Abstract

There is strong evidence that the amplitude of a light wave propagating through turbulence becomes Rayleigh distributed (i.e., the irradiance becomes exponentially distributed) in the limit of strong turbulence, which implies that the log-amplitude variance tends to π<sup>2</sup>/24. We find that the theory by Clifford <i>et al</i>. [J. Opt. Soc. Am. 64, 148–154 (1974)] for saturation of scintillation by strong refractive turbulence can be made to obey this limit for power-law refractive-index spectra. However, for a nonzero inner scale of turbulence (no matter how small), the theory predicts that log-amplitude variance tends to zero in the limit of strong turbulence. A generalization of the theory is derived that obeys the π<sup>2</sup>/24 limit for arbitrary refractive-index spectra, a nonzero inner scale being a particular case. The new theory has no arbitrary parameters. Both old and new modulation transfer functions have different behavior for nonzero inner scale at both very large and very small spatial wave numbers when compared with the case of zero inner scale. This differing behavior affects the log-amplitude variance even if the Fresnelzone size is much greater than the inner scale, provided that the lateral coherence length of phase is less than the inner scale. This differing behavior also applies at all spatial wave numbers if the Rytov variance is strongly affected by the inner scale. For strong (but finite) turbulence strength, the predicted log-amplitude variance is larger for a smaller ratio of Fresnel-zone size to inner scale, which is in quantitative agreement with observations.

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  1. S. F. Clifford, G. R. Ochs, and R. W. Lawrence, "Saturation of optical scintillation by strong turbulence," J. Opt. Soc. Am. 64, 148–154 (1974).
  2. R. J. Hill and S. F. Clifford, "Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation," J. Opt. Soc. Am. 68, 892–899 (1978).
  3. R. J. Hill, "Models of the scalar spectrum for turbulent advection," J. Fluid Mech. 88, 541–562 (1978).
  4. S. F. Clifford and H. T. Yura, "Equivalence of two theories of strong optical scintillation," J. Opt. Soc. Am. 64, 1641–1644 (1974).
  5. R. J. Hill and M. H. Ackley, "Function routines for integrals involving the Bessel functions J0 and J1," NOAA Tech. Rep. no. ERL 410-WPL 55 (U.S. Government Printing Office, Washington, D.C., 1980).
  6. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).
  7. S. F. Clifford and R. J. Hill, "Relation between irradiance and log-amplitude variance for optical scintillation described by the K distribution," J. Opt. Soc. Am. 71, 112–114 (1981).
  8. R. J. Hill and S. F. Clifford, "The bump in the variance of logintensity," in Technical Digest of Topical Meeting on Optical Propagation through Turbulence, Rain, and Fog (Optical Society of America, Washington, D.C., 1977).
  9. G. R. Ochs, "Measurements of 0.63 µm laser-beam scintillation in strong atmospheric turbulence," ESSA Tech. Rep. no. ERL 154-WPL 10 (U.S. Government Printing Office, Washington, D.C., 1969).

1981

1978

1974

Ackley, M. H.

R. J. Hill and M. H. Ackley, "Function routines for integrals involving the Bessel functions J0 and J1," NOAA Tech. Rep. no. ERL 410-WPL 55 (U.S. Government Printing Office, Washington, D.C., 1980).

Clifford, S. F.

Fante, R. L.

R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).

Hill, R. J.

S. F. Clifford and R. J. Hill, "Relation between irradiance and log-amplitude variance for optical scintillation described by the K distribution," J. Opt. Soc. Am. 71, 112–114 (1981).

R. J. Hill and S. F. Clifford, "Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation," J. Opt. Soc. Am. 68, 892–899 (1978).

R. J. Hill, "Models of the scalar spectrum for turbulent advection," J. Fluid Mech. 88, 541–562 (1978).

R. J. Hill and S. F. Clifford, "The bump in the variance of logintensity," in Technical Digest of Topical Meeting on Optical Propagation through Turbulence, Rain, and Fog (Optical Society of America, Washington, D.C., 1977).

R. J. Hill and M. H. Ackley, "Function routines for integrals involving the Bessel functions J0 and J1," NOAA Tech. Rep. no. ERL 410-WPL 55 (U.S. Government Printing Office, Washington, D.C., 1980).

Lawrence, R. W.

Ochs, G. R.

S. F. Clifford, G. R. Ochs, and R. W. Lawrence, "Saturation of optical scintillation by strong turbulence," J. Opt. Soc. Am. 64, 148–154 (1974).

G. R. Ochs, "Measurements of 0.63 µm laser-beam scintillation in strong atmospheric turbulence," ESSA Tech. Rep. no. ERL 154-WPL 10 (U.S. Government Printing Office, Washington, D.C., 1969).

Yura, H. T.

J. Fluid Mech.

R. J. Hill, "Models of the scalar spectrum for turbulent advection," J. Fluid Mech. 88, 541–562 (1978).

J. Opt. Soc. Am.

Other

R. J. Hill and S. F. Clifford, "The bump in the variance of logintensity," in Technical Digest of Topical Meeting on Optical Propagation through Turbulence, Rain, and Fog (Optical Society of America, Washington, D.C., 1977).

G. R. Ochs, "Measurements of 0.63 µm laser-beam scintillation in strong atmospheric turbulence," ESSA Tech. Rep. no. ERL 154-WPL 10 (U.S. Government Printing Office, Washington, D.C., 1969).

R. J. Hill and M. H. Ackley, "Function routines for integrals involving the Bessel functions J0 and J1," NOAA Tech. Rep. no. ERL 410-WPL 55 (U.S. Government Printing Office, Washington, D.C., 1980).

R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).

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