Abstract

It has been widely accepted and taken for granted that when a light wave propagates through a locally isotropic turbulent atmosphere the temporal-frequency spectra of the log-amplitude, phase, and angle-of-arrival fluctuations at high frequency have a power law behavior with a scaling index -8/3. However, our experimental results with laser irradiance fluctuation show that if the high-frequency temporal spectrum is fitted to a power law, the scaling index deviates from -8/3 in many cases. Thus we take a new look at the wave propagation theory through numerical evaluation, using Kolmogorov, von Kármán, Hill, and Frehlich turbulence spectrum models. It is found that the main contribution of the turbulence spectrum to the wave log-amplitude, phase, and phase-difference high-frequency temporal spectra is in the dissipation range rather than in the inertial range. Consequently, the turbulence inner scale plays an important role in the wave temporal spectra. The larger the inner scale and the smaller the wind velocity, the more noticeable the effect of the turbulence spectrum in the dissipation range on the wave temporal spectra.

© 1999 Optical Society of America

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References

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1999 (1)

R. Rao, S. Wang, X. Liu, “Characteristics of the power spectrum of laser irradiance scintillation in a real atmosphere,” Chin. J. Lasers A26, 411–414 (1999).

1998 (1)

1997 (2)

1995 (1)

1994 (1)

1993 (1)

1992 (2)

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

D. S. Acton, R. J. Sharbaugh, J. R. Roehrig, D. Tiszauer, “Wave-front tilt power spectral density from image motion of solar pores,” Appl. Opt. 31, 4280–4284 (1992).
[CrossRef] [PubMed]

1983 (1)

1978 (3)

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

V. I. Tatarskii, M. M. Dubovikov, A. A. Praskovsky, M. Yu. Karyakin, “Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow,” J. Fluid Mech. 238, 683–698 (1978).
[CrossRef]

1976 (2)

D. P. Greenwood, D. L. Fried, “Power spectra requirements for wave-front-compensative systems,” J. Opt. Soc. Am. 66, 193–206 (1976).
[CrossRef]

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

1975 (1)

P. Sulem, U. Frisch, “Bounds on energy flux for finite energy turbulence,” J. Fluid Mech. 72, 417–423 (1975).
[CrossRef]

1972 (1)

1971 (1)

1970 (1)

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

Acton, D. S.

Agabi, A.

Aitken, G. J. M.

Avila, R.

Borgnino, J.

Butts, R. R.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Clifford, S. F.

Collins, S. A.

Conan, J.-M.

Davis, C. A.

Dubovikov, M. M.

V. I. Tatarskii, M. M. Dubovikov, A. A. Praskovsky, M. Yu. Karyakin, “Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow,” J. Fluid Mech. 238, 683–698 (1978).
[CrossRef]

Fante, R. L.

Frehlich, R.

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

Fried, D. L.

Frisch, U.

P. Sulem, U. Frisch, “Bounds on energy flux for finite energy turbulence,” J. Fluid Mech. 72, 417–423 (1975).
[CrossRef]

Graves, J. E.

Greenwood, D. P.

Hill, R. J.

Hogge, C. B.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Ishimaru, A.

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), pp. 129–170.

Karyakin, M. Yu.

V. I. Tatarskii, M. M. Dubovikov, A. A. Praskovsky, M. Yu. Karyakin, “Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow,” J. Fluid Mech. 238, 683–698 (1978).
[CrossRef]

Lawrence, R. S.

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

Liu, X.

R. Rao, S. Wang, X. Liu, “Characteristics of the power spectrum of laser irradiance scintillation in a real atmosphere,” Chin. J. Lasers A26, 411–414 (1999).

Madec, P.-Y.

Martin, F.

McGaughey, D. R.

Mckenna, D. L.

Monin, A. S.

A. S. Monin, A. M. Yaglom, Statistical Fluid Mechanics, Vol. 2 (MIT Press, New York, 1975).

Northcott, M. J.

Praskovsky, A. A.

V. I. Tatarskii, M. M. Dubovikov, A. A. Praskovsky, M. Yu. Karyakin, “Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow,” J. Fluid Mech. 238, 683–698 (1978).
[CrossRef]

Rao, R.

R. Rao, S. Wang, X. Liu, “Characteristics of the power spectrum of laser irradiance scintillation in a real atmosphere,” Chin. J. Lasers A26, 411–414 (1999).

Reinhardt, G. W.

Roddier, F.

Roehrig, J. R.

Roggemann, M. C.

Rousset, G.

Sharbaugh, R. J.

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, Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978).

Sulem, P.

P. Sulem, U. Frisch, “Bounds on energy flux for finite energy turbulence,” J. Fluid Mech. 72, 417–423 (1975).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Waves Propagating in a Turbulent Atmosphere (Nauka, Moscow, 1967).

Tatarskii, V. I.

V. I. Tatarskii, M. M. Dubovikov, A. A. Praskovsky, M. Yu. Karyakin, “Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow,” J. Fluid Mech. 238, 683–698 (1978).
[CrossRef]

Tiszauer, D.

Walters, D. L.

Wang, S.

R. Rao, S. Wang, X. Liu, “Characteristics of the power spectrum of laser irradiance scintillation in a real atmosphere,” Chin. J. Lasers A26, 411–414 (1999).

Welsh, B. M.

Whiteley, M. R.

Yaglom, A. M.

A. S. Monin, A. M. Yaglom, Statistical Fluid Mechanics, Vol. 2 (MIT Press, New York, 1975).

Ziad, A.

Appl. Opt. (2)

Chin. J. Lasers (1)

R. Rao, S. Wang, X. Liu, “Characteristics of the power spectrum of laser irradiance scintillation in a real atmosphere,” Chin. J. Lasers A26, 411–414 (1999).

IEEE Trans. Antennas Propag. (1)

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wave-front distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

J. Atmos. Sci. (1)

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

J. Fluid Mech. (3)

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

P. Sulem, U. Frisch, “Bounds on energy flux for finite energy turbulence,” J. Fluid Mech. 72, 417–423 (1975).
[CrossRef]

V. I. Tatarskii, M. M. Dubovikov, A. A. Praskovsky, M. Yu. Karyakin, “Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow,” J. Fluid Mech. 238, 683–698 (1978).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (5)

Proc. IEEE (1)

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

Other (4)

V. I. Tatarski, Waves Propagating in a Turbulent Atmosphere (Nauka, Moscow, 1967).

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, Berlin, 1978), pp. 129–170.

A. S. Monin, A. M. Yaglom, Statistical Fluid Mechanics, Vol. 2 (MIT Press, New York, 1975).

J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978).

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Figures (11)

Fig. 1
Fig. 1

Example of fitting the log-intensity fluctuation spectrum of laser irradiance in the atmosphere into five straight segments. Seg-3 corresponds to the scaling region, and its absolute slope is taken as the scaling index α.

Fig. 2
Fig. 2

Diurnal variation of the scaling index α of the log-intensity spectrum of a diverged 0.6328-μm laser propagating 1000 m in the atmosphere. Experiments were carried out from 9:00 on October 15 to 9:00 on October 16, 1998.

Fig. 3
Fig. 3

Schematic diagram showing the contribution of the turbulence spectrum to the wave temporal spectra. The contribution of the turbulence spectrum at the spatial wave number located in the light-gray region is neglected, and the integration evaluation is performed with the turbulence spectrum at the spatial wave number located in the moderate-gray and dark regions. The dark region corresponds to the turbulence inertial range. l0=1 mm, L0=1 m, and ν=1 m/s.

Fig. 4
Fig. 4

Integrand in the log-amplitude temporal spectrum for f=1, 10, 100, and 1000 Hz. The Frehlich spectrum is used, with l0=1 mm and f0=10.

Fig. 5
Fig. 5

Integrand in the phase temporal spectrum. Conditions are the same as for Fig. 4.

Fig. 6
Fig. 6

Wave log-amplitude, phase, and phase-difference temporal spectra evaluated with the Kolmogorov turbulence model. Parameters are shown in the figure.

Fig. 7
Fig. 7

Wave log-amplitude, phase, and phase-difference temporal spectra evaluated with the Hill turbulence model. l0=1 mm; other parameters are shown in the figure.

Fig. 8
Fig. 8

Wave log-amplitude, phase, and phase-difference temporal spectra evaluated with the Hill turbulence model. l0=2 mm; other parameters are shown in the figure.

Fig. 9
Fig. 9

Wave log-amplitude, phase, and phase-difference temporal spectra evaluated with the Frehlich turbulence model. f0=40/s; other parameters are shown in the figure.

Fig. 10
Fig. 10

Wave log-amplitude, phase, and phase-difference temporal spectra evaluated with the Frehlich turbulence model. f0=20/s; other parameters are shown in the figure.

Fig. 11
Fig. 11

The temporal spectrum of the log-intensity fluctuation of a 0.6328-μm laser radiation propagating 1000 m through the atmosphere.

Equations (16)

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Vn(K)K-η,
Φn(K)K-(η+2).
FA(K, 0)1-λ2K4π2L sin 4π2Lλ2KK-(η+2),
Wfln I(f )f-α,α=η+1,
Wχ,S(f )=8π2k20Ldz2πf/vdK KΦn(K)[(Kv)2-(2πf )2]1/2×1cosK2z(L-z)kL,
WδS(f )=32π2k20Ldz sin2πρfzvL×2πf/vdK KΦn(K)[(Kv)2-(2πf )2]1/2×1+cosK2z(L-z)kL.
Wχ,S(f )=8π2k2 2πfLv2 01dx Φn(x, f )[1±I2(x, f )]x21-x2,
WδS(f )=32π2k2 2πfLv201dx Φn(x, f )[I1(f )+I2(x, f )/2-(I3(x, f )+I4(x, f ))/8]x21-x2,
I1(f )=[1-sin(b)/b]/2,
I2(x, f )=2πa cosa4Ca2π+sina4Sa2π,
I3(x, f )=2πacos(b+a)24a+cos(b-a)24a×Ca2π 1+ba+Ca2π 1-ba,
I4(x, f )=2πa sin(b+a)24a+sin(b-a)24a×Sa2π 1+ba+Sa2π 1-ba,
Φn(K)=0.033Cn2K-11/3f(Kl0).
f(x)=1.
f(x)=n=04anxnexp(-δx),
f(x)=[1+l02/(L0x)2]exp[-(x/5.92)2].

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