Abstract

The most commonly used expression for the wave structure and mutual coherence function for an optical wave propagating in a turbulent atmosphere, which is based on an unphysical extrapolation of the Kolmogorov spectrum, is shown in general to be incorrect. For a modified spectrum, we show that the correction to the wave structure and mutual coherence functions, the implied resolution, and the resulting signal-to-noise (S/N) ratio using heterodyne detection, are considerable. Approximate expressions for the coherence function, valid over three distinct propagation distance regions, are derived, and experimental evidence in support of our results is cited.

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  2. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
  3. D. L. Fried, Proc. IEEE 55, 57 (1967).
  4. G. M. B. Bouricius and S. F. Clifford, J. Opt. Soc. Am. 60, 1484 (1970).
  5. For short propagation paths, the wave and phase structure function are identical (see Ref. 1).
  6. R. G. Buser, J. Opt. Soc. Am. 61, 496 (1971).
  7. In deriving Eq. (1), we have assumed that Φn is not a function of propagation distance. The modification of Eq. (1) to include an explicit dependence on range is that zΦn(K)→ ∫02Φ(K,z′)dz′. For spherical wave propagation let z[1-J0(Kp)]→∫02ds′×[1-J0(Kpz′/z)].
  8. J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
  9. The quantity 2π/L0, rather than 1/L0, is introduced in Eq. (7) because we are comparing a wavenumber with a length. In any case, this parameter is to be regarded as the reciprocal of the wave-number where the spectrum, in the low-frequency regime, begins to deviate from a K-11/3 dependence. As has been noted, the resulting dependence on ρ is insensitive to the details of the low-frequency behavior of the spectrum, but depends only on the value of K where the spectrum begins to level off.
  10. D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).

Bouricius, G. M. B.

G. M. B. Bouricius and S. F. Clifford, J. Opt. Soc. Am. 60, 1484 (1970).

Buser, R. G.

R. G. Buser, J. Opt. Soc. Am. 61, 496 (1971).

Clifford, S. F.

G. M. B. Bouricius and S. F. Clifford, J. Opt. Soc. Am. 60, 1484 (1970).

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).

D. L. Fried, Proc. IEEE 55, 57 (1967).

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Stanley, N. R.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Strohbehn, J. W.

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

Tatarski, V. I.

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

Other

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

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

D. L. Fried, Proc. IEEE 55, 57 (1967).

G. M. B. Bouricius and S. F. Clifford, J. Opt. Soc. Am. 60, 1484 (1970).

For short propagation paths, the wave and phase structure function are identical (see Ref. 1).

R. G. Buser, J. Opt. Soc. Am. 61, 496 (1971).

In deriving Eq. (1), we have assumed that Φn is not a function of propagation distance. The modification of Eq. (1) to include an explicit dependence on range is that zΦn(K)→ ∫02Φ(K,z′)dz′. For spherical wave propagation let z[1-J0(Kp)]→∫02ds′×[1-J0(Kpz′/z)].

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

The quantity 2π/L0, rather than 1/L0, is introduced in Eq. (7) because we are comparing a wavenumber with a length. In any case, this parameter is to be regarded as the reciprocal of the wave-number where the spectrum, in the low-frequency regime, begins to deviate from a K-11/3 dependence. As has been noted, the resulting dependence on ρ is insensitive to the details of the low-frequency behavior of the spectrum, but depends only on the value of K where the spectrum begins to level off.

D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).

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