Abstract

Various methods of correlation analysis that have been used to deduce crosswind from a drifting scintillation pattern are briefly described and then compared with regard to their immunity to noise and their accuracy when faced with nonuniformities along the propagation path or changes in the characteristics of the turbulence. Of the techniques considered, none is ideal; but a new technique, using complete knowledge of the cross-covariance function, proves to be advantageous in a wide variety of situations.

© 1981 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. S. F. Clifford, G. R. Ochs, Ting-i Wang, Appl. Opt. 14, 2844 (1975).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. T. Wang, Science Monthly (Chinese), Taipei, Taiwan 9, No. 2, 48 (1978).
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    [CrossRef]
  6. A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 229 (1941).
  7. A. Peskoff, Proc. IEEE 59, 324 (1971).
    [CrossRef]
  8. R. W. Lee, J. Opt. Soc. Am. 64, 1295 (1974).
    [CrossRef]
  9. T. Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).
    [CrossRef] [PubMed]
  10. L. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).
    [CrossRef]
  11. A. Ishimaru, IEEE Trans. Antennas Propag. AP-20, 10 (1972).
    [CrossRef]
  12. P. A. Mandics, R. W. Lee, A. T. Waterman, Radio Sci. 8, 185 (1973).
    [CrossRef]
  13. J. C. Harp, Ph.D. Thesis, AFCRL-71-0451, SV-SEL-71-042, Scientific Report 1 (1971).
  14. P. A. Mandics, Ph.D. Dissertation, Stanford U., Stanford, Calif. (1971).
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    [CrossRef]
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    [CrossRef]
  17. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.
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  19. S. N. Mitra, Proc. IEEE 96-III, 441 (1949).
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    [CrossRef]
  21. M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
    [CrossRef]
  22. S. F. Clifford, G. R. Ochs, R. S. Lawrence, J. Opt. Soc. Am. 64, 148 (1974).
    [CrossRef]
  23. G. R. Ochs, E. J. Goldenstein, R. F. Quintana, NOAA Technical Memorandum ERL WPL-32 (Oct.1977).
  24. R. J. Hill, S. F. Clifford, J. Opt. Soc. Am. 68, 892 (1978).
    [CrossRef]

1978 (3)

1976 (1)

1975 (1)

1974 (4)

1973 (1)

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

1972 (2)

1971 (1)

A. Peskoff, Proc. IEEE 59, 324 (1971).
[CrossRef]

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]

1967 (1)

M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
[CrossRef]

1950 (1)

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. B 63, 106 (1950).
[CrossRef]

1949 (1)

S. N. Mitra, Proc. IEEE 96-III, 441 (1949).

1941 (1)

A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 229 (1941).

Briggs, B. H.

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. B 63, 106 (1950).
[CrossRef]

Clifford, S. F.

Cohen, M. H.

M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
[CrossRef]

Goldenstein, E. J.

G. R. Ochs, E. J. Goldenstein, R. F. Quintana, NOAA Technical Memorandum ERL WPL-32 (Oct.1977).

Gundermann, E. J.

M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
[CrossRef]

Hardebeck, H. E.

M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
[CrossRef]

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).

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, 229 (1941).

Lawrence, R. S.

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, Ph.D. Dissertation, Stanford U., Stanford, Calif. (1971).

Mitra, S. N.

S. N. Mitra, Proc. IEEE 96-III, 441 (1949).

Ochs, G. R.

Peskoff, A.

A. Peskoff, Proc. IEEE 59, 324 (1971).
[CrossRef]

Phillips, G. J.

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. B 63, 106 (1950).
[CrossRef]

Quintana, R. F.

G. R. Ochs, E. J. Goldenstein, R. F. Quintana, NOAA Technical Memorandum ERL WPL-32 (Oct.1977).

Sharp, L. E.

M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
[CrossRef]

Shen, L.

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

Shinn, D. H.

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. B 63, 106 (1950).
[CrossRef]

Tatarskii, V. I.

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

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation translated from Russian, TT68-50464 (U.S. Department of Commerce, Springfield, Va., 1971).

Wang, T.

Wang, Ting-i

Waterman, A. T.

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

Appl. Opt. (4)

Astrophys. J. (1)

M. H. Cohen, E. J. Gundermann, H. E. Hardebeck, L. E. Sharp, Astrophys. J. 147, 449 (1967).
[CrossRef]

Dokl. Akad. Nauk. SSSR (1)

A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 229 (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. (4)

Proc. IEEE (3)

S. N. Mitra, Proc. IEEE 96-III, 441 (1949).

A. Peskoff, Proc. IEEE 59, 324 (1971).
[CrossRef]

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

Proc. Phys. Soc. B (1)

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. B 63, 106 (1950).
[CrossRef]

Radio Sci. (1)

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

Science Monthly (Chinese), Taipei, Taiwan (1)

T. Wang, Science Monthly (Chinese), Taipei, Taiwan 9, No. 2, 48 (1978).

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 U., Stanford, Calif. (1971).

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

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation translated from Russian, TT68-50464 (U.S. Department of Commerce, Springfield, Va., 1971).

G. R. Ochs, E. J. Goldenstein, R. F. Quintana, NOAA Technical Memorandum ERL WPL-32 (Oct.1977).

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of an optical wind sensor using extended incoherent source and detectors.

Fig. 2
Fig. 2

Typical normalized time-lagged autocovariance and cross-covariance functions of the optical wind sensor described in Fig. 1 (see text for definitions of τp, τc, τf and S0).

Fig. 3
Fig. 3

Schematic diagram of measuring path-averaged crosswind using covariance technique (see text for details).

Fig. 4
Fig. 4

Contour plot in ρτ plane to illustrate the different techniques for measuring crosswind.

Fig. 5
Fig. 5

Simulated autocovariance and cross-covariance curves for different values of the standard deviation σv of the crosswind along the path. C n 2 is assumed uniform along the path.

Fig. 6
Fig. 6

Effect of nonuniformity of C n 2 along the path to the autocovariance and cross-covariance functions. (Crosswind is assumed uniform along the path.) u0 denotes the location (u0 = 0 for transmitting end and u0 = 1 for receiving end) of a strongly turbulent slab (thickness is 1/10 of the path length) with C n 2 ten times greater than the C n 2 on the rest of the path.

Fig. 7
Fig. 7

Turbulent screen with wave number K moves at a speed v at path position z across a diverging beam. At the receiving plane, the pattern velocity is vL/z, the pattern wave number becomes Kz/L. Resulting frequency Kz/L(vL/z) = Kv is unchanged.

Fig. 8
Fig. 8

Simulated autocovariance and cross-covariance functions when both wind and C n 2 fluctuations exist along the path. Crosswind is assumed to be a 2-D Gaussian random variable with mean v ¯ = 1 and standard deviation σvx and σvy (x axis parallel to mean wind). Turbulence structure parameter C n 2 is assumed to be a log-normal random variable with mean C n 2 = 1 (for simplicity) and standard deviation of log C n 2 = σ c. (In the plot, σc = 1 implies one standard deviation per decade.)

Fig. 9
Fig. 9

Resulting autocovariance and cross-covariance functions when incoherent noise is present.

Fig. 10
Fig. 10

Resulting autocovariance and cross-covariance functions when coherent noise is present.

Tables (5)

Tables Icon

Table I Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with a Crosswind that Varies Along Propagation Path a

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Table II Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with Nonuniform Distribution Along the Propagation Path of C n 2 a

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Table III Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with Uncorrelated Nonuniform Distributions of Wind and C n 2 Along the Path a

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Table IV Our Qualitative Evaluation of Effectiveness of Five Wind-Measuring Techniques when Faced with Various Disturbing Factors

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Table V Tabulation of Observed Standard Deviations of the Ratio of Various Optical Measurements to Propeller Anemometer Measurements a

Equations (23)

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σ T 2 = 0.124 k 7 / 6 L 11 / 6 C n 2 ,
D r + D t > 2 ( σ T 2 ) 3 / 5 ( λ L ) 1 / 2 ,
C χ ( ρ , τ ) = 0.132 π 2 k 2 0 L d z C n 2 ( z ) 0 d K K - 8 / 3 sin 2 [ K 2 z ( L - z ) 2 k L ] × J 0 [ K | ρ z L - v ( z ) τ | ] × [ 2 J 1 ( K D r z 2 L ) K D r z 2 L ] 2 { 2 J 1 [ K D t 2 ( 1 - z L ) ] K D t 2 ( 1 - z L ) } 2 ,
Φ n ( K ) = 0.33 C n 2 ( z ) K - 11 / 3 ;             L 0 - 1 < K < l 0 - 1 ,
V p ~ ρ / τ p ,
V s ~ S 0 .
V f ~ 1 / τ f .
V b ~ [ ρ / ( 2 τ c ) ] .
( C a + C b + C c ) - ( C d + C e + C f + C g ) + ( C h + C i + C j + C k ) - ( C l + C m + C n ) = 0 ,
V c ~ 1 / T .
C χ ( ρ , τ ) f [ ( ρ - v ¯ τ ) 2 + σ v 2 τ 2 ] ,
τ p = ρ v ¯ / ( v ¯ 2 + σ v 2 ) ,
V p ~ ρ τ p = v ¯ + σ v 2 v ¯ .
S 0 C χ τ | τ = 0 = - 2 ρ v ¯ f ,
V s ~ S 0 ~ v ¯ .
τ f ~ ( v ¯ 2 + σ v 2 ) - 1 / 2 .
V f ~ ( 1 / τ f ) ~ ( v ¯ 2 + σ v 2 ) 1 / 2 .
( ρ - v ¯ τ c ) 2 + σ v 2 τ c 2 = ( v ¯ 2 + σ v 2 ) τ c 2
τ c = ρ / ( 2 v ¯ ) .
V B ~ [ ρ / ( 2 τ c ) ] = v ¯ .
C 12 ( τ ) = S 1 ( t ) S 2 ( t + τ ) S 1 2 1 / 2 S 2 2 1 / 2 ,
C 12 ( τ ) = S 1 ( t ) S 2 ( t + τ ) + N 1 ( t ) N 2 ( t + τ ) S 1 2 + N 1 2 .
C 11 ( τ ) = S 1 ( t ) S 1 ( t + τ ) + N 1 ( t ) N 1 ( t + τ ) S 1 2 + N 1 2 .

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