].

1968 (1)

A. S. Gurvich, “The determination of turbulence characteristics from light scattering experiments,” Atmos. Oceanic Phys. 4, 90–95 (1968).

1966 (1)

A. S. Gurvich, B. N. Meleshkin, “Determining the microscale of turbulence from light intensity fluctuations,” Izv. Akad Nauk SSSR Fiz. Atmos. Okeana 2, 688–694 (1966).[Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 2, 417–420 (1966)].

1951 (1)

C. G. Little, “A diffraction theory of the scintillation of stars on optical and radio wave-lengths,” Mon. Not. R. Astron. Soc. 111, 289–302 (1951).

1949 (1)

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

Andrews, L. C.

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

Artem’ev, A. V.

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence-function spectra,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 734–738 (1971).[Radiophys. Quantum Electron. 14, 580–583 (1971)].

Azar, Z.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurements of the inner scale of turbulence,” J. Phys. D 21, 541–544 (1988).
[CrossRef]

Z. Azar, E. Azoulay, M. Tur, “Optical bichromatic correlation method for the remote sensing of inner scale,” in Conference on Lasers and Electro-Optics, Vol. 14 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–5.

Azoulay, E.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurements of the inner scale of turbulence,” J. Phys. D 21, 541–544 (1988).
[CrossRef]

Z. Azar, E. Azoulay, M. Tur, “Optical bichromatic correlation method for the remote sensing of inner scale,” in Conference on Lasers and Electro-Optics, Vol. 14 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–5.

V. Thiermann, E. Azoulay, “A two wavelength laser scintillometer for monitoring surface layer fluxes under near neutral conditions,” in Proceedings of the International Laser Radar Conference (University of Florence, Florence, Italy) (1988), pp. 70–73.

Ben-Yosef, N.

N. Ben-Yosef, 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] [PubMed]

E. Goldner, N. Ben-Yosef, “Sample size influence on optical scintillation analysis. 2: Simulation approach,” Appl. Opt. 27, 2172–2177 (1988).
[CrossRef] [PubMed]

Bracher, C.

Briccolani, E.

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Charnotskii, M. I.

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite-size source scintillations in a random medium,” Waves Random Media 1, 223–243 (1991).
[CrossRef]

Churnside, J. H.

A. Consortini, F. Cochetti, J. H. Churnside, R. J. Hill, “Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation,” J. Opt. Soc. Am. A 10, 2354–2362 (1993).
[CrossRef]

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. 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 for strong path-integrated refractive turbulence,” J. Opt. Soc. Am. A 4, 727–733 (1987).
[CrossRef]

Churnside, J.H.

Clifford, S. F.

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, 675–685 (1981).
[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]

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

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
[CrossRef]

Cochetti, F.

Coles, W. A.

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

Coles, W.A.

W.A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillations in the atmosphere,” J. Opt. Soc. Am. 72, 1041–1048 (1982).
[CrossRef]

Conforti, G.

A. Consortini, Y. Y. Sun, L. Z. Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

A. Consortini, E. Briccolani, G. Conforti, “Strong-scintillation-statistics deterioration 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 measurements,” J. Opt. Soc. Am. A 1, 1075–1077 (1984).
[CrossRef]

A. Consortini, K. A. O’Donnell, G. Conforti, “Determination of the inner scale of atmospheric turbulence through laser beam wander,” in Optics and the Information Age (14th Congress of the International Commission for Optics), H. H. Arsenault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.813, 117–118 (1987).

Consortini, A.

A. Consortini, F. Cochetti, J. H. Churnside, R. J. Hill, “Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation,” J. Opt. Soc. Am. A 10, 2354–2362 (1993).
[CrossRef]

A. Consortini, K. A. O’Donnell, “Beam wandering of thin parallel beams through atmospheric turbulence,” Waves Random Media 3, S11–S28 (1991).
[CrossRef]

A. Consortini, Y. Y. Sun, L. Z. Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

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

A. Consortini, E. Briccolani, G. Conforti, “Strong-scintillation-statistics deterioration 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 measurements,” J. Opt. Soc. Am. A 1, 1075–1077 (1984).
[CrossRef]

A. Consortini, P. Pandolfini, C. Romanelli, R. Vanni, “Turbulence investigation of small scale by angle-of-arrival fluctuations of a laser beam,” Opt. Acta 27, 1221–1228 (1980).
[CrossRef]

A. Consortini, L. Ronchi, “Laser propagation through atmospheric turbulence,” Alta Freq. 10, 769–772 (1974).

A. Consortini, “Measurements of the angle of arrival fluctuations of a laser beam due to turbulence,” in Optical Propagation in the Atmosphere, AGARD Conf. Proc. No. 183 (National Technical Information Service, Springfield, Va., 1976), pp. 26.1–26.7.

A. Consortini, K. A. O’Donnell, G. Conforti, “Determination of the inner scale of atmospheric turbulence through laser beam wander,” in Optics and the Information Age (14th Congress of the International Commission for Optics), H. H. Arsenault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.813, 117–118 (1987).

A. Consortini, “Role of the inner scale of atmospheric turbulence in optical propagation and methods to measure it,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (Elsevier, New York, 1990), pp. 73–90.

Davis, C. A.

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

Elliot, R. A.

R. A. Elliot, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3323 (1979).
[CrossRef]

Feit, M. D.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Filice, J. P.

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

Flatté, S. M.

Fleck, J. A.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Frehlich, R.

R. Frehlich, “Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer,” J. Atmos. Sci. 49, 1494–1509 (1992).
[CrossRef]

Frehlich, R. G.

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

R. G. Frehlich, “The effects of global intermittency on wave propagation in random media,” Appl. Opt. 33, 5764–5769 (1994).
[CrossRef] [PubMed]

R. G. Frehlich, “Variance of focal-plane centroids,” J. Opt. Soc. Am. A 7, 2119–2140 (1990).
[CrossRef]

R. G. Frehlich, G. R. Ochs, “Effects of saturation on the optical scintillometer,” Appl. Opt. 29, 548–553 (1990).
[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]

R. G. Frehlich, “Estimation of the parameters of the atmospheric turbulence spectrum using measurements of the spatial intensity covariance,” Appl. Opt. 27, 2194–2198 (1988).
[CrossRef] [PubMed]

R. G. Frehlich, S. M. Wandzura, R. J. Hill, “Log-amplitude covariance for waves propagating through very strong turbulence,” J. Opt. Soc. Am. A 4, 2158–2161 (1987).
[CrossRef]

W.A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillations in the atmosphere,” J. Opt. Soc. Am. 72, 1041–1048 (1982).
[CrossRef]

Frehlich, R.G.

Fritz, R. B.

G. R. Ochs, R. B. Fritz, “Observations of spherical-wave scintillation in strong refractive-index turbulence,” NOAA Tech. Memo. ERL WPL-154 (National Technical Information Service, Springfield, Va., 1988).

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

K. S. Gochelashvily, 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 transmitter2,” Kvant. Elektron. 1, 1156–1165 (1974).[Sov. J. Quantum Electron. 4, 632–637 (1974)].

Goldner, E.

N. Ben-Yosef, 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] [PubMed]

E. Goldner, N. Ben-Yosef, “Sample size influence on optical scintillation analysis. 2: Simulation approach,” Appl. Opt. 27, 2172–2177 (1988).
[CrossRef] [PubMed]

Gomboyev, N. Ts.

N. Ts. Gomboyev, E. V. Zubritskiy, G. F. Malygina, V. L. Mironov, S. S. Khmelevtsov, “Determination of internal scale of turbulence from optical measurements,” in Proceedings of the Third All-Union Symposium on Propagation of Laser Radiation in the Atmosphere (Institute of Atmospheric Physics, Tomsk, Russia, 1975), pp. 183–184. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Gozani, J.

J. Gozani, “Wave propagation in an intermittent quasi-homogeneous turbulent medium,” Opt. Lett. 17, 559–561 (1992).
[CrossRef] [PubMed]

Gracheva, M. E.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, “Similarity relations for strong fluctuations of light in a turbulent medium,” Zh. Eksp. Teor. Fiz. 67, 2035–2046 (1974).[Sov. Phys. JETP 40, 1011–1016 (1974)].

Grassl, H.

V. Thiermann, H. Grassl, “The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation,” Boundary-Layer Meteorol. 58, 367–389 (1992).
[CrossRef]

Gray, D. A.

D. A. Gray, A. T. Waterman, “Measurement of fine-scale atmospheric structure using an optical propagation technique,” J. Geophys. Res. 75, 1077–1083 (1970).
[CrossRef]

Gurvich, A. S.

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

A. S. Gurvich, V. I. Tatarskii, “Coherence and intensity fluctuations of light in the turbulent atmosphere,” Radio Sci. 10, 3–14 (1975).
[CrossRef]

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, “Similarity relations for strong fluctuations of light in a turbulent medium,” Zh. Eksp. Teor. Fiz. 67, 2035–2046 (1974).[Sov. Phys. JETP 40, 1011–1016 (1974)].

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence-function spectra,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 734–738 (1971).[Radiophys. Quantum Electron. 14, 580–583 (1971)].

A. S. Gurvich, “The determination of turbulence characteristics from light scattering experiments,” Atmos. Oceanic Phys. 4, 90–95 (1968).

A. S. Gurvich, B. N. Meleshkin, “Determining the microscale of turbulence from light intensity fluctuations,” Izv. Akad Nauk SSSR Fiz. Atmos. Okeana 2, 688–694 (1966).[Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 2, 417–420 (1966)].

Hill, R. J.

A. Consortini, F. Cochetti, J. H. Churnside, R. J. Hill, “Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation,” J. Opt. Soc. Am. A 10, 2354–2362 (1993).
[CrossRef]

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]

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]

R. G. Frehlich, S. M. Wandzura, R. J. Hill, “Log-amplitude covariance for waves propagating through very strong turbulence,” J. Opt. Soc. Am. A 4, 2158–2161 (1987).
[CrossRef]

J. H. Churnside, R. J. Hill, “Probability density of irradiance 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 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, “Theory of measuring the path-averaged inner scale of turbulence by spatial filtering of optical scintillation,” Appl. Opt. 21, 1201–1211 (1982).
[CrossRef] [PubMed]

R. J. Hill, “Theory of saturation of optical scintillation by strong turbulence: plane-wave variance and covariance and spherical-wave covariance,” J. Opt. Soc. Am. 72, 212–221 (1982).
[CrossRef]

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, 675–685 (1981).
[CrossRef]

R. J. Hill, G. R. Ochs, “Fine calibration of large-aperture optical scintillometers and an optical estimate of the inner scale of turbulence,” Appl. Opt. 17, 3608–3612 (1978).
[CrossRef] [PubMed]

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

R. J. Hill, “Optical propagation in turbulent water,” J. Opt. Soc. Am. 68, 1067–1072 (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]

R. J. Hill, “Effects of large-scale intermittency of turbulence on scalar spectra at high wave numbers,” NOAA Tech. Memo. ERL 409-WPL 54 (National Technical Information Service, Springfield, Va., 1980).

R. J. Hill, W. D. Otto, J. R. Jordan, “Operation of the fluxes scintillometer,” NOAA Tech. Memo. ERL ETL-241 (National Technical Information Service, Springfield, Va., 1994).

Jetter, A.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurements of the inner scale of turbulence,” J. Phys. D 21, 541–544 (1988).
[CrossRef]

Jordan, J. R.

R. J. Hill, W. D. Otto, J. R. Jordan, “Operation of the fluxes scintillometer,” NOAA Tech. Memo. ERL ETL-241 (National Technical Information Service, Springfield, Va., 1994).

Kallistratova, M. A.

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

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, “Similarity relations for strong fluctuations of light in a turbulent medium,” Zh. Eksp. Teor. Fiz. 67, 2035–2046 (1974).[Sov. Phys. JETP 40, 1011–1016 (1974)].

Kerr, J. R.

R. A. Elliot, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3323 (1979).
[CrossRef]

Khmelevtsov, S. S.

V. P. Lukin, V. L. Mironov, V. V. Pokasov, S. S. Khmelevtsov, “Optical phase measurements of refractive-index fluctuations,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 12, 550–553 (1976).[Izv. Akad. Sci. USSR Atmos. Oceanic Phys. 12, 333–335 (1976)].

N. Ts. Gomboyev, E. V. Zubritskiy, G. F. Malygina, V. L. Mironov, S. S. Khmelevtsov, “Determination of internal scale of turbulence from optical measurements,” in Proceedings of the Third All-Union Symposium on Propagation of Laser Radiation in the Atmosphere (Institute of Atmospheric Physics, Tomsk, Russia, 1975), pp. 183–184. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Klyatskin, V. I.

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).[Sov. Phys. JETP 46, 252–260 (1977)].

V. I. Klyatskin, V. I. Tatarskii, “A new method of successive approximations in the problem of the propagation of waves in a medium having random large-scale inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 1400–1415 (1971).[Radiophys. Quantum Electron. 14, 1100–1111 (1971)].

V. I. Klyatskin, V. I. Tatarskii, “The parabolic equation approximation for propagation of waves in a medium with random inhomogeneities,” Zh. Eksp. Teor. Fiz. 58, 624–634 (1970).[Sov. Phys. JETP 31, 335–339 (1970)].

V. I. Klyatskin, “Applicability of the approximation of a Markov random process in problems relating to the propagation of light in a medium with random inhomogeneities,” Zh. Eksp. Teor. Fiz. 57, 952–958 (1969).[Sov. Phys. JETP 30, 520–523 (1970)].

Kohnle, A.

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurements of the inner scale of turbulence,” J. Phys. D 21, 541–544 (1988).
[CrossRef]

Lawrence, R. S.

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
[CrossRef]

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

Little, C. G.

C. G. Little, “A diffraction theory of the scintillation of stars on optical and radio wave-lengths,” Mon. Not. R. Astron. Soc. 111, 289–302 (1951).

Livingston, P. M.

P. M. Livingston, “Proposed method of inner scale measurement in a turbulent atmosphere,” Appl. Opt. 11, 684–687 (1972).
[CrossRef] [PubMed]

Lukin, I. V.

A. F. Zhukov, I. V. Lukin, R. Sh. Tsvyk, “Amplitude measurements of inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 29–32. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Lukin, V. P.

V. P. Lukin, V. L. Mironov, V. V. Pokasov, S. S. Khmelevtsov, “Optical phase measurements of refractive-index fluctuations,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 12, 550–553 (1976).[Izv. Akad. Sci. USSR Atmos. Oceanic Phys. 12, 333–335 (1976)].

Mahrt, L.

L. Mahrt, “Intermittency of atmospheric turbulence,” J. Atmos. Sci. 46, 79–95 (1989).
[CrossRef]

Malygina, G. F.

N. Ts. Gomboyev, E. V. Zubritskiy, G. F. Malygina, V. L. Mironov, S. S. Khmelevtsov, “Determination of internal scale of turbulence from optical measurements,” in Proceedings of the Third All-Union Symposium on Propagation of Laser Radiation in the Atmosphere (Institute of Atmospheric Physics, Tomsk, Russia, 1975), pp. 183–184. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Martin, J.

S. M. Flatté, G. 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]

J. Martin, “Simulation of wave propagation in random media: theory and applications,” in Wave Propagation in Random Media (Scintillation), V. I. Tatarskii, A. Ishimaru, V. U. Zavorotny, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 463–486.

Martin, J. M.

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]

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
[CrossRef] [PubMed]

Martvel’, F. E.

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

Meleshkin, B. N.

A. S. Gurvich, B. N. Meleshkin, “Determining the microscale of turbulence from light intensity fluctuations,” Izv. Akad Nauk SSSR Fiz. Atmos. Okeana 2, 688–694 (1966).[Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 2, 417–420 (1966)].

Mironov, V. L.

V. P. Lukin, V. L. Mironov, V. V. Pokasov, S. S. Khmelevtsov, “Optical phase measurements of refractive-index fluctuations,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 12, 550–553 (1976).[Izv. Akad. Sci. USSR Atmos. Oceanic Phys. 12, 333–335 (1976)].

N. Ts. Gomboyev, E. V. Zubritskiy, G. F. Malygina, V. L. Mironov, S. S. Khmelevtsov, “Determination of internal scale of turbulence from optical measurements,” in Proceedings of the Third All-Union Symposium on Propagation of Laser Radiation in the Atmosphere (Institute of Atmospheric Physics, Tomsk, Russia, 1975), pp. 183–184. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Monastyrnyy, Ye. A.

Ye. A. Monastyrnyy, G. Ya Patrushev, A. I. Petrov, V. V. Pokasov, “Method for determining the inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 26–28. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
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O’Donnell, K. A.

A. Consortini, K. A. O’Donnell, “Beam wandering of thin parallel beams through atmospheric turbulence,” Waves Random Media 3, S11–S28 (1991).
[CrossRef]

A. Consortini, K. A. O’Donnell, G. Conforti, “Determination of the inner scale of atmospheric turbulence through laser beam wander,” in Optics and the Information Age (14th Congress of the International Commission for Optics), H. H. Arsenault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.813, 117–118 (1987).

Obukhov, A. M.

A. M. Obukhov, “The 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]

R. G. Frehlich, G. R. Ochs, “Effects of saturation on the optical scintillometer,” Appl. Opt. 29, 548–553 (1990).
[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, G. R. Ochs, “Fine calibration of large-aperture optical scintillometers and an optical estimate of the inner scale of turbulence,” Appl. Opt. 17, 3608–3612 (1978).
[CrossRef] [PubMed]

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

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
[CrossRef]

G. R. Ochs, “Measurements of 0.63 μm laser-beam scintillation in strong atmospheric turbulence,” ESSA Tech. Rep. ERL 154-WPL 10 (National Technical Information Service, Springfield, Va., 1969).

G. R. Ochs, R. B. Fritz, “Observations of spherical-wave scintillation in strong refractive-index turbulence,” NOAA Tech. Memo. ERL WPL-154 (National Technical Information Service, Springfield, Va., 1988).

Otto, W. D.

R. J. Hill, W. D. Otto, J. R. Jordan, “Operation of the fluxes scintillometer,” NOAA Tech. Memo. ERL ETL-241 (National Technical Information Service, Springfield, Va., 1994).

Pandolfini, P.

A. Consortini, P. Pandolfini, C. Romanelli, R. Vanni, “Turbulence investigation of small scale by angle-of-arrival fluctuations of a laser beam,” Opt. Acta 27, 1221–1228 (1980).
[CrossRef]

Parry, G.

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

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

Petrov, A. I.

Ye. A. Monastyrnyy, G. Ya Patrushev, A. I. Petrov, V. V. Pokasov, “Method for determining the inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 26–28. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Pevgov, V. G.

K. S. Gochelashvily, 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 transmitter2,” Kvant. Elektron. 1, 1156–1165 (1974).[Sov. J. Quantum Electron. 4, 632–637 (1974)].

Phillips, R. L.

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

Pincus, P. A.

R. A. Elliot, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3323 (1979).
[CrossRef]

Ping, L. Z.

A. Consortini, Y. Y. Sun, L. Z. Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

Pokasov, V. V.

V. P. Lukin, V. L. Mironov, V. V. Pokasov, S. S. Khmelevtsov, “Optical phase measurements of refractive-index fluctuations,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 12, 550–553 (1976).[Izv. Akad. Sci. USSR Atmos. Oceanic Phys. 12, 333–335 (1976)].

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, “Similarity relations for strong fluctuations of light in a turbulent medium,” Zh. Eksp. Teor. Fiz. 67, 2035–2046 (1974).[Sov. Phys. JETP 40, 1011–1016 (1974)].

Ye. A. Monastyrnyy, G. Ya Patrushev, A. I. Petrov, V. V. Pokasov, “Method for determining the inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 26–28. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Pusey, P. N.

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

Romanelli, C.

A. Consortini, P. Pandolfini, C. Romanelli, R. Vanni, “Turbulence investigation of small scale by angle-of-arrival fluctuations of a laser beam,” Opt. Acta 27, 1221–1228 (1980).
[CrossRef]

Ronchi, L.

A. Consortini, L. Ronchi, “Laser propagation through atmospheric turbulence,” Alta Freq. 10, 769–772 (1974).

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

K. S. Gochelashvily, 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 transmitter2,” Kvant. Elektron. 1, 1156–1165 (1974).[Sov. J. Quantum Electron. 4, 632–637 (1974)].

Strohbehn, J. W.

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

J. W. Strohbehn, “The feasibility of laser experiments for measuring the permittivity spectrum of the turbulent atmosphere,” J. Geophys. Res. 75, 1067–1076 (1970).
[CrossRef]

Sun, Y. Y.

A. Consortini, Y. Y. Sun, L. Z. Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, V. U. Zavorotnyi, “Wave propagation in random media with fluctuating turbulent parameters,” J. Opt. Soc. Am. A 2, 2069–2076 (1985).
[CrossRef]

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).[Sov. Phys. JETP 46, 252–260 (1977)].

A. S. Gurvich, V. I. Tatarskii, “Coherence and intensity fluctuations of light in the turbulent atmosphere,” Radio Sci. 10, 3–14 (1975).
[CrossRef]

V. I. Klyatskin, V. I. Tatarskii, “A new method of successive approximations in the problem of the propagation of waves in a medium having random large-scale inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 1400–1415 (1971).[Radiophys. Quantum Electron. 14, 1100–1111 (1971)].

V. I. Klyatskin, V. I. Tatarskii, “The parabolic equation approximation for propagation of waves in a medium with random inhomogeneities,” Zh. Eksp. Teor. Fiz. 58, 624–634 (1970).[Sov. Phys. JETP 31, 335–339 (1970)].

V. I. Tatarskii, “Light propagation in a medium with random refractive index inhomogeneities in the Markov random process approximation,” Zh. Eksp. Teor. Fiz. 56, 2106–2117 (1969).[Sov. Phys. JETP 29, 1133–1138 (1969)].

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, Jerusalem, 1971).

Tatarskii, V.I.

V.I. Tatarskii, “Some new aspects in the problem of waves and turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

Thiermann, V.

V. Thiermann, H. Grassl, “The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation,” Boundary-Layer Meteorol. 58, 367–389 (1992).
[CrossRef]

E. Azoulay, V. Thiermann, A. Jetter, A. Kohnle, Z. Azar, “Optical measurements of the inner scale of turbulence,” J. Phys. D 21, 541–544 (1988).
[CrossRef]

V. Thiermann, E. Azoulay, “A two wavelength laser scintillometer for monitoring surface layer fluxes under near neutral conditions,” in Proceedings of the International Laser Radar Conference (University of Florence, Florence, Italy) (1988), pp. 70–73.

Time, N. S.

N. S. Time, “Estimation of the turbulence spectrum in the dissipation range from measurements of laser light fluctuations,” Atmos. Oceanic Phys. 8, 48–49 (1972).

Tsvyk, R. Sh.

A. F. Zhukov, I. V. Lukin, R. Sh. Tsvyk, “Amplitude measurements of inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 29–32. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Tur, M.

M. Tur, “Numerical solutions for the fourth moment of a plane wave propagating in a random medium,” J. Opt. Soc. Am. 72, 1683–1691 (1982).
[CrossRef]

Z. Azar, E. Azoulay, M. Tur, “Optical bichromatic correlation method for the remote sensing of inner scale,” in Conference on Lasers and Electro-Optics, Vol. 14 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–5.

Vanni, R.

A. Consortini, P. Pandolfini, C. Romanelli, R. Vanni, “Turbulence investigation of small scale by angle-of-arrival fluctuations of a laser beam,” Opt. Acta 27, 1221–1228 (1980).
[CrossRef]

Walters, D. L.

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

Wandzura, S. M.

Wang, G.

Wang, T.

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

Waterman, A. T.

D. A. Gray, A. T. Waterman, “Measurement of fine-scale atmospheric structure using an optical propagation technique,” J. Geophys. Res. 75, 1077–1083 (1970).
[CrossRef]

Ya Patrushev, G.

Ye. A. Monastyrnyy, G. Ya Patrushev, A. I. Petrov, V. V. Pokasov, “Method for determining the inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 26–28. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Yadlowsky, M.

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

Yakushkin, I. G.

I. G. Yakushkin, “Asymptotic calculations of field-intensity fluctuations in a turbulent medium for long paths,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 18, 1660–1666 (1975).[Radiophys. Quantum Electron. 18, 1224–1229 (1975)].

Zavorotnyi, V. U.

V. I. Tatarskii, V. U. Zavorotnyi, “Wave propagation in random media with fluctuating turbulent parameters,” J. Opt. Soc. Am. A 2, 2069–2076 (1985).
[CrossRef]

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

V. U. Zavorotnyi, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Zh. Eksp. Teor. Fiz. 73, 481–497 (1977).[Sov. Phys. JETP 46, 252–260 (1977)].

Zhukov, A. F.

A. F. Zhukov, I. V. Lukin, R. Sh. Tsvyk, “Amplitude measurements of inner scale of turbulence,” in Proceedings of the All-Union Symposium on Laser and Acoustic Monitoring of the Atmosphere, Part II (Institute of Atmospheric Optics, Tomsk, Russia, 1984), pp. 29–32. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Zubritskiy, E. V.

N. Ts. Gomboyev, E. V. Zubritskiy, G. F. Malygina, V. L. Mironov, S. S. Khmelevtsov, “Determination of internal scale of turbulence from optical measurements,” in Proceedings of the Third All-Union Symposium on Propagation of Laser Radiation in the Atmosphere (Institute of Atmospheric Physics, Tomsk, Russia, 1975), pp. 183–184. (English translation available from National Translation Center, Library of Congress, Washington, D.C.)

Alta Freq (1)

A. Consortini, L. Ronchi, “Laser propagation through atmospheric turbulence,” Alta Freq. 10, 769–772 (1974).

Appl. Opt (5)

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

C. A. Davis, D. L. Walters, “Atmospheric inner-scale effects on normalized irradiance variance,” Appl. Opt. 33, 8406–8411 (1994).
[CrossRef] [PubMed]

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

R. G. Frehlich, “The effects of global intermittency on wave propagation in random media,” Appl. Opt. 33, 5764–5769 (1994).
[CrossRef] [PubMed]

R. A. Elliot, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3323 (1979).
[CrossRef]

Appl. Opt (9)

J. M. Martin, S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
[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. G. Frehlich, G. R. Ochs, “Effects of saturation on the optical scintillometer,” Appl. Opt. 29, 548–553 (1990).
[CrossRef] [PubMed]

R. G. Frehlich, “Estimation of the parameters of the atmospheric turbulence spectrum using measurements of the spatial intensity covariance,” Appl. Opt. 27, 2194–2198 (1988).
[CrossRef] [PubMed]

R. J. Hill, “Theory of measuring the path-averaged inner scale of turbulence by spatial filtering of optical scintillation,” Appl. Opt. 21, 1201–1211 (1982).
[CrossRef] [PubMed]

R. J. Hill, G. R. Ochs, “Fine calibration of large-aperture optical scintillometers and an optical estimate of the inner scale of turbulence,” Appl. Opt. 17, 3608–3612 (1978).
[CrossRef] [PubMed]

P. M. Livingston, “Proposed method of inner scale measurement in a turbulent atmosphere,” Appl. Opt. 11, 684–687 (1972).
[CrossRef] [PubMed]

N. Ben-Yosef, 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] [PubMed]

E. Goldner, N. Ben-Yosef, “Sample size influence on optical scintillation analysis. 2: Simulation approach,” Appl. Opt. 27, 2172–2177 (1988).
[CrossRef] [PubMed]

Appl. Phys (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Atmos. Oceanic Phys (2)

A. S. Gurvich, “The determination of turbulence characteristics from light scattering experiments,” Atmos. Oceanic Phys. 4, 90–95 (1968).

N. S. Time, “Estimation of the turbulence spectrum in the dissipation range from measurements of laser light fluctuations,” Atmos. Oceanic Phys. 8, 48–49 (1972).

Boundary-Layer Meteorol (1)

V. Thiermann, H. Grassl, “The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation,” Boundary-Layer Meteorol. 58, 367–389 (1992).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Radiofiz (1)

V. I. Klyatskin, V. I. Tatarskii, “A new method of successive approximations in the problem of the propagation of waves in a medium having random large-scale inhomogeneities,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 1400–1415 (1971).[Radiophys. Quantum Electron. 14, 1100–1111 (1971)].

Izv. Akad Nauk SSSR Fiz. Atmos. Okeana (1)

A. S. Gurvich, B. N. Meleshkin, “Determining the microscale of turbulence from light intensity fluctuations,” Izv. Akad Nauk SSSR Fiz. Atmos. Okeana 2, 688–694 (1966).[Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 2, 417–420 (1966)].

Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana (1)

V. P. Lukin, V. L. Mironov, V. V. Pokasov, S. S. Khmelevtsov, “Optical phase measurements of refractive-index fluctuations,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 12, 550–553 (1976).[Izv. Akad. Sci. USSR Atmos. Oceanic Phys. 12, 333–335 (1976)].

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

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

Izv. Vyssh. Uchebn. Zaved. Radiofiz (1)

A. V. Artem’ev, A. S. Gurvich, “Experimental study of coherence-function spectra,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 14, 734–738 (1971).[Radiophys. Quantum Electron. 14, 580–583 (1971)].

Izv. Vyssh. Uchebn. Zaved. Radiofiz (2)

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

I. G. Yakushkin, “Asymptotic calculations of field-intensity fluctuations in a turbulent medium for long paths,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 18, 1660–1666 (1975).[Radiophys. Quantum Electron. 18, 1224–1229 (1975)].

J. Opt. Soc. Am (1)

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

J. Atmos. Sci (2)

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A. Consortini, “Role of the inner scale of atmospheric turbulence in optical propagation and methods to measure it,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (Elsevier, New York, 1990), pp. 73–90.

A. Consortini, “Measurements of the angle of arrival fluctuations of a laser beam due to turbulence,” in Optical Propagation in the Atmosphere, AGARD Conf. Proc. No. 183 (National Technical Information Service, Springfield, Va., 1976), pp. 26.1–26.7.

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R. J. Hill, W. D. Otto, J. R. Jordan, “Operation of the fluxes scintillometer,” NOAA Tech. Memo. ERL ETL-241 (National Technical Information Service, Springfield, Va., 1994).

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Figures (5)

Fig. 1
Fig. 1

(a) σ I 2 is shown versus σ Rytov 2 . From top to bottom, the order of the curves corresponds to the values of l 0/RF from top to bottom in the legend. The straight solid line shows σ I 2 = σ Rytov 2 . (b) Similar to (a) but showing larger values of σ Rytov 2 . The circles are values from Fig. (a). The curves connect points calculated by Flatté et al. 35 From top to bottom, the circles and curves are in the same order as the values of l 0/RF in the legend.

Fig. 2
Fig. 2

σ ln I 2 versus σ Rytov 2 . From top to bottom along the far right edge, the order of the curves is the same as the order of the values of l 0/RF in the legend. The straight solid line shows σ ln I 2 = σ Rytov 2 .

Fig. 3
Fig. 3

Mean of log irradiance is shown versus σ Rytov 2 . From top to bottom, the order of the curves is the same as the order of the values of l 0/RF in the legend. The solid curve shows ln I = σ Rytov 2 / 2 .

Fig. 4
Fig. 4

(a) Scaled irradiance variance versus β0. (b) Scaled log-irradiance variance versus β0. (c) Scaled mean of log irradiance versus β0. The legend gives the values of l 0/RF from top to bottom that correspond to the curves from top to bottom on the left-hand side of the figure.

Fig. 5
Fig. 5

Ratio of the variance of log irradiance when the heuristic theory is used to the variance of log irradiance from simulations. The legend gives the values of l 0/RF from top to bottom that correspond to the curves from top to bottom at σ Rytov 2 = 1 .

Equations (8)

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

σ I 2 = ( I 1 ) 2 ,
ln I ,
σ ln I 2 = ( ln I ln I ) 2 .
σ Rytov 2 = σ I 2 = σ ln I 2 = 2 ln I .
Φ n ( κ ) = 0 . 033 C n 2 κ 11 / 3 f ( κ l 0 ) .
σ Rytov 2 = β 0 2 σ ˜ 2 ( l 0 / R F ) ,
β 0 2 = 0 . 496 k 7 / 6 L 11 / 6 C n 2 ,
σ ˜ 2 ( l 0 / R F ) = 10 . 5 0 1 d u 0 d x x 8 / 3 f ( x l 0 / R F )                     × sin 2 [ x 2 u ( 1 u ) / 2 ] .

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