Abstract

A dual-channel fiber-coupled laser heterodyne system operating at a 1.55-µm wavelength is used to investigate phase fluctuations induced on a laser beam by propagation through turbulent air. Two receivers are used to characterize spatial and temporal variations produced by a turbulent layer of air in the laboratory. The system is also used for measurements through extended turbulence along an 80-m outdoor atmospheric path. Phase structure functions, power spectral densities, and cross correlations are presented.

© 2003 Optical Society of America

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References

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  1. K. D. Ridley, S. Watson, E. Jakeman, M. Harris, “Heterodyne measurements of laser light scattering by a turbulent phase screen,” Appl. Opt. 41, 532–542 (2002).
    [CrossRef] [PubMed]
  2. M. Harris, G. Constant, C. Ward, “Continuous-wave bistatic laser Doppler wind sensor,” Appl. Opt. 40, 1501–1506 (2001).
    [CrossRef]
  3. M. Lax, “Classical noise. V. Noise in self-sustained oscillators,” Phys. Rev. 160, 290–307 (1967).
    [CrossRef]
  4. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), chap. 8, pp. 407–413.
  5. S. F. Clifford, “Temporal-frequency spectra for a spherical wave propagating through atmospheric turbulence,” J. Opt. Soc. Am. 61, 1285–1292 (1971).
    [CrossRef]
  6. U. Frisch, R. Morf, “Intermittency in non-linear dynamics and singularities at complex times,” Phys. Rev. A 23, 2673–2704 (1981).
    [CrossRef]
  7. N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
    [CrossRef]
  8. M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
    [CrossRef]
  9. X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
    [CrossRef] [PubMed]
  10. L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, Vol. PM53 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1998), p. 138.
  11. R. P. Beland, “Propagation through atmospheric turbulence,” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds., Vol. PM10 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1993), Vol. 2, Chap. 2.
  12. V. P. Lukin, V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
    [CrossRef] [PubMed]
  13. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
    [CrossRef]
  14. See Ref. 10, pp. 178–179.
  15. S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, M. H. Ackley, “Phase variations in atmospheric optical propagation,” J. Opt. Soc. Am. 61, 1279–1284 (1971).
    [CrossRef]

2002 (1)

2001 (2)

M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
[CrossRef]

M. Harris, G. Constant, C. Ward, “Continuous-wave bistatic laser Doppler wind sensor,” Appl. Opt. 40, 1501–1506 (2001).
[CrossRef]

1995 (1)

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

1990 (1)

X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
[CrossRef] [PubMed]

1981 (2)

U. Frisch, R. Morf, “Intermittency in non-linear dynamics and singularities at complex times,” Phys. Rev. A 23, 2673–2704 (1981).
[CrossRef]

V. P. Lukin, V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
[CrossRef] [PubMed]

1975 (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

1971 (2)

1967 (1)

M. Lax, “Classical noise. V. Noise in self-sustained oscillators,” Phys. Rev. 160, 290–307 (1967).
[CrossRef]

Ackley, M. H.

Andrews, L. C.

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, Vol. PM53 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1998), p. 138.

Beland, R. P.

R. P. Beland, “Propagation through atmospheric turbulence,” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds., Vol. PM10 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1993), Vol. 2, Chap. 2.

Bouricius, G. M. B.

Clifford, S. F.

Constant, G.

Cross, M. C.

M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
[CrossRef]

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Fischer, P. F.

M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
[CrossRef]

Frisch, U.

U. Frisch, R. Morf, “Intermittency in non-linear dynamics and singularities at complex times,” Phys. Rev. A 23, 2673–2704 (1981).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), chap. 8, pp. 407–413.

Greenside, H. S.

M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
[CrossRef]

Harris, M.

Jakeman, E.

Kadanoff, L.

X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
[CrossRef] [PubMed]

Konno, H.

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Lax, M.

M. Lax, “Classical noise. V. Noise in self-sustained oscillators,” Phys. Rev. 160, 290–307 (1967).
[CrossRef]

Lebchaber, A.

X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
[CrossRef] [PubMed]

Lukin, V. P.

Morf, R.

U. Frisch, R. Morf, “Intermittency in non-linear dynamics and singularities at complex times,” Phys. Rev. A 23, 2673–2704 (1981).
[CrossRef]

Ochs, G. R.

Ohtomo, N.

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Paul, M. R.

M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
[CrossRef]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, Vol. PM53 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1998), p. 138.

Pokasov, V. V.

Ridley, K. D.

Sano, M.

X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
[CrossRef] [PubMed]

Sumi, A.

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Tanaka, Y.

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Terachi, S.

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Tokiwano, K.

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Ward, C.

Watson, S.

Wu, X.-Z.

X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Phys. Soc. Jpn. (1)

N. Ohtomo, K. Tokiwano, Y. Tanaka, A. Sumi, S. Terachi, H. Konno, “Exponential characteristics of power spectral densities caused by chaotic phenomena,” J. Phys. Soc. Jpn. 64, 1104–1113 (1995).
[CrossRef]

Phys. Rev. (1)

M. Lax, “Classical noise. V. Noise in self-sustained oscillators,” Phys. Rev. 160, 290–307 (1967).
[CrossRef]

Phys. Rev. A (1)

U. Frisch, R. Morf, “Intermittency in non-linear dynamics and singularities at complex times,” Phys. Rev. A 23, 2673–2704 (1981).
[CrossRef]

Phys. Rev. Lett. (2)

M. R. Paul, M. C. Cross, P. F. Fischer, H. S. Greenside, “Power law behaviour of power spectra in low Prandtl number Rayleigh-Benard convection,” Phys. Rev. Lett. 87, 0154501 (2001).
[CrossRef]

X.-Z. Wu, L. Kadanoff, A. Lebchaber, M. Sano, “Frequency power spectrum of temperature fluctuations in free convection,” Phys. Rev. Lett. 64, 2140–2143 (1990).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Other (4)

See Ref. 10, pp. 178–179.

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, Vol. PM53 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1998), p. 138.

R. P. Beland, “Propagation through atmospheric turbulence,” in The Infrared and Electro-Optical Systems Handbook, J. S. Accetta, D. L. Shumaker, eds., Vol. PM10 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1993), Vol. 2, Chap. 2.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), chap. 8, pp. 407–413.

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Figures (9)

Fig. 1
Fig. 1

Optical layout. AOM, acousto-optic modulator; PD, photodiode; A/D, analog-to-digital converter.

Fig. 2
Fig. 2

Plot of phase structure function for the turbulent airflow. Circles, vertical separations; squares, horizontal separations.

Fig. 3
Fig. 3

Temporal cross correlation of the phase shifts at two points on the wave front for five different vertical separations. The curve for the smallest separation, r = 9 mm, has the highest value at delay time zero, and the others decrease in order down to the largest separation, r = 41 mm.

Fig. 4
Fig. 4

Delay of the phase cross-correlation peak as a function of separation distance r in the vertical direction. The fitted straight line gives a vertical speed of 0.75 m/s.

Fig. 5
Fig. 5

Values of the normalized cross correlation as a function of separation distance r in the vertical direction. The squares show the values at zero delay and the circles show the peak in the cross-correlation curves. The differences between the two give an indication of the relative importance of evolution and translation of the airflow.

Fig. 6
Fig. 6

Power spectrum of the phase derivative fluctuations plotted with both logarithmic (upper plot) and linear (lower plot) vertical axes.

Fig. 7
Fig. 7

Phase structure function for horizontal separations over the 80-m atmospheric path. The squares are measured values, the circles are values inferred from measurements of the intensity fluctuations, and the solid line is a fit of a 5/3 power law to the measured values.

Fig. 8
Fig. 8

Four phase difference spectra. The upper trace is for 450-mm probe separation, the second trace is for 30 mm, the third for 6 mm, and the lower trace is a background reading with no atmospheric fluctuations. The solid curves are fits of Eq. (7). PSD, power spectral density.

Fig. 9
Fig. 9

Histogram of intensity fluctuations. The solid curve is a log-normal probability density function.

Equations (16)

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

ϕn=ϕn-1+sgnxn-1yn-yn-1xn×arccosxn-1xn+yn-1ynxn-12+yn-12xn2+yn21/2,
E=x+iy=C+N,
CNR=|C|2|N|2,
Δθs2=12CNR.
14BCNR
Δθd=φt-φt+td.
φ0-φτ2=2|τ|tc,
ρΔθdτ=φ0-φtdφτ-φτ+td=|τ-td|+td-τtc.
SΔθdf=2 0 ρΔθdτcos2πfτdτ=1-cos2πftdtcπf2.
td<18πCNRBfFWHM1/2.
ϕx, y=k 0L nx, y, zdz,
|ϕ1-ϕ2|2=2.91k2Cn2Lr5/3,
|ϕ1-ϕ2|2=1.09k2Cn2Lr5/3.
n2=I2I2.
n2=1+0.5Cn2k7/6L11/6.
Wf=0.066Cn2k2Lν5/31-sin2πrf/ν2πrf/νf-8/3.

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