Abstract

The frequency spectrum of angle-of-arrival (AOA) fluctuations of optical waves propagating through atmospheric turbulence carries information of wind speed transverse to the propagation path. We present the retrievals of the transverse wind speed, vb, from the AOA spectra measured with a Schmidt–Cassegrain telescope equipped with a CCD camera by estimating the “knee frequency,” the intersection of two power laws of the AOA spectrum. The rms difference between 30s estimates of vb retrieved from the measured AOA spectra and 30s averages of the transverse horizontal wind speed measured with an ultrasonic anemometer was 11cms1 for a 1 h period, during which the transverse horizontal wind speed varied between 0 and 80cms1. Potential and limitations of angle-of-arrival anemometry are discussed

© 2007 Optical Society of America

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References

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  1. G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London, Ser. A 164, 476-490 (1938).
    [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. 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, 1360-1370 (1968).
    [CrossRef]
  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. R. Rao, S. Wang, X. Liu, and Z. Gong, "Turbulence spectrum effect on wave temporal-frequency spectra for light propagating through the atmosphere," J. Opt. Soc. Am. A 16, 2755-2761 (1999).
    [CrossRef]
  7. A. Lüdi and A. Magun, "Near-horizontal line-of-sight millimeter-wave propagation measurements for the determination of outer length scales and anisotropy of turbulent refractive index fluctuations in the lower troposphere," Radio Sci. 37, 12.1-12.19 (2002).
    [CrossRef]
  8. 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]
  9. Y. Cheon and A. Muschinski, "Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence," J. Opt. Soc. Am. A 24, 415-422 (2007).
    [CrossRef]
  10. C. B. Hogge and R. R. Butts, "Frequency spectra for the geometrical representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
    [CrossRef]
  11. G. A. Tyler, "Bandwidth considerations for tracking through turbulence," J. Opt. Soc. Am. A 11, 358-367 (1994).
    [CrossRef]
  12. D. S. Acton, R. J. Sharbaugh, J. R. Roehrig, and D. Tiszauer, "Wave-front tilt power spectral density from the image motion of solar pores," Appl. Opt. 31, 4280-4284 (1992).
    [CrossRef] [PubMed]
  13. D. R. McGaughey and G. J. M. Aitken, "Temporal analysis of stellar wave-front-tilt data," J. Opt. Soc. Am. A 14, 1967-1974 (1997).
    [CrossRef]
  14. F. F. Hall, "The Boulder Atmospheric Observatory," Opt. News 3 (2) 14-18 (1977).
  15. J. C. Kaimal and J. E. Gaynor, "The Boulder Atmospheric Observatory," J. Clim. Appl. Meteorol. 22, 863-880 (1983).
    [CrossRef]
  16. Lord Rayleigh, "Investigations in optics, with special reference to the spectroscope," Philos. Mag. VIII, 261-274 (1879).
  17. A. S. Gurvich and M. A. Kallistratova, "Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations," Radiophys. Quantum Electron. 11, 37-40 (1968).
    [CrossRef]
  18. R. Berry and J. Burnell, The Handbook of Astronomical Image Processing (Willmann-Bell, 2005).
  19. S. B. Howell, Handbook of CCD Astronomy (Cambridge U. Press, 2000).
  20. N. S. Nightingale and D. F. Buscher, "Interferometric seeing measurements at the La Palma Observatory," Mon. Not. R. Astron. Soc. 251, 155-166 (1991).
  21. M. A. Kallistratova and A. I. Kon, "Fluctuations in the angle of arrival of light waves from an extended source in a turbulent atmosphere," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 9, 636-639 (1966).
  22. H. A. Panofsky and J. A. Dutton, Atmospheric Turbulence Models and Methods for Engineering Applications (Wiley, 1984).
  23. R. W. Lee and J. C. Harp, "Weak scattering in random media, with applications to remote probing," Proc. IEEE 57, 375-406 (1969).
    [CrossRef]
  24. A. D. Wheelon, Electromagnetic Scintillation. I. Geometrical Optics (Cambridge U. Press, 2001).
  25. R. W. Lee, "Remote probing using spatially filtered apertures," J. Opt. Soc. Am. 64, 1295-1303 (1974).
    [CrossRef]
  26. S. F. Clifford and R. J. Lataitis, "Spatial and temporal filtering of scintillation in remote sensing," IEEE Trans. Antennas Propag. AP-35, 597-604 (1987).
    [CrossRef]

2007 (1)

2002 (1)

A. Lüdi and A. Magun, "Near-horizontal line-of-sight millimeter-wave propagation measurements for the determination of outer length scales and anisotropy of turbulent refractive index fluctuations in the lower troposphere," Radio Sci. 37, 12.1-12.19 (2002).
[CrossRef]

1999 (1)

1997 (1)

1994 (1)

1992 (1)

1991 (1)

N. S. Nightingale and D. F. Buscher, "Interferometric seeing measurements at the La Palma Observatory," Mon. Not. R. Astron. Soc. 251, 155-166 (1991).

1987 (1)

S. F. Clifford and R. J. Lataitis, "Spatial and temporal filtering of scintillation in remote sensing," IEEE Trans. Antennas Propag. AP-35, 597-604 (1987).
[CrossRef]

1983 (1)

J. C. Kaimal and J. E. Gaynor, "The Boulder Atmospheric Observatory," J. Clim. Appl. Meteorol. 22, 863-880 (1983).
[CrossRef]

1976 (1)

C. B. Hogge and R. R. Butts, "Frequency spectra for the geometrical representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
[CrossRef]

1974 (1)

1971 (1)

1970 (1)

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]

1969 (1)

R. W. Lee and J. C. Harp, "Weak scattering in random media, with applications to remote probing," Proc. IEEE 57, 375-406 (1969).
[CrossRef]

1968 (2)

A. S. Gurvich and M. A. Kallistratova, "Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations," Radiophys. Quantum Electron. 11, 37-40 (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, 1360-1370 (1968).
[CrossRef]

1966 (1)

M. A. Kallistratova and A. I. Kon, "Fluctuations in the angle of arrival of light waves from an extended source in a turbulent atmosphere," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 9, 636-639 (1966).

1938 (1)

G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London, Ser. A 164, 476-490 (1938).
[CrossRef]

1879 (1)

Lord Rayleigh, "Investigations in optics, with special reference to the spectroscope," Philos. Mag. VIII, 261-274 (1879).

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (2)

C. B. Hogge and R. R. Butts, "Frequency spectra for the geometrical representation of wavefront distortions due to atmospheric turbulence," IEEE Trans. Antennas Propag. AP-24, 144-154 (1976).
[CrossRef]

S. F. Clifford and R. J. Lataitis, "Spatial and temporal filtering of scintillation in remote sensing," IEEE Trans. Antennas Propag. AP-35, 597-604 (1987).
[CrossRef]

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

M. A. Kallistratova and A. I. Kon, "Fluctuations in the angle of arrival of light waves from an extended source in a turbulent atmosphere," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 9, 636-639 (1966).

J. Clim. Appl. Meteorol. (1)

J. C. Kaimal and J. E. Gaynor, "The Boulder Atmospheric Observatory," J. Clim. Appl. Meteorol. 22, 863-880 (1983).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

Mon. Not. R. Astron. Soc. (1)

N. S. Nightingale and D. F. Buscher, "Interferometric seeing measurements at the La Palma Observatory," Mon. Not. R. Astron. Soc. 251, 155-166 (1991).

Philos. Mag. (1)

Lord Rayleigh, "Investigations in optics, with special reference to the spectroscope," Philos. Mag. VIII, 261-274 (1879).

Proc. IEEE (2)

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]

R. W. Lee and J. C. Harp, "Weak scattering in random media, with applications to remote probing," Proc. IEEE 57, 375-406 (1969).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

G. I. Taylor, "The spectrum of turbulence," Proc. R. Soc. London, Ser. A 164, 476-490 (1938).
[CrossRef]

Radio Sci. (1)

A. Lüdi and A. Magun, "Near-horizontal line-of-sight millimeter-wave propagation measurements for the determination of outer length scales and anisotropy of turbulent refractive index fluctuations in the lower troposphere," Radio Sci. 37, 12.1-12.19 (2002).
[CrossRef]

Radiophys. Quantum Electron. (2)

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, 1360-1370 (1968).
[CrossRef]

A. S. Gurvich and M. A. Kallistratova, "Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations," Radiophys. Quantum Electron. 11, 37-40 (1968).
[CrossRef]

Other (7)

R. Berry and J. Burnell, The Handbook of Astronomical Image Processing (Willmann-Bell, 2005).

S. B. Howell, Handbook of CCD Astronomy (Cambridge U. Press, 2000).

F. F. Hall, "The Boulder Atmospheric Observatory," Opt. News 3 (2) 14-18 (1977).

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 U. Press, 2001).

H. A. Panofsky and J. A. Dutton, Atmospheric Turbulence Models and Methods for Engineering Applications (Wiley, 1984).

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Figures (10)

Fig. 1
Fig. 1

Diagram of position of the instruments and the propagation path at Boulder Atmospheric Observatory (BAO) near Erie, Colorado, generated from DeLorme Topo USA 3.0. BAO, BAO tower; TS, telescope; HT and ST, self-logging thermometer towers and ultrasonic anemometer tower, respectively; LG, light.

Fig. 2
Fig. 2

Experimental setup with the 14-in. telescope, ultrasonic anemometer, and self-logging thermometers at BAO.

Fig. 3
Fig. 3

Image of four lights measured at 21:00:10 LT, September 27, 2006.

Fig. 4
Fig. 4

Sequence of subimages ( 51 × 51 pixels) of the bottom left-hand light, measured at 21:00:10.9–21:00:11.6 LT, September 27, 2006. The first row, first column is the first image, the first row, fourth column is the fourth image.

Fig. 5
Fig. 5

AOA time series for (a) the horizontal direction and (b) the vertical direction of the bottom left-hand light measured on September 27, 2006.

Fig. 6
Fig. 6

Vertical AOA, α ¯ z (thin curve) of the bottom left-hand light and the vertical temperature gradient (thick curve) between 1 and 2 m measured by the self-logging thermometers at 56 m from the telescope with 5 s averaging time measured on September 27, 2006.

Fig. 7
Fig. 7

Averaged frequency spectra of AOA fluctuations for the horizontal direction (solid line) and the vertical direction (dashed line) of the bottom left-hand light measured on September 27, 2006. Each spectrum is for 10 s of time duration. The black dots and open circles are the frequency spectra averaged over intervals of equal logarithmic width for horizontal and vertical directions of 2 min of time duration, respectively. The observation time was 21:20:10–21:22:10 LT.

Fig. 8
Fig. 8

Averaged over logarithmically equidistant steps, observed and fitted frequency spectra of horizontal AOA fluctuations of the bottom left-hand light measured on September 27, 2006. The observation time was 21:06:10–21:06:40 LT. The dots are for the observed spectrum, and the solid curve is for the fitted spectrum.

Fig. 9
Fig. 9

Scatter plot of the knee frequency, f k , from the frequency spectra of horizontal AOA fluctuations (bottom left-hand light) versus the time-averaged transverse horizontal wind speed measured by the ultrasonic anemometer, v b , measured on September 27, 2006. The dots are the data inside the bound ( ± 2 σ d ) , the open circles are the data out of the bound, and the solid line is the calibration line. The calibration line is f k = 2.0 m 1 × v b + 0.19 Hz . The averaging time is 30 s .

Fig. 10
Fig. 10

Comparison of v aoa c with v b (top panel) and rms difference between v aoa c and v b (bottom panel) measured on September 27, 2006. The solid curve is for the 30 s averaged transverse horizontal wind speed measured by the ultrasonic anemometer. The filled and open circles (top panel) are for the calibrated path-averaged transverse horizontal wind speeds retrieved from the frequency spectra of the horizontal AOAs fluctuations for 30 s of time duration for the bottom left-hand and bottom right-hand lights as viewed from the telescope, respectively. The filled and open circles (bottom panel) show the rms difference between v aoa c and v b for the bottom left- and right-hand lights for 5 min of averaging time, respectively.

Equations (32)

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W δ S ( f ) = 32 π 2 k 2 0 L d x sin 2 ( π b f x v b L ) 2 π f v b d K K Φ n ( K ) 1 + cos [ K 2 x ( L x ) k L ] ( K v b ) 2 ( 2 π f ) 2 ,
S α ( f ) = 32 π 2 b 2 0 L d x sin 2 [ π b f x v b ( x ) L ] 2 π f v b ( x ) d K K Φ n ( K , x ) 1 + cos [ K 2 x ( L x ) k L ] [ K v b ( x ) ] 2 ( 2 π f ) 2 .
cos [ K 2 x ( L x ) k L ] 1 .
K 2 k L .
2 π f v b 2 k L .
f 2 π v b λ L .
f F = v b λ L ,
S α ( f ) = 64 π 2 b 2 0 L d x sin 2 [ π b f x v b ( x ) L ] 2 π f v b ( x ) d K K Φ n ( K , x ) [ K v b ( x ) ] 2 ( 2 π f ) 2 .
Φ n ( K , x ) = c T C n 2 ( x ) K 11 3
c T = 3 Γ ( 8 3 ) 8 π 2 = 0.03305 ,
σ = [ K v b ( x ) 2 π f ] 2 1 .
S α ( f ) = 2 7 3 9 π 7 6 Γ ( 5 6 ) b 2 f 8 3 0 L C n 2 ( x ) v b 5 3 ( x ) sin 2 [ π b f x v b ( x ) L ] d x ,
0 σ 1 2 ( 1 + σ ) 11 6 d σ = 4 15 π 3 2 3 Γ ( 2 3 ) Γ ( 5 6 ) .
S α ( f ) = 2 4 3 9 π 7 6 Γ ( 5 6 ) C n 2 v b 5 3 L b 2 f 8 3 [ 1 sin ( 2 π b f v b ) 2 π b f v b ] ,
f 1 2 π v b b ,
S α ( f ) = 0.06524 C n 2 v b 5 3 L b 2 f 8 3 .
S α ( f ) = 0.06524 2 3 π 2 C n 2 v b 1 3 L f 2 3 .
f k = 6 2 π v b b ,
W p ( f , x ) = C n 2 ( x ) v b 5 3 ( x ) sin 2 [ π b f x v b ( x ) L ] .
W g ( f , x ) = sin 2 ( π b f x v b L ) .
f < 1 4 v b b .
x c ( f ) = 0 L W g ( f , x ) x d x 0 L W g ( f , x ) d x ,
f = 1 π v b b = 0.81 f k .
W a ( x ) = C n 2 ( x ) v b 5 3 ( x ) ,
S α ( f ) = p ( C n 2 , v b ) S α ( f ; C n 2 , v b ) d C n 2 d v b ,
S α F A ( f ) D 3 L C n 2 v b 8 3 f 11 3 .
( α y α z ) = 1 F ( Δ y i Δ z j ) = ( Δ α y i Δ α z j ) ,
( α ¯ y α ¯ z ) = i , j ( Δ α y i Δ α z j ) I i j i , j I i j ,
C = i = 1 N [ log 10 S α , i t ( f , C n 2 , v ̃ b ) log 10 S α , i m ( f , C n 2 , v ̃ b ) ] 2 ,
S α , i t ( f , C n 2 , v ̃ b ) = 0.065 C n 2 L v ̃ b 5 3 D 2 [ 1 sin ( 2 π D f v ̃ b ) 2 π D f v ̃ b ] f 8 3 + S noise ,
v aoa c = b f k 0.39 p 0 p 1 .
f k = 2.0 m 1 × v b + 0.19 Hz.

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