Abstract

A generalized Huygens–Fresnel integral, valid for optical wave propagation through random inhomogeneities in the presence of any complex optical system characterized by an ABCD ray matrix, is used to derive a general expression for the mutual coherence function (MCF) associated with a Gaussian-beam wave in the weak-fluctuation regime. The mean irradiance obtained from this expression shows excellent agreement with all known asymptotic relations. By introducing a pair of effective beam parameters Θt and Λt that account for additional diffraction on the receiving aperture, resulting from turbulence, the normalized MCF and the related degree of coherence are formally extended into the regime of strong fluctuations. Results for the normalized MCF from this heuristic approach compare well with numerical calculations obtained directly from the formal solution of the parabolic equation. Also, the implied spatial coherence length from this analysis in moderate-to-strong-fluctuation regimes generally agrees more closely with numerical solutions of the parabolic equation than do previous approximate solutions. All calculations are based on the modified von Kármán spectrum for direct comparison with established results.

© 1994 Optical Society of America

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    [CrossRef]

1993

W. B. Miller, J. C. Ricklin, L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
[CrossRef]

L. C. Andrews, W. B. Miller, J. C. Ricklin, “Geometrical representation of Gaussian beams propagating through complex paraxial optical systems,” Appl. Opt. 32, 5918–5929 (1993).
[CrossRef] [PubMed]

L. C. Andrews, S. Vester, C. E. Richardson, “Analytic expressions for the wave structure function based on a bump spectral model for refractive index fluctuations,” J. Mod. Opt. 40, 931–938 (1993).
[CrossRef]

H. T. Yura, S. G. Hanson, T. P. Grum, “Speckle: statistics and interferometric decorrelation effects in complex ABCDoptical systems,” J. Opt. Soc. Am. 10, 316–323 (1993).
[CrossRef]

1989

1987

1983

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

1980

M. S. Belen’kii, V. L. Mironov, “Mean diffracted rays of an optical beam in a turbulent medium,” J. Opt. Soc. Am. 70, 159–163 (1980).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

1977

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

1976

1975

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–809 (1975).
[CrossRef]

1974

1972

1971

1970

1967

I. Z. Feizulin, Yu. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. 10, 33–35 (1967).
[CrossRef]

Andrews, L. C.

W. B. Miller, J. C. Ricklin, L. C. Andrews, “Log-amplitude variance and wave structure function: a new perspective for Gaussian beams,” J. Opt. Soc. Am. A 10, 661–672 (1993).
[CrossRef]

L. C. Andrews, W. B. Miller, J. C. Ricklin, “Geometrical representation of Gaussian beams propagating through complex paraxial optical systems,” Appl. Opt. 32, 5918–5929 (1993).
[CrossRef] [PubMed]

L. C. Andrews, S. Vester, C. E. Richardson, “Analytic expressions for the wave structure function based on a bump spectral model for refractive index fluctuations,” J. Mod. Opt. 40, 931–938 (1993).
[CrossRef]

L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (McGraw-Hill, New York, 1992).

Belen’kii, M. S.

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Mean diffracted rays of an optical beam in a turbulent medium,” J. Opt. Soc. Am. 70, 159–163 (1980).
[CrossRef]

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

Beran, M. J.

Brown, W. P.

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–809 (1975).
[CrossRef]

Fante, R. L.

R. L. Fante, “Mutual coherence function and frequency of a laser beam propagating through atmospheric turbulence,” J. Opt. Soc. Am. 64, 592–598 (1974).
[CrossRef]

R. L. Fante, “Wave propagation in random media: a systems approach,” in Progress in Optics XXII, E. Wolf, ed. (Elsevier, New York, 1985).

Feizulin, I. Z.

I. Z. Feizulin, Yu. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. 10, 33–35 (1967).
[CrossRef]

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–809 (1975).
[CrossRef]

Grum, T. P.

H. T. Yura, S. G. Hanson, T. P. Grum, “Speckle: statistics and interferometric decorrelation effects in complex ABCDoptical systems,” J. Opt. Soc. Am. 10, 316–323 (1993).
[CrossRef]

Hanson, S. G.

Ho, T. L.

Ishimaru, A.

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 5.

Kon, A. I.

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

Kravtsov, Yu. A.

I. Z. Feizulin, Yu. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. 10, 33–35 (1967).
[CrossRef]

Lutomirski, R. F.

Lutomirski, R. T.

Miller, W. B.

Mironov, V. L.

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Mean diffracted rays of an optical beam in a turbulent medium,” J. Opt. Soc. Am. 70, 159–163 (1980).
[CrossRef]

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–809 (1975).
[CrossRef]

Richardson, C. E.

L. C. Andrews, S. Vester, C. E. Richardson, “Analytic expressions for the wave structure function based on a bump spectral model for refractive index fluctuations,” J. Mod. Opt. 40, 931–938 (1993).
[CrossRef]

Ricklin, J. C.

Seigman, A. E.

A. E. Seigman, Lasers (University Science Books, Mill Valley, Calif., 1986).

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–809 (1975).
[CrossRef]

Tavis, M. T.

Vester, S.

L. C. Andrews, S. Vester, C. E. Richardson, “Analytic expressions for the wave structure function based on a bump spectral model for refractive index fluctuations,” J. Mod. Opt. 40, 931–938 (1993).
[CrossRef]

Whitman, A. M.

Yura, H. T.

Appl. Opt.

J. Mod. Opt.

L. C. Andrews, S. Vester, C. E. Richardson, “Analytic expressions for the wave structure function based on a bump spectral model for refractive index fluctuations,” J. Mod. Opt. 40, 931–938 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Proc. IEEE

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–809 (1975).
[CrossRef]

Radiophys. Quantum Electron.

I. Z. Feizulin, Yu. A. Kravtsov, “Broadening of a laser beam in a turbulent medium,” Radiophys. Quantum Electron. 10, 33–35 (1967).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Phase fluctuations when focusing light in a turbulent atmosphere,” Radiophys. Quantum Electron. 12, 1096–1101 (1983).
[CrossRef]

Sov. J. Quantum Electron.

M. S. Belen’kii, A. I. Kon, V. L. Mironov, “Turbulent distortions of the spatial coherence of a laser beam,” Sov. J. Quantum Electron. 7, 287–290 (1977).
[CrossRef]

M. S. Belen’kii, V. L. Mironov, “Coherence of the field of a laser beam in a turbulent atmosphere,” Sov. J. Quantum Electron. 10, 595–597 (1980).
[CrossRef]

Other

A. Ishimaru, “The beam wave case and remote sensing,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 5.

J. C. Ricklin, “Optical turbulence effects on Gaussian beam wave propagation in the unstable surface boundary layer,” M.S. thesis (New Mexico State University, Las Cruces, N.M., 1990).

L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (McGraw-Hill, New York, 1992).

A. E. Seigman, Lasers (University Science Books, Mill Valley, Calif., 1986).

R. L. Fante, “Wave propagation in random media: a systems approach,” in Progress in Optics XXII, E. Wolf, ed. (Elsevier, New York, 1985).

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