Abstract

The feasibility of detecting clear-air turbulence layers (CAT) by measuring the covariance function of the fluctuations in log amplitude of an optical signal propagated through the atmosphere is discussed. In particular, the problem of determining Cn2(z), the magnitude of the refractive-index fluctuations, is investigated. It is extremely unlikely that CAT can be detected from such measurements. Variations of the log-amplitude covariance function induced by CAT layers are so small that they will normally be masked by variations expected in other atmospheric parameters, such as changes of the spectral density of the refractive index or nonhomogeneity of the medium. There appears to be more promise in measurements that more directly measure the wind; further studies of this type are recommended.

© 1970 Optical Society of America

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References

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  1. A. Peskoff, J. Opt. Soc. Am. 58, 1032 (1968).
    [CrossRef]
  2. D. L. Fried, Proc. IEEE 57, 415 (1969).
    [CrossRef]
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1961).
  4. B. R. Bean, Proc. Conf. on Tropospheric Wave Propagation, 30 Sept.–2 Oct. 1968, The Inst. of Elec. Engr., London, Conference Publication No. 48.
  5. J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
    [CrossRef]
  6. J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
    [CrossRef]
  7. R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
    [CrossRef]

1970 (1)

J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
[CrossRef]

1969 (2)

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

D. L. Fried, Proc. IEEE 57, 415 (1969).
[CrossRef]

1968 (2)

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
[CrossRef]

A. Peskoff, J. Opt. Soc. Am. 58, 1032 (1968).
[CrossRef]

Bean, B. R.

B. R. Bean, Proc. Conf. on Tropospheric Wave Propagation, 30 Sept.–2 Oct. 1968, The Inst. of Elec. Engr., London, Conference Publication No. 48.

Fried, D. L.

D. L. Fried, Proc. IEEE 57, 415 (1969).
[CrossRef]

Harp, J. C.

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

Lee, R. W.

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

Peskoff, A.

Strohbehn, J. W.

J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
[CrossRef]

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
[CrossRef]

Tatarski, V. I.

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

J. Geophys. Res. (1)

J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (3)

D. L. Fried, Proc. IEEE 57, 415 (1969).
[CrossRef]

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

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
[CrossRef]

Other (2)

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

B. R. Bean, Proc. Conf. on Tropospheric Wave Propagation, 30 Sept.–2 Oct. 1968, The Inst. of Elec. Engr., London, Conference Publication No. 48.

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Figures (4)

Fig. 1
Fig. 1

Normalized covariance function of log-amplitude fluctuations plotted as a function of ρ ( k / h ) 1 2, where ρ is the separation between two receivers, k is the wavenumber, and h the scale height of the exponential layer. The parameter C2, the magnitude of the CAT layer, is varied. The other parameters are h = 8 km, L = 10 km, W = 1 km, k = 107 m−1, and α = 11/6. ——C1 = 1, C2 = 0; – – –C1 = 1, C2 = 1; — · —C1 = 1, C2 = 10.

Fig. 2
Fig. 2

Similar to Fig. 1, except that the height of the CAT layer is varied. The scale height of the exponential layer, h, is 8 km, k = 107 m−1. ——C1 = 1, C2 = 0; – – –C1 = 1, C2 = 1, L = 10 km, W = 1 km; △△: C1 = 1, C2 = 1, L = 5 km, W = 1 km; ××: C1 = 1, C2 = 1, L = 1 km, W = 200 m; □□: C1 = 1, C2 = 10, L = 1 km, W = 200 m.

Fig. 3
Fig. 3

Similar to Fig. 1, except the spectral shape Φn0(κ) is varied. Other parameters are C1 = 1, C2 = 0, h = 8 km, k = 107 m−1. — —: α = 7/6; — · —: α = 9/6; ——: α = 11/6; – – –: α = 13/6.

Fig. 4
Fig. 4

A plot of Φn0(κ) and the weighting function for the integral in Eq. (6). Φn0(κ) = exp(−κ2/(628)2)/(1 + 100κ2)11/6. h = 8 km, L = 10 km, W = 1 km, and k = 107 m−1. ——: C1 = 1, C2 = 0; — —: C1 = 1, C2 = 0.1; — · —: C1 = 1, C2 = 1.

Equations (6)

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Φ n ( κ , r ) = C n 2 ( r ) Φ n 0 ( κ ) ,
Φ n 0 ( κ ) = exp ( - κ 2 / κ m 2 ) / ( 1 + κ 2 L 0 2 ) α ,
C n 2 ( z ) = C 1 e - z / h + C 2 ( z ) C 2 ( z ) = { C 2 L - W / 2 < z < L + W / 2 0 otherwise .
B χ ( ρ ) = 4 π 2 k 2 0 d z C n 2 ( z ) 0 d κ κ Φ n 0 ( κ ) × J 0 ( κ ρ ) sin 2 ( κ 2 z 2 k ) .
B χ ( ρ ) = 4 π 2 k 2 0 d κ κ Φ n 0 ( κ ) J 0 ( κ ρ ) × 0 d z C n 2 ( z ) sin 2 ( κ 2 z 2 k ) .
B χ ( ρ ) = 2 π k 2 0 d κ κ Φ n 0 ( κ ) J 0 ( κ ρ ) { C 1 h 1 + k 2 / κ 4 h 2 + C 2 W [ 1 - 2 k κ 2 W sin κ 2 W 2 k cos L κ 2 k ] } .