Abstract

We demonstrate the feasibility of using a naturally illuminated scene, such as a hillside or forest, as a passive optical source to measure the path-averaged crosswind between the scene and the observer. The resultant path weighting function for the crosswind cannot be varied arbitrarily, but we can obtain a useful range of weighting functions by adjusting the geometry of the receiver.

© 1975 Optical Society of America

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References

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  1. R. S. Lawrence, G. R. Ochs, S. F. Clifford, Appl. Opt. 11, 239 (1972).
    [CrossRef] [PubMed]
  2. R. W. Lee, J. Opt. Soc. Am. 10, 1295 (1974).
    [CrossRef]
  3. T-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).
    [CrossRef] [PubMed]
  4. L. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).
    [CrossRef]
  5. A. Ishimaru, IEEE Trans. Antennas Propag. AP-20, 10 (1972).
    [CrossRef]
  6. P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
    [CrossRef]
  7. J. C. Harp, Ph.D. Thesis, AFCRL-71-0451, SV-SEL-71-042, Scientific Report 1 (1971).
  8. P. A. Mandics, Ph.D. Dissertation, Stanford Univ., Stanford, Calif. (1971).
  9. A. G. Kjelaas, G. R. Ochs, J. Appl. Meteorol. 13, 242 (1974).
    [CrossRef]
  10. R. W. Lee, J. C. Harp, Proc. IEEE 57, 375 (1969).
    [CrossRef]
  11. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.
  12. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
    [CrossRef]
  13. A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 299 (1941).
  14. S. F. Clifford, G. R. Ochs, T-i. Wang, NOAA Tech. Rept. ERL 312-WPL-35 (1974).
  15. G. R. Ochs, G. F. Miller, E. J. Goldenstein, NOAA Tech. Memo ERL WPL-11 (1974).

1974 (3)

A. G. Kjelaas, G. R. Ochs, J. Appl. Meteorol. 13, 242 (1974).
[CrossRef]

R. W. Lee, J. Opt. Soc. Am. 10, 1295 (1974).
[CrossRef]

T-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).
[CrossRef] [PubMed]

1973 (1)

P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
[CrossRef]

1972 (2)

1971 (1)

1970 (1)

L. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).
[CrossRef]

1969 (1)

R. W. Lee, J. C. Harp, Proc. IEEE 57, 375 (1969).
[CrossRef]

1941 (1)

A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 299 (1941).

Clifford, S. F.

Goldenstein, E. J.

G. R. Ochs, G. F. Miller, E. J. Goldenstein, NOAA Tech. Memo ERL WPL-11 (1974).

Harp, J. C.

R. W. Lee, J. C. Harp, Proc. IEEE 57, 375 (1969).
[CrossRef]

J. C. Harp, Ph.D. Thesis, AFCRL-71-0451, SV-SEL-71-042, Scientific Report 1 (1971).

Ishimaru, A.

A. Ishimaru, IEEE Trans. Antennas Propag. AP-20, 10 (1972).
[CrossRef]

Kjelaas, A. G.

A. G. Kjelaas, G. R. Ochs, J. Appl. Meteorol. 13, 242 (1974).
[CrossRef]

Kolmogorov, A. N.

A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 299 (1941).

Lawrence, R. S.

Lee, R. W.

R. W. Lee, J. Opt. Soc. Am. 10, 1295 (1974).
[CrossRef]

P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
[CrossRef]

R. W. Lee, J. C. Harp, Proc. IEEE 57, 375 (1969).
[CrossRef]

Mandics, P. A.

P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
[CrossRef]

P. A. Mandics, Ph.D. Dissertation, Stanford Univ., Stanford, Calif. (1971).

Miller, G. F.

G. R. Ochs, G. F. Miller, E. J. Goldenstein, NOAA Tech. Memo ERL WPL-11 (1974).

Ochs, G. R.

T-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).
[CrossRef] [PubMed]

A. G. Kjelaas, G. R. Ochs, J. Appl. Meteorol. 13, 242 (1974).
[CrossRef]

R. S. Lawrence, G. R. Ochs, S. F. Clifford, Appl. Opt. 11, 239 (1972).
[CrossRef] [PubMed]

G. R. Ochs, G. F. Miller, E. J. Goldenstein, NOAA Tech. Memo ERL WPL-11 (1974).

S. F. Clifford, G. R. Ochs, T-i. Wang, NOAA Tech. Rept. ERL 312-WPL-35 (1974).

Shen, L.

L. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.

Wang, T-i

Wang, T-i.

S. F. Clifford, G. R. Ochs, T-i. Wang, NOAA Tech. Rept. ERL 312-WPL-35 (1974).

Waterman, A. T.

P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
[CrossRef]

Appl. Opt. (2)

Dokl. Akad. Nauk. SSSR (1)

A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 299 (1941).

IEEE Trans. Antennas Propag. (2)

L. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).
[CrossRef]

A. Ishimaru, IEEE Trans. Antennas Propag. AP-20, 10 (1972).
[CrossRef]

J. Appl. Meteorol. (1)

A. G. Kjelaas, G. R. Ochs, J. Appl. Meteorol. 13, 242 (1974).
[CrossRef]

J. Opt. Soc. Am. (2)

Proc. IEEE (1)

R. W. Lee, J. C. Harp, Proc. IEEE 57, 375 (1969).
[CrossRef]

Radio Sci. (1)

P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
[CrossRef]

Other (5)

J. C. Harp, Ph.D. Thesis, AFCRL-71-0451, SV-SEL-71-042, Scientific Report 1 (1971).

P. A. Mandics, Ph.D. Dissertation, Stanford Univ., Stanford, Calif. (1971).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.

S. F. Clifford, G. R. Ochs, T-i. Wang, NOAA Tech. Rept. ERL 312-WPL-35 (1974).

G. R. Ochs, G. F. Miller, E. J. Goldenstein, NOAA Tech. Memo ERL WPL-11 (1974).

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Figures (11)

Fig. 1
Fig. 1

One-dimensional spatial spectrum of 35-mm color slide showing two vehicles against a background of trees. The abscissa is scaled to actual dimensions at the vehicles.

Fig. 2
Fig. 2

Geometry of the light source and the receiver. The light at (ρ,0) is perturbed by the turbulent phase screen at z to produce scintillation in the receiving plane at (ρ,L). The sinusoidal phase screen has a spatial wavenumber K.

Fig. 3
Fig. 3

Wind weighting function for a receiving array with a normalized spatial wavelength dn = 0.5. The scene spectrum is assumed to follow a power-law spectrum with the slope −α.

Fig. 4
Fig. 4

Wind weighting function for a receiving array with a normalized spatial wavelength of dn = 1. The scene spectrum is assumed to follow a power-law spectrum with the slope −α.

Fig. 5
Fig. 5

Wind weighting function for a receiving array with a normalized spatial wavelength dn = 2. The scene spectrum is assumed to follow a power-law spectrum with the slope −α.

Fig. 6
Fig. 6

Wind weighting function for a receiving array with a normalized spatial wavelength of dn = 4. The scene spectrum is assumed to follow a power-law spectrum with the slope −α.

Fig. 7
Fig. 7

Wind path weighting for receiving array normalized spatial wavelength dn varying from 0.5 to 4.0. The scene spectrum is assumed to follow an exponential spectrum exp[−KL)1/2/A] with A = KsL)1/2 = 0.5 in this figure.

Fig. 8
Fig. 8

Wind path weighting for a fixed receiving spatial wavelength dn = 1. The scene spectrum is assumed to follow an exponential spectrum exp[−KL)1/2/A] with A = KsL)1/2 varying from 0.25 to ∞.

Fig. 9
Fig. 9

Experimental and theoretical results of a ⅓ Fresnel zone circular aperture transmitter and a receiving array with spatial wavelength dn.

Fig. 10
Fig. 10

Experimental wind weighting functions for a trailer in bright sunlight and the receiving array with a spatial wavelength dn. The functions have been normalized by setting the largest ordinate of each curve to unity.

Fig. 11
Fig. 11

A comparison of the transverse wind speed measured by the optical system (upper trace) with the average of wind speeds measured by five anemometers, equally spaced on half of the 500-m path nearest the instrument. The gain of the optical system was increased to displace the curves.

Equations (30)

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d E = 1 i k a d z exp [ i K 2 z ( L z ) 2 k L ] cos [ K · ρ 1 ( z / L ) + K · ρ ( 1 z / L ) + K · b ] ,
d P a k a d z sin [ K 2 z ( L z ) 2 k L ] cos [ K · ρ 1 ( z / L ) + K · ρ ( 1 z / L ) + K · b ] .
d P = k a d z sin [ K 2 z ( L z ) 2 k L ] d 2 ρ q ( ρ ) cos [ K · ρ 1 ( z / L ) + K · ρ ( 1 z / L ) + K · b ]
d P ( ρ 1 ) = k a d z sin [ K 2 z ( L z ) 2 k L ] d 2 r 1 t ( r 1 ) d 2 ρ q ( ρ ) cos [ K · ( ρ 1 + r 1 ) ( z / L ) + K · ρ ( 1 z / L ) + K · b ] ,
d C x = 0 L d z 1 d P ( ρ 1 , z 1 ) 0 L d z 2 d P * ( ρ 2 , z 2 ) ,
C x ( ρ 1 , ρ 2 ) = k 2 0 L d z 1 0 L d z 2 sin [ K 2 z 1 ( L z 1 ) 2 k L ] sin [ K 2 z 2 ( L z 2 ) 2 k L ] d 2 r 1 d 2 r 2 t ) ( r 1 ) t * ( r 2 ) d 2 ρ d 2 ρ q ( ρ ) q * ( ρ ) a ( K , z 1 ) cos [ K · ( ρ 1 + r 1 ) ( z 1 / L ) + K · ρ ( 1 z 1 / L ) + K · b 1 ] a * ( K , z 2 ) cos [ K · ( ρ 2 + r 2 ) ( z 2 / L ) + K · ρ ( 1 z 2 / L ) + K · b 2 ] .
= 2 F n ( K , z 1 z 2 ) cos { K · [ ( ρ 1 + r 1 ) z 1 ( ρ 2 + r 2 ) z 2 ] / L + K · [ ρ ( 1 z 1 / L ) ρ ( 1 z 2 / L ) ] } ,
C x ( ρ ) = 4 π k 2 0 L d z d 2 K Φ n ( K ) sin 2 [ K 2 z ( L z ) 2 k L ] d 2 r 1 d 2 r 2 t ( r 1 ) t * ( r 2 ) d 2 ρ d 2 ρ q ( ρ ) q * ( ρ ) cos [ K · ( r 1 r 2 + ρ ) z / L + K · ( ρ ρ ) ( 1 z / L ) ] ,
C x ( ρ ) = 4 π k 2 ( 2 π ) 8 0 L d z d 2 K sin 2 [ K 2 z ( L z ) 2 k L ] cos ( K · ρ z / L ) Φ n ( K ) | T ( K z / L ) | 2 | Q [ K ( 1 z / L ) ] | 2 ,
Q ( K ) 1 ( 2 π ) 2 d 2 ρ q ( ρ ) exp ( i K · ρ )
T ( K ) 1 ( 2 π ) 2 d 2 ρ t ( ρ ) exp ( i K · ρ ) .
C X N ( ρ , τ ) = N 1 0 L d z d 2 K sin 2 [ K 2 z ( L z ) 2 k L ] cos [ K · ρ ( z / L ) K · v τ ] Φ n ( K ) | T ( K z / L ) | 2 | Q [ K ( 1 z / L ) ] | 2 ,
N = 0 L d z d 2 K sin 2 [ K 2 z ( L z ) 2 k L ] Φ n ( K ) | T | 2 | Q | 2 .
m N = N 1 0 L d z d 2 K sin 2 [ K 2 z ( L z ) 2 k L ] ( K · v ) sin ( K · ρ z / L ) Φ n ( K ) | T ) ( K z / L ) | 2 | Q [ K ( 1 z / L ) ] | 2 .
Φ n ( K ) = 0.033 C n 2 ( z ) K 11 / 3 .
| T ( K z / L ) | 2 = ( D 2 16 π ) 2 [ 2 J 1 ( K D z / α L ) ( K D z / α L ) ] 2 ;
t ( ρ ) = cos ( K 0 x + c ) δ ( y ) ,
| T | 2 = 1 ( 2 π ) 4 | d 2 ρ cos ( K 0 x ) δ ( y ) exp ( i K · ρ ) | 2
| T ( K z / L ) | 2 δ [ K x ( z / L ) K 0 ] + δ [ K x ( z / L ) + K 0 ] .
m N = N 1 1 K 0 sin ϕ 0 L d z C n 2 ( z ) υ ( z ) ( z / L ) 2 / 3 d K 1 × sin 2 [ ( K 0 2 + K 1 2 ) ( L / z 1 ) L / 2 k ] ( K 0 2 + K 1 2 ) 11 / 6 F ( K 1 , K 0 , z / L )
N 1 = 0 L d z C n 2 ( z ) ( z / L ) 5 / 3 d K 1 × sin 2 [ ( K 0 2 + K 1 2 ) ( L / z 1 ) L / 2 k ] ( K 0 2 + K 1 2 ) 11 / 6 F ( K 1 , K 0 , z / L ) ,
m N = t 0 sin ϕ ( λ L ) 1 / 2 0 1 d u C n 2 ( u ) υ ( u ) W f ( u ) 0 1 d u C n 2 ( u ) u W f ( u ) ,
W f ( u ) = u 2 / 3 0 d t sin 2 [ ( t 0 2 + t 1 2 ) ( 1 / u 1 ) / 4 π ] ( t 0 2 + t 1 2 ) 11 / 6 F ( t , t 0 , u ) .
m N = t 0 sin ϕ A ( λ L ) 1 / 2 0 1 d u υ ( u ) W f ( u ) ,
A = 0 1 d u u W f ( u ) .
W f ( u ) = u 2 / 3 + α ( 1 u ) α 0 d t sin 2 [ ( t 0 2 + t 1 2 ) ( 1 / u 1 ) / 4 π ] ( t 0 2 + t 1 2 ) 11 / 6 + α / 2 .
W f ( u ) = u 2 / 3 0 d t sin 2 [ ( t 0 2 + t 1 2 ) ( 1 / u 1 ) / 4 π ] ( t 0 2 + t 1 2 ) 11 / 6 exp [ ( t 0 2 + t 1 2 ) 1 / 2 ( 1 / u 1 ) / K s ( λ L ) 1 / 2 ] .
A 0 = i = 1 N W i A i ,
A 0 A j = i = 1 N W i A i A j ; j = 1 , 2 , . . . N .
| Q ( K ) | 2 [ 2 J 1 ( K D / 2 ) ( K D / 2 ) ] 2 .

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