Abstract

The temporal cross-correlation function of the angle-of-arrival (AOA) fluctuations of two optical waves propagating through atmospheric turbulence carries information regarding the average wind velocity transverse to the propagation path. We present and discuss two estimators for the retrieval of the path-averaged beam-transverse horizontal wind velocity, vt. Both methods retrieve vt from the temporal cross-correlation function of AOA fluctuations obtained from two closely spaced light-emitting diodes (LEDs). The first method relies on the time delay of the peak (TDP) of the cross-correlation function, and the second method exploits its slope at zero lag (SZL). Over a 9 h period during which vt varied between 1.3ms1 and 2.0ms1, the maximum rms difference between optically retrieved and in situ measured 10 s estimates of vt was found to be 0.18ms1 for the TDP estimator and 0.23ms1 for the SZL estimator. Applicability and limitations of these two optical wind retrieval techniques are discussed.

© 2012 Optical Society of America

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References

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  1. B. H. Briggs and M. Spencer, “Horizontal movements in the ionosphere,” Rep. Prog. Phys. 17, 245–280 (1954).
    [CrossRef]
  2. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  3. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translation, 1971).
  4. Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
    [CrossRef]
  5. R. S. Lawrence and J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1545 (1970).
    [CrossRef]
  6. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, “Use of scintillations to measure average wind across a light beam,” Appl. Opt. 11, 239–243 (1972).
    [CrossRef]
  7. S. F. Clifford, G. R. Ochs, and T. I. Wang, “Optical wind sensing by observing scintillations of a random scene,” Appl. Opt. 14, 2844–2850 (1975).
    [CrossRef]
  8. A. S. Gurvich, M. A. Kallistratova, and N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Radiophys. Quantum Electron. 11, 771–776 (1968).
    [CrossRef]
  9. S. F. Clifford, “Temporal-frequency spectra for a spherical wave propagating through atmospheric turbulence,” J. Opt. Soc. Am. 61, 1285–1292 (1971).
    [CrossRef]
  10. Y. Cheon, V. Hohreiter, M. Behn, and A. Muschinski, “Angle-of-arrival anemometry by means of a large-aperture Schmidt–Cassegrain telescope equipped with a CCD camera,” J. Opt. Soc. Am. A 24, 3478–3492 (2007).
    [CrossRef]
  11. A. D. Wheelon, Electromagnetic Scintillation—I. Geometrical Optics (Cambridge University, 2001).
  12. G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. A 164, 476–490 (1938).
    [CrossRef]
  13. L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. VIII, 261–274 (1879).
  14. M. Behn, V. Hohreiter, and A. Muschinski, “A scalable data-logging system with serial interfaces and integrated GPS time-stamping,” J. Atmos. Ocean. Technol. 25, 1568–1578 (2008).
    [CrossRef]
  15. A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, vol. 25 of Topics in Applied Physics, J. W. Strohbehn, ed. (Springer, 1978), pp. 129–170.
  16. R. J. Lataitis, S. F. Clifford, and C. L. Holloway, “An alternative method for inferring winds from spaced-antenna radar measurements,” Radio Sci. 30, 463–474 (1995).
    [CrossRef]
  17. J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
    [CrossRef]
  18. B. H. Briggs, “On the analysis of moving patterns in geophysics—I. Correlation analysis,” J. Atmos. Terr. Phys. 30, 1777–1788 (1968).
    [CrossRef]
  19. T. I. Wang, G. R. Ochs, and R. S. Lawrence, “Wind measurements by the temporal cross-correlation of the optical scintillations,” Appl. Opt. 20, 4073–4081 (1981).
    [CrossRef]
  20. S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, 1978), pp. 9–43.

2008

M. Behn, V. Hohreiter, and A. Muschinski, “A scalable data-logging system with serial interfaces and integrated GPS time-stamping,” J. Atmos. Ocean. Technol. 25, 1568–1578 (2008).
[CrossRef]

2007

1995

R. J. Lataitis, S. F. Clifford, and C. L. Holloway, “An alternative method for inferring winds from spaced-antenna radar measurements,” Radio Sci. 30, 463–474 (1995).
[CrossRef]

1981

1975

1972

1971

S. F. Clifford, “Temporal-frequency spectra for a spherical wave propagating through atmospheric turbulence,” J. Opt. Soc. Am. 61, 1285–1292 (1971).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
[CrossRef]

1970

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

1968

B. H. Briggs, “On the analysis of moving patterns in geophysics—I. Correlation analysis,” J. Atmos. Terr. Phys. 30, 1777–1788 (1968).
[CrossRef]

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Radiophys. Quantum Electron. 11, 771–776 (1968).
[CrossRef]

1954

B. H. Briggs and M. Spencer, “Horizontal movements in the ionosphere,” Rep. Prog. Phys. 17, 245–280 (1954).
[CrossRef]

1938

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

1879

L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. VIII, 261–274 (1879).

Barabanenkov, Y. N.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
[CrossRef]

Behn, M.

M. Behn, V. Hohreiter, and A. Muschinski, “A scalable data-logging system with serial interfaces and integrated GPS time-stamping,” J. Atmos. Ocean. Technol. 25, 1568–1578 (2008).
[CrossRef]

Y. Cheon, V. Hohreiter, M. Behn, and A. Muschinski, “Angle-of-arrival anemometry by means of a large-aperture Schmidt–Cassegrain telescope equipped with a CCD camera,” J. Opt. Soc. Am. A 24, 3478–3492 (2007).
[CrossRef]

Bradley, E. F.

J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

Briggs, B. H.

B. H. Briggs, “On the analysis of moving patterns in geophysics—I. Correlation analysis,” J. Atmos. Terr. Phys. 30, 1777–1788 (1968).
[CrossRef]

B. H. Briggs and M. Spencer, “Horizontal movements in the ionosphere,” Rep. Prog. Phys. 17, 245–280 (1954).
[CrossRef]

Businger, J. A.

J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

Cheon, Y.

Clifford, S. F.

R. J. Lataitis, S. F. Clifford, and C. L. Holloway, “An alternative method for inferring winds from spaced-antenna radar measurements,” Radio Sci. 30, 463–474 (1995).
[CrossRef]

S. F. Clifford, G. R. Ochs, and T. I. Wang, “Optical wind sensing by observing scintillations of a random scene,” Appl. Opt. 14, 2844–2850 (1975).
[CrossRef]

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, “Use of scintillations to measure average wind across a light beam,” Appl. Opt. 11, 239–243 (1972).
[CrossRef]

S. F. Clifford, “Temporal-frequency spectra for a spherical wave propagating through atmospheric turbulence,” J. Opt. Soc. Am. 61, 1285–1292 (1971).
[CrossRef]

S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, 1978), pp. 9–43.

Gurvich, A. S.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Radiophys. Quantum Electron. 11, 771–776 (1968).
[CrossRef]

Hohreiter, V.

M. Behn, V. Hohreiter, and A. Muschinski, “A scalable data-logging system with serial interfaces and integrated GPS time-stamping,” J. Atmos. Ocean. Technol. 25, 1568–1578 (2008).
[CrossRef]

Y. Cheon, V. Hohreiter, M. Behn, and A. Muschinski, “Angle-of-arrival anemometry by means of a large-aperture Schmidt–Cassegrain telescope equipped with a CCD camera,” J. Opt. Soc. Am. A 24, 3478–3492 (2007).
[CrossRef]

Holloway, C. L.

R. J. Lataitis, S. F. Clifford, and C. L. Holloway, “An alternative method for inferring winds from spaced-antenna radar measurements,” Radio Sci. 30, 463–474 (1995).
[CrossRef]

Ishimaru, A.

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, vol. 25 of Topics in Applied Physics, J. W. Strohbehn, ed. (Springer, 1978), pp. 129–170.

Izumi, Y.

J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Radiophys. Quantum Electron. 11, 771–776 (1968).
[CrossRef]

Kravtsov, Y. A.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
[CrossRef]

Lataitis, R. J.

R. J. Lataitis, S. F. Clifford, and C. L. Holloway, “An alternative method for inferring winds from spaced-antenna radar measurements,” Radio Sci. 30, 463–474 (1995).
[CrossRef]

Lawrence, R. S.

Muschinski, A.

M. Behn, V. Hohreiter, and A. Muschinski, “A scalable data-logging system with serial interfaces and integrated GPS time-stamping,” J. Atmos. Ocean. Technol. 25, 1568–1578 (2008).
[CrossRef]

Y. Cheon, V. Hohreiter, M. Behn, and A. Muschinski, “Angle-of-arrival anemometry by means of a large-aperture Schmidt–Cassegrain telescope equipped with a CCD camera,” J. Opt. Soc. Am. A 24, 3478–3492 (2007).
[CrossRef]

Ochs, G. R.

Rayleigh, L.

L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. VIII, 261–274 (1879).

Rytov, S. M.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
[CrossRef]

Spencer, M.

B. H. Briggs and M. Spencer, “Horizontal movements in the ionosphere,” Rep. Prog. Phys. 17, 245–280 (1954).
[CrossRef]

Strohbehn, J. W.

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

Tatarskii, V. I.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
[CrossRef]

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translation, 1971).

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. A 164, 476–490 (1938).
[CrossRef]

Time, N. S.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Radiophys. Quantum Electron. 11, 771–776 (1968).
[CrossRef]

Wang, T. I.

Wheelon, A. D.

A. D. Wheelon, Electromagnetic Scintillation—I. Geometrical Optics (Cambridge University, 2001).

Wyngaard, J. C.

J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

Appl. Opt.

J. Atmos. Ocean. Technol.

M. Behn, V. Hohreiter, and A. Muschinski, “A scalable data-logging system with serial interfaces and integrated GPS time-stamping,” J. Atmos. Ocean. Technol. 25, 1568–1578 (2008).
[CrossRef]

J. Atmos. Sci.

J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,” J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

J. Atmos. Terr. Phys.

B. H. Briggs, “On the analysis of moving patterns in geophysics—I. Correlation analysis,” J. Atmos. Terr. Phys. 30, 1777–1788 (1968).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Philos. Mag.

L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. VIII, 261–274 (1879).

Proc. IEEE

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

Proc. R. Soc. A

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

Radio Sci.

R. J. Lataitis, S. F. Clifford, and C. L. Holloway, “An alternative method for inferring winds from spaced-antenna radar measurements,” Radio Sci. 30, 463–474 (1995).
[CrossRef]

Radiophys. Quantum Electron.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Radiophys. Quantum Electron. 11, 771–776 (1968).
[CrossRef]

Rep. Prog. Phys.

B. H. Briggs and M. Spencer, “Horizontal movements in the ionosphere,” Rep. Prog. Phys. 17, 245–280 (1954).
[CrossRef]

Sov. Phys. Usp.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sov. Phys. Usp. 13, 551–575 (1971).
[CrossRef]

Other

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

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translation, 1971).

A. D. Wheelon, Electromagnetic Scintillation—I. Geometrical Optics (Cambridge University, 2001).

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, vol. 25 of Topics in Applied Physics, J. W. Strohbehn, ed. (Springer, 1978), pp. 129–170.

S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, 1978), pp. 9–43.

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Figures (9)

Fig. 1.
Fig. 1.

Side view of the experimental setup at the BAO site near Erie, Colorado. The length of the optical propagation path was 182 m, at the ends of which were placed a telescope with an aperture diameter of 36 cm and a rectangular array of LED lights at 1.77 m above ground level (AGL). Also placed along the propagation path were two towers equipped with sonics mounted at levels between 1.45 m and 4.84 m AGL.

Fig. 2.
Fig. 2.

Photograph of Tower 1. Each of the six equally spaced crossbars has a sonic mounted on the right-hand side. The center of the lowermost sonic’s measurement volume is at 1.43 m AGL, and that of the uppermost sonic is at 4.84 m AGL. Additional equipment includes a GPS receiver mounted on the other end of the lowest crossbar and two wind-noise filters (on the second and fifth crossbar) connected to two quartz-crystal barometers contained in the gray boxes attached to the tripod. The white box lying beside the base of the tower contains the data-logger, which records the sonic and barometer data and time-stamps them by means of the GPS signal.

Fig. 3.
Fig. 3.

A 1 h long segment of the vertical (α1) and the horizontal (β1) AOAs obtained from images of test light #1 (i.e., the lower left test light as seen from the telescope). Both signals have their means removed and represent 10 s averages.

Fig. 4.
Fig. 4.

A 3 s long time series of the horizontal AOAs from the lower left (β1) and lower right (β2) test lights, beginning at 0403:05 MDT. It can be clearly seen that β2 is delayed with respect to β1 by typically 0.1 s, which can be attributed to wind blowing across the lights from west to east.

Fig. 5.
Fig. 5.

The AOA cross-correlation function between β1 and β2. The TDP, τp, was obtained by finding the maximum of the parabolic approximation (solid curve around the AOA cross-correlation peak) of the AOA cross-correlation function around the peak. The SZL was obtained by finding the slope of the tangent (solid line around τ=0) by approximating the AOA cross-correlation function around zero lag with a third-degree polynomial.

Fig. 6.
Fig. 6.

Time series of optical retrievals (dotted line) and sonic measurements (solid line) of the beam-transverse component of the wind velocity. Both time series show 10 s estimates at the height of the propagation path (1.77 m AGL). While the optical measurements represent (nonuniformly weighted) path averages along the 182 m long propagation path, the sonic measurements represent averages of the outputs from the two lowermost sonics (1.45 and 2.13 m AGL) mounted on Tower 1, located 47 m away from the telescope. The optical estimates were obtained by using the TDP estimator.

Fig. 7.
Fig. 7.

Scatter plot of the optical (TDP method) retrievals and the sonic measurements of the horizontal wind velocities shown in Fig. 6.

Fig. 8.
Fig. 8.

Same as Fig. 6, except that the optical retrievals were obtained by using the SZL estimator.

Fig. 9.
Fig. 9.

Scatter plot of the optical (SZL method) retrievals and the sonic measurements of the horizontal wind velocities shown in Fig. 8.

Tables (2)

Tables Icon

Table 1. Standard Deviations of Beam-Transverse Velocity Measurements Presented in Figs. 6 and 7: (a) 10 s Sonic Averages, (b) 10 s Optical Retrievals Obtained by Using the TDP Estimator, (c) Differences Between 10 s Optical and Sonic Measurementsa

Tables Icon

Table 2. Standard Deviations of Beam-Transverse Velocity Measurements Presented in Figs. 8 and 9: (a) 10 s Sonic Averages, (b) 10 s Optical Retrievals Obtained by Using the SZL Estimator, and (c) Differences Between 10 s Optical and Sonic Measurementsa

Equations (26)

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dds(n(r⃗)dr⃗ds)=[n(r⃗)],
γ⃗=TRn˜(x,y,z;t)ds,
β(y;t)=x=0Ln˜(x,yxL;t)ydx.
Bβ1β2(y,y;τ)=x=0Lx=0Ln˜(x,yxL;t)yn˜(x,yxL;t+τ)ydxdx.
n˜(x,yxL;t)yn˜(x,yxL;t+τ)y=δ(xx)F(yy;τ),
F(yy;τ)=x=0Ln˜(x,yxL;t)yn˜(x,yxL;t+τ)ydx.
n˜(x,yxL;t+τ)y=n˜(x,yxLvyτ;t)y,
F(yy;τ)=x=0Ln˜(x,yxL;t)yn˜(x,yxLvyτ;t)ydx.
Bβ1β2(y,y;τ)=x=0Lx=0Ln˜(x,yxL;t)yn˜(x,yxLvyτ;t)yδ(xx)dxdx.
Cβ1β2[m]=1L1i=1Lβ˜1[i]β˜2[i+m]σβ12σβ22,
vt,TDP=γTDPdτp,
vt,SZL=γSZLCβ1β2(τ)τ|τ=0,
Cβ1β2(d,τ)=f[(dv¯τ)2+σv2τ2],
Cβ1β2(d,τ)τ|τ=τp=0.
[2(dv¯τp)v¯+2σv2τp]fτ|τ=τp=0.
τp=dv¯v¯2+σv2.
vt,TDP=γTDPv¯(1+σv2v¯2).
Cβ1β2(d,τ)τ|τ=0=2dv¯fτ|τ=0.
γSZL=12dfτ|τ=0.
β1N(t)=ejωtdZ1(ω)+ejωtdN1(ω),β2N(t)=ejωtdZ2(ω)+ejωtdN2(ω),
Bβ1Nβ2N(τ)=(ejωtdZ1(ω)+ejωtdN1(ω))*×(ejω(t+τ)dZ2(ω)+ejω(t+τ)dN2(ω)),
Bβ1Nβ2N(τ)=ej(ωω)tejωτdZ1*(ω)dZ2(ω)+ej(ωω)tejωτdZ1*(ω)dN2(ω)+ej(ωω)tejωτdN1*(ω)dZ2(ω)+ej(ωω)tejωτdN1*(ω)dN2(ω).
dZ1*(ω)dZ2(ω)=W12(ω)δ(ωω)dωdω,
Bβ1Nβ2N(τ)=ejωτW12(ω)dω.
Bβ1Nβ2N(τ)=Bβ1β2(τ).
Cβ1Nβ2N(τ)=Cβ1β2(τ)σβ12σβ22(σβ12+σN12)(σβ22+σN22),

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