Abstract

The fluctuations of spatially filtered starlight contain information about refractive turbulence strength ( Cn2) at the spatial filter wavenumber. If the turbulence at different heights in the atmosphere is moving at different speeds, the contribution to the fluctuations from those heights will occur at different frequencies. Therefore, the Cn2 profile can be inferred from the power spectrum of the fluctuations and the wind velocity profile. Vertical resolution is expected to be in the range of several hundred meters to about a kilometer. Turbulence strength measurements to better than 50% should be easily obtainable.

© 1988 Optical Society of America

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References

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  1. W. M. Protheroe, “The Motion and Structure of Stellar Shadow-Band Patterns,” Q. J. R. Meteorol. Soc. 90, 27 (1964).
    [CrossRef]
  2. A. A. Townsend, “The Interpretation of Stellar Shadow-Bands as a Consequence of Turbulent Mixing,” Q. J. R. Meteorol. Soc. 91, 1 (1965).
    [CrossRef]
  3. A. Peskoff, “Theory of Remote Sensing of Clear-Air Turbulence Profiles,” J. Opt. Soc. Am. 58, 1032 (1968).
    [CrossRef]
  4. D. L. Fried, “Remote Probing of the Optical Strength of Atmospheric Turbulence and of Wind Velocity,” Proc. IEEE 57, 415 (1969).
    [CrossRef]
  5. J. W. Strohbehn, “Remote Sensing of Clear-Air Turbulence,” J. Opt. Soc. Am. 60, 948 (1970).
    [CrossRef]
  6. L. Shen, “Remote Probing of Atmosphere and Wind Velocity by Millimeter Waves,” IEEE Trans. Antennas Propag. AP-18, 493 (1970).
    [CrossRef]
  7. J. Vernin, F. Roddier, “Experimental Determination of Two-Dimensional Spatiotemporal Power Spectra of Stellar Light Scintillation. Evidence for a Multilayer Structure of the Air Turbulence in the Upper Troposphere,” J. Opt. Soc. Am. 63, 270 (1973).
    [CrossRef]
  8. G. R. Ochs, T. Wang, R. S. Lawrence, S. F. Clifford, “Refractive-Turbulence Profiles Measured by One-Dimensional Spatial Filtering of Scintillations,” Appl. Opt. 15, 2504 (1976).
    [CrossRef] [PubMed]
  9. A. Rocca, F. Roddier, J. Vernin, “Detection of Atmospheric Turbulent Layers by Spatiotemporal and Spatioangular Correlation Measurements of Stellar-Light Scintillation,” J. Opt. Soc. Am. 64, 1000 (1974).
    [CrossRef]
  10. S. F. Clifford, J. H. Churnside, “Refractive Turbulence Profiling Using Synthetic Aperture Spatial Filtering of Scintillation,” Appl. Opt. 26, 1295 (1987).
    [CrossRef] [PubMed]
  11. D. C. Hogg et al., “An Automatic Profiler of the Temperature, Wind and Humidity in the Troposphere,” J. Appl. Meteorol. 22, 807 (1983).
    [CrossRef]
  12. R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
    [CrossRef]
  13. R. G. Strauch, D. A. Merritt, K. P. Moran, “Radar Wind Profilers in the Colorado Network,” NOAA Tech. Memo. ERL WPL-120 (1985).
  14. M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Mesoscale Wind Systems,” Meteorol. Mag. 113, 165 (1984).
  15. M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Fronts and Jet Streams” Mon. Weather Rev. 112, 1263 (1984).
    [CrossRef]
  16. R. W. Lee, J. C. Harp, “Weak Scattering in Random Media, with Applications to Remote Probing,” Proc. IEEE 57, 375 (1969).
    [CrossRef]
  17. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).
  18. S. Petterssen, Introduction to Meteorology (McGraw-Hill, New York, 1968), p. 187.
  19. 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-Verlag, New York, 1978), pp. 9–43.
    [CrossRef]
  20. R. E. Hufnagel, “Variations of Atmospheric Turbulence,” in Technical Digest of Topical Meeting on Optical Propagation through Turbulence (Optical Society of America, Washington, DC, 1974).
  21. W. L. Wolfe, G. J. Zissis, Eds., The Infrared Handbook (Office of Naval Research, Washington, 1978), pp. 3–19.

1987

1985

R. G. Strauch, D. A. Merritt, K. P. Moran, “Radar Wind Profilers in the Colorado Network,” NOAA Tech. Memo. ERL WPL-120 (1985).

1984

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Mesoscale Wind Systems,” Meteorol. Mag. 113, 165 (1984).

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Fronts and Jet Streams” Mon. Weather Rev. 112, 1263 (1984).
[CrossRef]

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

1983

D. C. Hogg et al., “An Automatic Profiler of the Temperature, Wind and Humidity in the Troposphere,” J. Appl. Meteorol. 22, 807 (1983).
[CrossRef]

1976

1974

1973

1970

J. W. Strohbehn, “Remote Sensing of Clear-Air Turbulence,” J. Opt. Soc. Am. 60, 948 (1970).
[CrossRef]

L. Shen, “Remote Probing of Atmosphere and Wind Velocity by Millimeter Waves,” IEEE Trans. Antennas Propag. AP-18, 493 (1970).
[CrossRef]

1969

D. L. Fried, “Remote Probing of the Optical Strength of Atmospheric Turbulence and of Wind Velocity,” Proc. IEEE 57, 415 (1969).
[CrossRef]

R. W. Lee, J. C. Harp, “Weak Scattering in Random Media, with Applications to Remote Probing,” Proc. IEEE 57, 375 (1969).
[CrossRef]

1968

1965

A. A. Townsend, “The Interpretation of Stellar Shadow-Bands as a Consequence of Turbulent Mixing,” Q. J. R. Meteorol. Soc. 91, 1 (1965).
[CrossRef]

1964

W. M. Protheroe, “The Motion and Structure of Stellar Shadow-Band Patterns,” Q. J. R. Meteorol. Soc. 90, 27 (1964).
[CrossRef]

Churnside, J. H.

Clifford, S. F.

Earnshaw, K. B.

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

Fried, D. L.

D. L. Fried, “Remote Probing of the Optical Strength of Atmospheric Turbulence and of Wind Velocity,” Proc. IEEE 57, 415 (1969).
[CrossRef]

Hample, T.

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Fronts and Jet Streams” Mon. Weather Rev. 112, 1263 (1984).
[CrossRef]

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Mesoscale Wind Systems,” Meteorol. Mag. 113, 165 (1984).

Harp, J. C.

R. W. Lee, J. C. Harp, “Weak Scattering in Random Media, with Applications to Remote Probing,” Proc. IEEE 57, 375 (1969).
[CrossRef]

Hogg, D. C.

D. C. Hogg et al., “An Automatic Profiler of the Temperature, Wind and Humidity in the Troposphere,” J. Appl. Meteorol. 22, 807 (1983).
[CrossRef]

Hufnagel, R. E.

R. E. Hufnagel, “Variations of Atmospheric Turbulence,” in Technical Digest of Topical Meeting on Optical Propagation through Turbulence (Optical Society of America, Washington, DC, 1974).

Lawrence, R. S.

Lee, R. W.

R. W. Lee, J. C. Harp, “Weak Scattering in Random Media, with Applications to Remote Probing,” Proc. IEEE 57, 375 (1969).
[CrossRef]

Merritt, D. A.

R. G. Strauch, D. A. Merritt, K. P. Moran, “Radar Wind Profilers in the Colorado Network,” NOAA Tech. Memo. ERL WPL-120 (1985).

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

Moran, K. P.

R. G. Strauch, D. A. Merritt, K. P. Moran, “Radar Wind Profilers in the Colorado Network,” NOAA Tech. Memo. ERL WPL-120 (1985).

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

Ochs, G. R.

Peskoff, A.

Petterssen, S.

S. Petterssen, Introduction to Meteorology (McGraw-Hill, New York, 1968), p. 187.

Protheroe, W. M.

W. M. Protheroe, “The Motion and Structure of Stellar Shadow-Band Patterns,” Q. J. R. Meteorol. Soc. 90, 27 (1964).
[CrossRef]

Rocca, A.

Roddier, F.

Shapiro, M. A.

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Mesoscale Wind Systems,” Meteorol. Mag. 113, 165 (1984).

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Fronts and Jet Streams” Mon. Weather Rev. 112, 1263 (1984).
[CrossRef]

Shen, L.

L. Shen, “Remote Probing of Atmosphere and Wind Velocity by Millimeter Waves,” IEEE Trans. Antennas Propag. AP-18, 493 (1970).
[CrossRef]

Strauch, R. G.

R. G. Strauch, D. A. Merritt, K. P. Moran, “Radar Wind Profilers in the Colorado Network,” NOAA Tech. Memo. ERL WPL-120 (1985).

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

Strohbehn, J. W.

Tatarskii, V. I.

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

Townsend, A. A.

A. A. Townsend, “The Interpretation of Stellar Shadow-Bands as a Consequence of Turbulent Mixing,” Q. J. R. Meteorol. Soc. 91, 1 (1965).
[CrossRef]

van de Kamp, D.

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Fronts and Jet Streams” Mon. Weather Rev. 112, 1263 (1984).
[CrossRef]

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Mesoscale Wind Systems,” Meteorol. Mag. 113, 165 (1984).

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

Vernin, J.

Wang, T.

Appl. Opt.

IEEE Trans. Antennas Propag.

L. Shen, “Remote Probing of Atmosphere and Wind Velocity by Millimeter Waves,” IEEE Trans. Antennas Propag. AP-18, 493 (1970).
[CrossRef]

J. Appl. Meteorol.

D. C. Hogg et al., “An Automatic Profiler of the Temperature, Wind and Humidity in the Troposphere,” J. Appl. Meteorol. 22, 807 (1983).
[CrossRef]

J. Atmos. Oceanic Technol.

R. G. Strauch, D. A. Merritt, K. P. Moran, K. B. Earnshaw, D. van de Kamp, “The Colorado Wind-Profiling Network,” J. Atmos. Oceanic Technol. 1, 37 (1984).
[CrossRef]

J. Opt. Soc. Am.

Meteorol. Mag.

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Mesoscale Wind Systems,” Meteorol. Mag. 113, 165 (1984).

Mon. Weather Rev.

M. A. Shapiro, T. Hample, D. van de Kamp, “Radar Wind Profiler Observations of Fronts and Jet Streams” Mon. Weather Rev. 112, 1263 (1984).
[CrossRef]

NOAA Tech. Memo. ERL WPL-120

R. G. Strauch, D. A. Merritt, K. P. Moran, “Radar Wind Profilers in the Colorado Network,” NOAA Tech. Memo. ERL WPL-120 (1985).

Proc. IEEE

R. W. Lee, J. C. Harp, “Weak Scattering in Random Media, with Applications to Remote Probing,” Proc. IEEE 57, 375 (1969).
[CrossRef]

D. L. Fried, “Remote Probing of the Optical Strength of Atmospheric Turbulence and of Wind Velocity,” Proc. IEEE 57, 415 (1969).
[CrossRef]

Q. J. R. Meteorol. Soc.

W. M. Protheroe, “The Motion and Structure of Stellar Shadow-Band Patterns,” Q. J. R. Meteorol. Soc. 90, 27 (1964).
[CrossRef]

A. A. Townsend, “The Interpretation of Stellar Shadow-Bands as a Consequence of Turbulent Mixing,” Q. J. R. Meteorol. Soc. 91, 1 (1965).
[CrossRef]

Other

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

S. Petterssen, Introduction to Meteorology (McGraw-Hill, New York, 1968), p. 187.

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-Verlag, New York, 1978), pp. 9–43.
[CrossRef]

R. E. Hufnagel, “Variations of Atmospheric Turbulence,” in Technical Digest of Topical Meeting on Optical Propagation through Turbulence (Optical Society of America, Washington, DC, 1974).

W. L. Wolfe, G. J. Zissis, Eds., The Infrared Handbook (Office of Naval Research, Washington, 1978), pp. 3–19.

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Figures (7)

Fig. 1
Fig. 1

Petterssen wind speed profile for 40°N latitude in winter. A constant direction is assumed.

Fig. 2
Fig. 2

Typical path weighting functions for the profile of Fig. 1 and the system parameters discussed in the text.

Fig. 3
Fig. 3

Typical wind profile from Doppler radar. Solid lines represent high-resolution mode and circles represent the lower resolution mode.

Fig. 4
Fig. 4

Typical path weighting functions for the high-resolution profile of Fig. 3 with a north–south spatial filter.

Fig. 5
Fig. 5

Typical path weighting functions for the low-resolution profile of Fig. 3 east–west (solid line) and north–south (dashed line) spatial filters.

Fig. 6
Fig. 6

Hufnagel turbulence strength ( C n 2) profile and typical corresponding values of the normalized power spectrum Sχf.

Fig. 7
Fig. 7

Hufnagel turbulence strength ( C n 2) profile and typical corresponding values of the relative measurement error Δ C n 2 / C n 2.

Equations (30)

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d χ ( ρ , z , t ) = k d z d ν ( K , z ) sin ( K 2 z 2 k ) exp { i K · [ ρ + v ( z ) t ] } ,
χ f ( ρ , t ) = d 2 ρ f R ( ρ - ρ ) d χ ( ρ , z , t ) ,
C χ f ( τ ) = [ χ f ( t ) - χ f ( t ) ] [ χ f * ( t + τ ) - χ f * ( t + τ ) ] ,
S χ f ( ω ) = 1 2 π - d τ C χ f ( τ ) exp ( - i ω τ ) .
C χ f ( τ ) = k 2 d 2 ρ f R ( ρ - ρ ) d 2 ρ f R * ( ρ - ρ ) × 0 d z 1 0 d z 2 d ν ( K , z 1 ) d ν * ( K , z 2 ) × sin ( K 2 z 1 2 k ) sin ( K 2 z 2 2 k ) exp { i K · [ ρ - v ( z 1 ) t ] - i K · [ ρ - v ( z 2 ) ( t + τ ) ] } .
d ν ( K , z 1 ) d ν * ( K , z 2 ) = 2 π δ ( z 1 - z 2 ) Φ n ( K , z 1 ) δ ( K - K ) d 2 K d 2 K ,
C χ f ( τ ) = 2 π k 2 0 d z d 2 K Φ n ( K , z ) sin 2 ( K 2 z 2 k ) F R ( K ) 2 × exp [ i K · v ( z ) τ ] ,
F R ( Λ ) = d 2 ρ f R ( ρ ) exp ( i Λ · ρ )
S χ f ( ω ) = 2 π k 2 0 d z d 2 K Φ n ( K , z ) × sin 2 ( K 2 z 2 k ) F R ( K ) 2 δ [ ω - K · v ( z ) ] .
S χ f ( ω ) = 2 π k 2 0 d z - d K y Φ n ( ω - K y v y v x , K y , z ) × sin 2 [ ω 2 z 2 k v 2 + v 2 z 2 k v x 2 ( K y - ω v y v 2 ) 2 ] × | F R ( ω - K y v y v x , K y ) | 2 / v x ,
F R ( K x , K y ) 2 δ ( K x - K R ) δ ( K y ) .
S χ f ( ω ) 0 d z Φ n ( K R , 0 , z ) sin 2 ( K R 2 z 2 k ) δ ( ω v x - K R ) / v x ,
f R ( x , y ) = ( π r 2 ) - 1 exp ( - x 2 + y 2 2 r 2 ) ( 1 + cos K R x ) ,
F R ( K x , K y ) = 2 exp [ - 1 2 r 2 ( K x - k R ) 2 - 1 2 r 2 K y 2 ] + 2 exp [ - 1 2 r 2 ( K x + K R ) 2 - 1 2 r 2 K y 2 ] .
S χ f ( ω ) = 8 π k 2 0 d z - d K y Φ n ( ω - K y v y v x , K y , z ) × sin 2 [ ω 2 z 2 k v 2 + v 2 z 2 k v x 2 ( K y - ω v y v 2 ) 2 ] × exp [ - K R 2 r 2 - ω 2 r 2 v 2 - v 2 v x 2 ( K y - ω v y v 2 ) 2 r 2 ] × [ 1 + cos h ( 2 ω - K y v y v x K R r 2 ) ] / v x .
S χ f ( ω ) = 8 π 3 / 2 k 2 r 0 d z Φ n ( ω v x v 2 , ω v y v 2 , z ) × sin 2 ( ω 2 z 2 k v 2 ) exp ( - K R 2 r 2 - ω 2 r 2 v 2 ) × [ 1 + cos h ( 2 ω v x v 2 K R r 2 ) ] / v .
ω v y v 2 - v x v r < K y < ω v y v 2 + v x v r ,
S χ f ( ω ) = 4 π 3 / 2 k 2 r - 1 0 d z Φ n ( ω v x v 2 , ω v y v 2 , z ) × sin 2 ( ω 2 z 2 k v 2 ) exp [ - K R 2 r 2 sin 2 θ v - r 2 v 2 ( ω - v x K R ) 2 ] / v .
W ( z ) = sin 2 ( ω 2 z 2 k v 2 ) exp [ - K R 2 r 2 sin 2 θ v - K R 2 r 2 cos 2 θ v ( ω v x K R - 1 ) 2 ] / v .
v = 3 + 9 × 10 - 3 z - 4 + 10 - 7 z 2 .
Δ z 2 v d v d z K R r ,
S χ f ( v 0 K R ) = 8 π 2 k 2 | d v d z | K R r 2 sin 2 ( K R 2 z 0 2 k ) Φ n ( K R , 0 , z 0 ) .
Φ n ( K R , 0 , z 0 ) = 0.033 K R - 11 / 3 C n 2 ( z 0 ) ,
C n 2 ( z ) = 8.2 × 10 - 56 W 2 z 10 exp ( z 1000 ) + 2.7 × 10 - 16 exp ( - z 1500 ) ,
W = [ 1 1500 5000 20000 v 2 ( z ) d z ] 1 / 2 .
C n 2 = 7.7 × 10 - 15 z - 23 for z < 3000 m = 1.7 × 10 - 52 z 10 exp ( - z 1000 ) + 27 × 10 - 16 exp ( - z 1500 ) for z > 3000 m .
C n 2 = | d v d z | K R 14 / 3 r 2 0.264 π 2 k 2 sin 2 ( K R 2 z 2 K ) S χ f = A S χ f ,
S χ f = 1 T 0 T d t [ i s ( t ) + i n ( t ) ] 2 ,
C n 2 = C n 2 + A N ,
( Δ C n 2 ) 2 = ( C n 2 + A N ) 2 Δ ω T ,

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