Abstract

We apply the theory of plane-wave scattering by spheres to calculate the variance, the space-time covariance, and the temporal-frequency spectrum of the amplitude fluctuations of a light wave passing through rainfall. The development includes the effects of various sizes of raindrops and their associated terminal velocities. We show that the time-lagged covariance function of two vertically spaced sensors can provide a practical remote measurement of path-averaged rain parameters, such as drop-size distribution and rain rate, without any assumptions about the form of the drop-size distribution.

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  1. T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 45, 301 (1966).
  2. T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 47, 723 (1968).
  3. D. Atlas, J. Meteorol. 10, 486 (1953).
  4. R. W. Wilson and A. A. Penzias, Nature 211, 1081 (1966).
  5. D. Atlas and C. W. Ulbrich, J. Rech. Atmos. VIII, 275 (1974).
  6. S. W. Kurnick, R. N. Zitter, and D. B. Williams, J. Opt. Soc. Am. 50, 578 (1960).
  7. A. Arnulf and J. Bricard, J. Opt. Soc. Am. 47, 491 (1957).
  8. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  9. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 4319 (National Technical Information Service, Springfield, Va., 1971).
  10. R. Gunn and G. D. Kinzer, J. Meteorol. 6, 243 (1949).
  11. T. S. Marshall and W. McK. Palmer, J. Meteorol. 4, 186 (1948).
  12. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
  13. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 749–750.
  14. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 707.

Arnulf, A.

A. Arnulf and J. Bricard, J. Opt. Soc. Am. 47, 491 (1957).

Atlas, D.

D. Atlas, J. Meteorol. 10, 486 (1953).

D. Atlas and C. W. Ulbrich, J. Rech. Atmos. VIII, 275 (1974).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 749–750.

Bricard, J.

A. Arnulf and J. Bricard, J. Opt. Soc. Am. 47, 491 (1957).

Chu, T. S.

T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 45, 301 (1966).

T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 47, 723 (1968).

Clifford, S. F.

S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 707.

Gunn, R.

R. Gunn and G. D. Kinzer, J. Meteorol. 6, 243 (1949).

Hogg, D. C.

T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 47, 723 (1968).

T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 45, 301 (1966).

Kinzer, G. D.

R. Gunn and G. D. Kinzer, J. Meteorol. 6, 243 (1949).

Kurnick, S. W.

S. W. Kurnick, R. N. Zitter, and D. B. Williams, J. Opt. Soc. Am. 50, 578 (1960).

Marshall, T. S.

T. S. Marshall and W. McK. Palmer, J. Meteorol. 4, 186 (1948).

Palmer, W. McK.

T. S. Marshall and W. McK. Palmer, J. Meteorol. 4, 186 (1948).

Penzias, A. A.

R. W. Wilson and A. A. Penzias, Nature 211, 1081 (1966).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 707.

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 4319 (National Technical Information Service, Springfield, Va., 1971).

Ulbrich, C. W.

D. Atlas and C. W. Ulbrich, J. Rech. Atmos. VIII, 275 (1974).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Williams, D. B.

S. W. Kurnick, R. N. Zitter, and D. B. Williams, J. Opt. Soc. Am. 50, 578 (1960).

Wilson, R. W.

R. W. Wilson and A. A. Penzias, Nature 211, 1081 (1966).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 749–750.

Zitter, R. N.

S. W. Kurnick, R. N. Zitter, and D. B. Williams, J. Opt. Soc. Am. 50, 578 (1960).

Other (14)

T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 45, 301 (1966).

T. S. Chu and D. C. Hogg, Bell Syst. Tech. J. 47, 723 (1968).

D. Atlas, J. Meteorol. 10, 486 (1953).

R. W. Wilson and A. A. Penzias, Nature 211, 1081 (1966).

D. Atlas and C. W. Ulbrich, J. Rech. Atmos. VIII, 275 (1974).

S. W. Kurnick, R. N. Zitter, and D. B. Williams, J. Opt. Soc. Am. 50, 578 (1960).

A. Arnulf and J. Bricard, J. Opt. Soc. Am. 47, 491 (1957).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 4319 (National Technical Information Service, Springfield, Va., 1971).

R. Gunn and G. D. Kinzer, J. Meteorol. 6, 243 (1949).

T. S. Marshall and W. McK. Palmer, J. Meteorol. 4, 186 (1948).

S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 749–750.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 707.

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