Abstract

The problem of propagation of pulsed beam waves in an atmosphere with turbulence, rain, or fog is investigated using the temporal moments method. Exact analytical expressions are derived for the mean arrival time and the mean square pulse width for the pulsed beam after it has propagated through the turbulent atmosphere. The results are valid even for strong scattering conditions. Numerical examples indicate that at optical frequencies, the effects of the atmospheric turbulence on the pulses are small except perhaps for picosecond pulses. However, the effects of clouds on optical pulsed beams can be quite severe. At microwave frequencies, scattering by rain may have very large effects on the pulses.

© 1977 Optical Society of America

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  1. D. Mintzer, "Wave propagation in a randomly inhomogeneous medium," J. Acoust. Soc. Am. 25, 922–927 (1953).
  2. H. H. Su and M. A. Plonus, "Optical pulse propagation in a turbulent medium," J. Opt. Soc. Am. 61, 256–260 (1971).
  3. C. S. Gardner and M. A. Plonus, "Optical pulses in atmospheric turbulence," J. Opt. Soc. Am. 64, 68–77 (1974).
  4. L. M. Erukhimov, I. G. A. Zarnitsyna, and P. I. Kirsh, "Selective properties and shape of pulse signals that has passed through a statistically inhomogeneous layer of arbitrary thickness," Radiophys. Quantum Electron. 16, 436–441 (1973).
  5. C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Ant. Prop. AP-22, 624–627 (1974).
  6. L. C. Lee and J. R. Jokipii, "Strong Scintillations in Astrophysics," Astrophys. J. 201, 532–543 (1975).
  7. S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence," Radio Sci. 11, 551–559 (1976).
  8. L. C. Baird, "Moments of a wave packet," Am. J. Phys. 40, 327–329 (1972).
  9. D. G. Anderson and J. I. H. Askne, "Wave packets in strongly dispersive media," Proc. IEEE 62, 1518–1523 (1974).
  10. A. I. Kon, V. L. Mironov, and V. V. Mosov, "Fluctuations of the centers of gravity of light beams in a turbulent atmosphere," Radiophys. Quantum. Electron. 17, 1501–1511 (1974).
  11. K. C. Yeh and C. H. Liu, "An investigation of temporal moments of stochastic waves, " Radio Sci. (to be published).
  12. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).
  13. I. P. Shkarofsky, "Generalized turbulence space-correlation and wave-number spectrum-function pairs," Can. J. Phys. 46, 2133–2152 (1968).
  14. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 5319 (National Technical Information Service, Springfield, Va., 1971).
  15. R. S. Iyer, "Arrival times of satellite-broadened laser pulses." IEEE Trans. Aerospace Elect. Sys. 12, 577–582, (1976).

1976 (2)

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence," Radio Sci. 11, 551–559 (1976).

R. S. Iyer, "Arrival times of satellite-broadened laser pulses." IEEE Trans. Aerospace Elect. Sys. 12, 577–582, (1976).

1975 (1)

L. C. Lee and J. R. Jokipii, "Strong Scintillations in Astrophysics," Astrophys. J. 201, 532–543 (1975).

1974 (3)

C. S. Gardner and M. A. Plonus, "Optical pulses in atmospheric turbulence," J. Opt. Soc. Am. 64, 68–77 (1974).

A. I. Kon, V. L. Mironov, and V. V. Mosov, "Fluctuations of the centers of gravity of light beams in a turbulent atmosphere," Radiophys. Quantum. Electron. 17, 1501–1511 (1974).

C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Ant. Prop. AP-22, 624–627 (1974).

1973 (1)

L. M. Erukhimov, I. G. A. Zarnitsyna, and P. I. Kirsh, "Selective properties and shape of pulse signals that has passed through a statistically inhomogeneous layer of arbitrary thickness," Radiophys. Quantum Electron. 16, 436–441 (1973).

1972 (1)

L. C. Baird, "Moments of a wave packet," Am. J. Phys. 40, 327–329 (1972).

1971 (1)

1968 (1)

I. P. Shkarofsky, "Generalized turbulence space-correlation and wave-number spectrum-function pairs," Can. J. Phys. 46, 2133–2152 (1968).

1953 (1)

D. Mintzer, "Wave propagation in a randomly inhomogeneous medium," J. Acoust. Soc. Am. 25, 922–927 (1953).

Anderson, D. G.

D. G. Anderson and J. I. H. Askne, "Wave packets in strongly dispersive media," Proc. IEEE 62, 1518–1523 (1974).

Askne, J. I. H.

D. G. Anderson and J. I. H. Askne, "Wave packets in strongly dispersive media," Proc. IEEE 62, 1518–1523 (1974).

Baird, L. C.

L. C. Baird, "Moments of a wave packet," Am. J. Phys. 40, 327–329 (1972).

Erukhimov, L. M.

L. M. Erukhimov, I. G. A. Zarnitsyna, and P. I. Kirsh, "Selective properties and shape of pulse signals that has passed through a statistically inhomogeneous layer of arbitrary thickness," Radiophys. Quantum Electron. 16, 436–441 (1973).

Fante, R. L.

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

Gardner, C. S.

Hong, S. T.

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence," Radio Sci. 11, 551–559 (1976).

Ishimaru, A.

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence," Radio Sci. 11, 551–559 (1976).

Iyer, R. S.

R. S. Iyer, "Arrival times of satellite-broadened laser pulses." IEEE Trans. Aerospace Elect. Sys. 12, 577–582, (1976).

Jokipii, J. R.

L. C. Lee and J. R. Jokipii, "Strong Scintillations in Astrophysics," Astrophys. J. 201, 532–543 (1975).

Kirsh, P. I.

L. M. Erukhimov, I. G. A. Zarnitsyna, and P. I. Kirsh, "Selective properties and shape of pulse signals that has passed through a statistically inhomogeneous layer of arbitrary thickness," Radiophys. Quantum Electron. 16, 436–441 (1973).

Kon, A. I.

A. I. Kon, V. L. Mironov, and V. V. Mosov, "Fluctuations of the centers of gravity of light beams in a turbulent atmosphere," Radiophys. Quantum. Electron. 17, 1501–1511 (1974).

Lee, L. C.

L. C. Lee and J. R. Jokipii, "Strong Scintillations in Astrophysics," Astrophys. J. 201, 532–543 (1975).

Liu, C. H.

C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Ant. Prop. AP-22, 624–627 (1974).

K. C. Yeh and C. H. Liu, "An investigation of temporal moments of stochastic waves, " Radio Sci. (to be published).

Mintzer, D.

D. Mintzer, "Wave propagation in a randomly inhomogeneous medium," J. Acoust. Soc. Am. 25, 922–927 (1953).

Mironov, V. L.

A. I. Kon, V. L. Mironov, and V. V. Mosov, "Fluctuations of the centers of gravity of light beams in a turbulent atmosphere," Radiophys. Quantum. Electron. 17, 1501–1511 (1974).

Mosov, V. V.

A. I. Kon, V. L. Mironov, and V. V. Mosov, "Fluctuations of the centers of gravity of light beams in a turbulent atmosphere," Radiophys. Quantum. Electron. 17, 1501–1511 (1974).

Plonus, M. A.

Shkarofsky, I. P.

I. P. Shkarofsky, "Generalized turbulence space-correlation and wave-number spectrum-function pairs," Can. J. Phys. 46, 2133–2152 (1968).

Su, H. H.

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 5319 (National Technical Information Service, Springfield, Va., 1971).

Wernik, A. W.

C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Ant. Prop. AP-22, 624–627 (1974).

Yeh, K. C.

C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Ant. Prop. AP-22, 624–627 (1974).

K. C. Yeh and C. H. Liu, "An investigation of temporal moments of stochastic waves, " Radio Sci. (to be published).

Zarnitsyna, I. G. A.

L. M. Erukhimov, I. G. A. Zarnitsyna, and P. I. Kirsh, "Selective properties and shape of pulse signals that has passed through a statistically inhomogeneous layer of arbitrary thickness," Radiophys. Quantum Electron. 16, 436–441 (1973).

Am. J. Phys. (1)

L. C. Baird, "Moments of a wave packet," Am. J. Phys. 40, 327–329 (1972).

Astrophys. J. (1)

L. C. Lee and J. R. Jokipii, "Strong Scintillations in Astrophysics," Astrophys. J. 201, 532–543 (1975).

Can. J. Phys. (1)

I. P. Shkarofsky, "Generalized turbulence space-correlation and wave-number spectrum-function pairs," Can. J. Phys. 46, 2133–2152 (1968).

IEEE Trans. Aerospace Elect. Sys. (1)

R. S. Iyer, "Arrival times of satellite-broadened laser pulses." IEEE Trans. Aerospace Elect. Sys. 12, 577–582, (1976).

IEEE Trans. Ant. Prop. (1)

C. H. Liu, A. W. Wernik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Ant. Prop. AP-22, 624–627 (1974).

J. Acoust. Soc. Am. (1)

D. Mintzer, "Wave propagation in a randomly inhomogeneous medium," J. Acoust. Soc. Am. 25, 922–927 (1953).

J. Opt. Soc. Am. (2)

Radio Sci. (1)

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence," Radio Sci. 11, 551–559 (1976).

Radiophys. Quantum Electron. (1)

L. M. Erukhimov, I. G. A. Zarnitsyna, and P. I. Kirsh, "Selective properties and shape of pulse signals that has passed through a statistically inhomogeneous layer of arbitrary thickness," Radiophys. Quantum Electron. 16, 436–441 (1973).

Radiophys. Quantum. Electron. (1)

A. I. Kon, V. L. Mironov, and V. V. Mosov, "Fluctuations of the centers of gravity of light beams in a turbulent atmosphere," Radiophys. Quantum. Electron. 17, 1501–1511 (1974).

Other (4)

K. C. Yeh and C. H. Liu, "An investigation of temporal moments of stochastic waves, " Radio Sci. (to be published).

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

D. G. Anderson and J. I. H. Askne, "Wave packets in strongly dispersive media," Proc. IEEE 62, 1518–1523 (1974).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, IPST Catalog No. 5319 (National Technical Information Service, Springfield, Va., 1971).

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