Abstract

A new optical technique is described for measuring the path profiles of crosswind and of a refractive-index structure parameter Cn2 along a line-of-sight path. Different sizes of transmitters and receivers are used to control the path-weighting function so that it will peak at different path locations. Various linear combinations of these measurements yield the path profile of crosswind and Cn2. A prototype instrument has been built and tested. Experimental results show good agreement with the theoretical predictions.

© 1978 Optical Society of America

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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. 64, 1295 (1974).
    [Crossref]
  3. T-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).
    [Crossref] [PubMed]
  4. L. C. 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, “A Line-of-Sight Microwave Propagation Experiment for Resolving the Motions and Turbulent Structure of the Atmosphere,” Ph.D. Thesis, AFCRL-71-0451, SV-SEL 71-042, Scientific Report 1 (1971).
  8. P. A. Mandics, “Line-of-Sight Acoustical Probing of Atmospheric Turbulence,” Ph.D. Dissertation, Stanford U., 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. S. F. Clifford, G. R. Ochs, Ting-i Wang, Appl. Opt. 14, 2844 (1975).
    [Crossref] [PubMed]
  12. G. R. Ochs, S. F. Clifford, Ting-i Wang, Appl. Opt. 15, 403 (1976).
    [Crossref] [PubMed]
  13. Ting-i Wang, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 63, 334 (1978).
    [Crossref]
  14. G. R. Ochs, R. S. Lawrence, Ting-i Wang, P. Zieske, “Stellar-Scintillation Measurement of the Vertical Profile of Refractive-index Turbulence in the Atmosphere,” in Imaging through the Atmosphere (Soc. Photo-Opt. Instrum. Eng., 75, 48 (1976).
    [Crossref]
  15. G. R. Ochs, Ting-i Wang, R. S. Lawrence, S. F. Clifford, Appl. Opt. 15, 2504 (1976).
    [Crossref] [PubMed]
  16. G. R. Ochs, S. F. Clifford, Ting-i Wang, “Wind and Cn2 Profiling with Crossed Laser Beams and Spatial Filter Detectors,” NOAA Tech. Rept. ERL 367-WPL 45 (GPO, Washington, D.C., 1976).
  17. S. F. Clifford, G. R. Ochs, R. S. Lawrence, J. Opt. Soc. Am. 64, 148 (1974).
    [Crossref]
  18. A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941).
  19. R. J. Hill, S. F. Clifford, J. Opt. Soc. Am. 68, 892 (1978).
    [Crossref]

1978 (2)

Ting-i Wang, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 63, 334 (1978).
[Crossref]

R. J. Hill, S. F. Clifford, J. Opt. Soc. Am. 68, 892 (1978).
[Crossref]

1976 (2)

1975 (1)

1974 (4)

1973 (1)

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

1972 (2)

1970 (1)

L. C. 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.

Harp, J. C.

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

J. C. Harp, “A Line-of-Sight Microwave Propagation Experiment for Resolving the Motions and Turbulent Structure of the Atmosphere,” Ph.D. Thesis, AFCRL-71-0451, SV-SEL 71-042, Scientific Report 1 (1971).

Hill, R. J.

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.

G. R. Ochs, Ting-i Wang, R. S. Lawrence, S. F. Clifford, Appl. Opt. 15, 2504 (1976).
[Crossref] [PubMed]

S. F. Clifford, G. R. Ochs, R. S. Lawrence, J. Opt. Soc. Am. 64, 148 (1974).
[Crossref]

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

G. R. Ochs, R. S. Lawrence, Ting-i Wang, P. Zieske, “Stellar-Scintillation Measurement of the Vertical Profile of Refractive-index Turbulence in the Atmosphere,” in Imaging through the Atmosphere (Soc. Photo-Opt. Instrum. Eng., 75, 48 (1976).
[Crossref]

Lee, R. W.

R. W. Lee, J. Opt. Soc. Am. 64, 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, “Line-of-Sight Acoustical Probing of Atmospheric Turbulence,” Ph.D. Dissertation, Stanford U., Stanford, Calif. (1971).

Ochs, G. R.

Ting-i Wang, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 63, 334 (1978).
[Crossref]

G. R. Ochs, Ting-i Wang, R. S. Lawrence, S. F. Clifford, Appl. Opt. 15, 2504 (1976).
[Crossref] [PubMed]

G. R. Ochs, S. F. Clifford, Ting-i Wang, Appl. Opt. 15, 403 (1976).
[Crossref] [PubMed]

S. F. Clifford, G. R. Ochs, Ting-i Wang, Appl. Opt. 14, 2844 (1975).
[Crossref] [PubMed]

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]

S. F. Clifford, G. R. Ochs, R. S. Lawrence, J. Opt. Soc. Am. 64, 148 (1974).
[Crossref]

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

G. R. Ochs, S. F. Clifford, Ting-i Wang, “Wind and Cn2 Profiling with Crossed Laser Beams and Spatial Filter Detectors,” NOAA Tech. Rept. ERL 367-WPL 45 (GPO, Washington, D.C., 1976).

G. R. Ochs, R. S. Lawrence, Ting-i Wang, P. Zieske, “Stellar-Scintillation Measurement of the Vertical Profile of Refractive-index Turbulence in the Atmosphere,” in Imaging through the Atmosphere (Soc. Photo-Opt. Instrum. Eng., 75, 48 (1976).
[Crossref]

Shen, L. C.

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

Wang, T-i

Wang, Ting-i

Ting-i Wang, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 63, 334 (1978).
[Crossref]

G. R. Ochs, Ting-i Wang, R. S. Lawrence, S. F. Clifford, Appl. Opt. 15, 2504 (1976).
[Crossref] [PubMed]

G. R. Ochs, S. F. Clifford, Ting-i Wang, Appl. Opt. 15, 403 (1976).
[Crossref] [PubMed]

S. F. Clifford, G. R. Ochs, Ting-i Wang, Appl. Opt. 14, 2844 (1975).
[Crossref] [PubMed]

G. R. Ochs, S. F. Clifford, Ting-i Wang, “Wind and Cn2 Profiling with Crossed Laser Beams and Spatial Filter Detectors,” NOAA Tech. Rept. ERL 367-WPL 45 (GPO, Washington, D.C., 1976).

G. R. Ochs, R. S. Lawrence, Ting-i Wang, P. Zieske, “Stellar-Scintillation Measurement of the Vertical Profile of Refractive-index Turbulence in the Atmosphere,” in Imaging through the Atmosphere (Soc. Photo-Opt. Instrum. Eng., 75, 48 (1976).
[Crossref]

Waterman, A. T.

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

Zieske, P.

G. R. Ochs, R. S. Lawrence, Ting-i Wang, P. Zieske, “Stellar-Scintillation Measurement of the Vertical Profile of Refractive-index Turbulence in the Atmosphere,” in Imaging through the Atmosphere (Soc. Photo-Opt. Instrum. Eng., 75, 48 (1976).
[Crossref]

Appl. Opt. (5)

Dokl. Akad. Nauk SSSR (1)

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

IEEE Trans. Antennas Propag. (2)

L. C. 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. (4)

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 (4)

J. C. Harp, “A Line-of-Sight Microwave Propagation Experiment for Resolving the Motions and Turbulent Structure of the Atmosphere,” Ph.D. Thesis, AFCRL-71-0451, SV-SEL 71-042, Scientific Report 1 (1971).

P. A. Mandics, “Line-of-Sight Acoustical Probing of Atmospheric Turbulence,” Ph.D. Dissertation, Stanford U., Stanford, Calif. (1971).

G. R. Ochs, R. S. Lawrence, Ting-i Wang, P. Zieske, “Stellar-Scintillation Measurement of the Vertical Profile of Refractive-index Turbulence in the Atmosphere,” in Imaging through the Atmosphere (Soc. Photo-Opt. Instrum. Eng., 75, 48 (1976).
[Crossref]

G. R. Ochs, S. F. Clifford, Ting-i Wang, “Wind and Cn2 Profiling with Crossed Laser Beams and Spatial Filter Detectors,” NOAA Tech. Rept. ERL 367-WPL 45 (GPO, Washington, D.C., 1976).

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Figures (8)

Fig. 1
Fig. 1

The relative weights of the different portions of the path in determining the optically measured wind. The parameter β = ρL)−1/2 is the normalized separation of the sensors. These curves are calculated for a point source and for point sensors.

Fig. 2
Fig. 2

A front view of the receiver showing the three pairs of different-sized apertures.

Fig. 3
Fig. 3

Block diagram of the system.

Fig. 4
Fig. 4

The wind path-weighting functions using the six transmitter–receiver pairs shown in Table I. The horizontal axis is the relative path position, and T and R represent transmitting and receiving ends, respectively.

Fig. 5
Fig. 5

The wind path-weighting functions using linear combinations according to Eq. (13) and the coefficients listed in Table I. The horizontal axis is the relative path position, and T and R represent transmitting and receiving ends, respectively.

Fig. 6
Fig. 6

The C n 2 path-weighting functions using the six transmitter–receiver pairs shown in Table I. The horizontal axis is the relative path position, and T and R represent transmitting and receiving ends, respectively.

Fig. 7
Fig. 7

Experimentally measured wind path-weighting functions of the six transmitter–receiver pairs before linear combination. The horizontal axis is the relative path position, and T and R represent transmitting and receiving ends, respectively. The solid curves represent the theoretical weights. The dots are the measured weights averaged, in most cases, over 24-h periods. The error bars represent the standard deviation of the hourly averages throughout the measuring period. The pathlength is 500 m.

Fig. 8
Fig. 8

Similar to Fig. 7 but after the linear combinations.

Tables (1)

Tables Icon

Table I Transmitter Size [= αtL)1/2] and the Receiver Size [= αrL)1/2] for the Six Transmitter–Receiver Pairs

Equations (14)

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C x ( ρ ) = 2.94 0 1 d u σ T 2 ( u ) [ u ( 1 u ) ] 5 / 6 0 d y y 11 / 6 sin 2 y exp { σ T 2 [ u ( 1 u ) ] 5 / 6 F ( y ) } J 0 { [ 4 π y u 1 u ] 1 / 2 ρ } ,
F ( y ) = 7.02 y 5 / 6 0.7 y d ξξ 8 / 3 [ 1 J 0 ( ξ ) ] ,
C χ ( ρ ) = 0 1 d u C n 2 ( u ) W ( u ) ,
W ( u ) = 0.365 k 7 / 6 L 11 / 6 [ u ( 1 u ) ] 5 / 6 0 d y g ( u , y ) × J 0 { [ 4 π y u ( 1 u ) ] 1 / 2 ρ } ,
g ( u , y ) = y 11 / 6 sin 2 y exp { σ T 2 [ u ( 1 u ) ] 5 / 6 F ( y ) } .
m = 2.95 0 1 d u σ T 2 ( u ) [ u ( 1 u ) ] 1 / 3 ( ρ ˆ · v n ) × 0 d y g ( u , y ) ( 4 π y ) 1 / 2 J 1 [ ( 4 π y u 1 u ) 1 / 2 ρ ] ,
( λ L ) 1 / 2 m N = 0 1 d u υ ( u ) W 1 ( u ) / [ 0 1 d u W ( u ) ] ,
W 1 ( u ) = 0.365 k 7 / 6 L 11 / 6 [ u ( 1 u ) ] 1 / 3 0 d y g ( u , y ) ( 4 π y ) 1 / 2 × J 1 [ ( 4 π y u 1 u ) 1 / 2 ρ ] .
g ( u , y ) = g ( u , y ) { 2 J 1 [ ( π y u 1 u ) 1 / 2 α r ] ( π y u 1 u ) 1 / 2 α r } 2 × { 2 J 1 { [ π y ( 1 u ) u ] 1 / 2 α t } [ π y ( 1 u ) u ] 1 / 2 α t } 2 ,
α r + α t > 1.95 ( σ T 2 ) 3 / 5 .
σ I 2 = ( A B ) 2 / [ ( A 0 + B 0 ) 2 ]
C n 2 = ( K σ I 2 D t ) / L 3 ,
W n = C f ( R n 2 W n 2 + R n 1 W n 1 + W n + R n + 1 W n + 1 + R n + 2 W n + 2 ) ,
C f = ( R n 2 + R n 1 + 1 + R n + 1 + R n + 2 ) 1 ,

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