Abstract

A laser heterodyne system was used to measure the phase fluctuations imposed on a 1.5μm wavelength laser beam when double-passed over long atmospheric paths. Two distances were used: 2 and 17.5km. Results are given for intensity scintillation, phase fluctuation time series and spectra, and phase structure function. The results are found to agree well with theory: the spectrum of phase fluctuations follows the 8/3 power law predicted for Kolmogorov turbulence over 3 orders of magnitude in frequency. The methods reported here could be used to investigate large-scale temperature variations in the atmosphere.

© 2011 Optical Society of America

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References

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2010 (1)

2009 (1)

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

2003 (1)

2002 (1)

1999 (1)

1998 (1)

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

1994 (1)

1978 (1)

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

1971 (1)

1938 (1)

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London A 164, 476–490 (1938).
[CrossRef]

Acef, O.

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005).
[CrossRef]

Bryce, D.

Burris, H. R.

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Clairon, A.

Clifford, S. F.

Djerroud, K.

Gong, Z.

Harris, M.

K. D. Ridley, S. Watson, E. Jakeman, and M. Harris, “Heterodyne measurements of laser light scattering by a turbulent phase screen,” Appl. Opt. 41, 532–542 (2002).
[CrossRef] [PubMed]

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

Hill, R. J.

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[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, 1978), pp. 129–170.

Jakeman, E.

Karlsson, C.

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

Lemonde, P.

Letalick, D.

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

Liu, X.

Mahon, R.

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Man, C. N.

Moore, C. I.

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Pearson, G. N.

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005).
[CrossRef]

Rabinovich, W. S.

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Rao, R.

Ridley, K. D.

Samain, E.

Suite, M. R.

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Tatarskii, V. I.

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

Taylor, G. I.

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London A 164, 476–490 (1938).
[CrossRef]

Thomas, L. M.

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Tyler, G. A.

Vaughan, J. M.

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

Wang, S.

Watson, S.

Wolf, P.

Appl. Opt. (2)

J. Fluid Mech. (1)

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

J. Mod. Opt. (1)

M. Harris, G. N. Pearson, J. M. Vaughan, D. Letalick, and C. Karlsson, “The role of laser coherence length in continuous-wave coherent laser radar,” J. Mod. Opt. 45, 1567–1581 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Proc. R. Soc. London A (1)

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London A 164, 476–490 (1938).
[CrossRef]

Proc. SPIE (1)

R. Mahon, C. I. Moore, H. R. Burris, W. S. Rabinovich, M. R. Suite, and L. M. Thomas, “Power spectra of a free space optical link in a maritime environment,” Proc. SPIE 7464, 746407(2009).
[CrossRef]

Other (4)

E. Jakeman and K. D. Ridley, Modeling Fluctuations in Scattered Wave (Taylor and Francis, 2006).
[CrossRef]

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

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

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 2005).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Experimental layout. Solid lines are fiber optics and dotted lines electronic connections. (a) Fiber-optic receivers, (b) fiber-optic beam splitters. For clarity, the electrical path is only shown for one receiver channel, the second is identical.

Fig. 2
Fig. 2

Examples of 1 s time series of the heterodyne signal, plotted as in-phase and quadrature components. The three different plots show data taken for different atmospheric conditions: from low scintillation in (a) to high scintillation in (c).

Fig. 3
Fig. 3

Intensity histograms. Plots (a), (b), and (c) correspond to the time series shown in Fig. 2. The solid lines are least-squares fits to Eq. (3); the corresponding values of α are 15.3 for (a), 3.5 for (b), and 0.96 for (c).

Fig. 4
Fig. 4

Data from Fig. 3 replotted on a logarithmic axis to better show the behavior in the tails of the distributions.

Fig. 5
Fig. 5

Phase structure function plotted on logarithmic axes, the solid line is a fit of the 5 / 3 power law characteristic of Kolmogorov turbulence.

Fig. 6
Fig. 6

Power spectral density of phase differences for 80 mm probe separation. The solid line is the result of Eq. (4) for a spherical wave and the dotted line shows the 11 / 3 power-law line predicted as the high-frequency limit for a Gaussian beam [10].

Fig. 7
Fig. 7

Beam path for 17.5 km experiment.

Fig. 8
Fig. 8

Unwrapped phase time series of 10 min duration.

Fig. 9
Fig. 9

Power spectral density of data in Fig. 8.

Fig. 10
Fig. 10

Power spectral density of phase differences.

Fig. 11
Fig. 11

Power spectral density of phase fluctuations for the 17.5 km path under higher scintillation conditions. The solid line is a fitted power law with slope 8 / 3 .

Fig. 12
Fig. 12

Power spectral density of phase (circles) and phase differences (squares) from the same data set used for Fig. 11.

Equations (6)

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S 2 = I 2 I 2 1 ,
p ( I ) = 2 ( α β ) α + β 2 Γ ( α ) Γ ( β ) I α + β 2 1 K α β ( 2 α β I ) .
p ( I ) = 2 α 2 α Γ ( α ) 2 I α 1 K 0 ( 2 α I ) .
D φ ( x 1 x 2 ) = [ φ ( x 1 ) φ ( x 2 ) ] 2 ,
D φ ( r ) = 1.09 k 2 C n 2 L r 5 3 ,
W ( f ) = 0.033 C n 2 k 2 L v 5 3 ( 1 sin ( 2 π r f / v ) 2 π r f / v ) f 8 3 ,

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