Abstract

Quadratic structure functions are sometimes used to describe the phase of partially coherent waves. The physical significance of such structure functions, that they describe a tilted but unwarped phase, limits their applicability to propagation calculations. Calculation of processes in which the principal effects are due to phase-front tilting may be simplified by recognizing that fact.

© 1980 Optical Society of America

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  1. R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652–1658 (1971).
  2. A. I. Kon and V. I. Tatarskii, "On the theory of the propagation of partially coherent light beams in a turbulent atmosphere," Radiophys. Quantum Electron. 15, 1187–1192 (1972).
  3. I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci. 11, 775–778 (1976).
  4. W. H. Carter and E. Wolf, "Coherence and radiometry with quasihomogeneous planar sources," J. Opt. Soc. Am. 66, 785–796 (1977).
  5. J. C. Leader, "Atmospheric propagation of partially coherent radiation," J. Opt. Soc. Am. 68, 175–185 (1978).
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  9. R. L. Fante, "Electromagnetic beam propagation in turbulent media," Proc. IEEE 63, 1669–1692 (1975).
  10. S. F. Clifford, "The classical theory of wave propagation in a turbulent medium," in Laser Beam Propagation in the Atmosphere, edited by J. W. Strobehn (Springer-Verlag, Berlin, Heidelberg, 1978), pp. 9–43.
  11. D. L. Fried, "Statistics of a geometrical representation of wavefront distortion," J. Opt. Soc. Am. 55, 1427–1435 (1965).
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  13. G. C. Valley and S. M. Wandzura, "Spatial correlation of phase-expansion coefficients for propagation through atmospheric turbulence," J. Opt. Soc. Am. 69, 712–717 (1979).
  14. The editor has suggested that it be made clear that "through tilts" does not necessarily mean "only a tilt." An example would be the optical transfer and point-spread functions (both second moments) of an imaging system whose performance is degraded by deep phase fluctuations across the receiving aperture. It can be shown that in this limit these functions depend only on the variance of local tilts (first partial derivatives) of the phase error, even if the overall tilt is removed (short-exposure case). Higher moments (intensity correlations) depend, however, on tilt-tilt correlations [see point (iii) in the conclusions]. Thus, in the strong phase fluctuation case, an "effective short-exposure quadratic structure function" can be used, but only for calculation of second moments. However, it is necessary to know the original tilt-tilt correlation length (information not contained in a QSF) in order to determine this effective structure function.
  15. R. Dashen, "Path integrals for waves in random media," J. Math. Phys. 20, 894–922 (1979).
  16. R. L. Fante, "Intensity scintillations of an EM wave in extremely strong turbulence," IEEE Trans. Antennas Propag. AP-25, 266–268 (1977).

1979 (5)

1978 (1)

1977 (2)

R. L. Fante, "Intensity scintillations of an EM wave in extremely strong turbulence," IEEE Trans. Antennas Propag. AP-25, 266–268 (1977).

W. H. Carter and E. Wolf, "Coherence and radiometry with quasihomogeneous planar sources," J. Opt. Soc. Am. 66, 785–796 (1977).

1976 (1)

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci. 11, 775–778 (1976).

1972 (1)

A. I. Kon and V. I. Tatarskii, "On the theory of the propagation of partially coherent light beams in a turbulent atmosphere," Radiophys. Quantum Electron. 15, 1187–1192 (1972).

1971 (1)

1966 (1)

1965 (1)

Carter, W. H.

W. H. Carter and E. Wolf, "Coherence and radiometry with quasihomogeneous planar sources," J. Opt. Soc. Am. 66, 785–796 (1977).

Clifford, S. F.

S. F. Clifford, "The classical theory of wave propagation in a turbulent medium," in Laser Beam Propagation in the Atmosphere, edited by J. W. Strobehn (Springer-Verlag, Berlin, Heidelberg, 1978), pp. 9–43.

Dashen, R.

R. Dashen, "Path integrals for waves in random media," J. Math. Phys. 20, 894–922 (1979).

Fante, R. L.

R. L. Fante, "Intensity scintillations of an EM wave in extremely strong turbulence," IEEE Trans. Antennas Propag. AP-25, 266–268 (1977).

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

Fried, D. L.

Hong, S. T.

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci. 11, 775–778 (1976).

Ishimaru, A.

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci. 11, 775–778 (1976).

Kon, A. I.

A. I. Kon and V. I. Tatarskii, "On the theory of the propagation of partially coherent light beams in a turbulent atmosphere," Radiophys. Quantum Electron. 15, 1187–1192 (1972).

Leader, J. C.

Lutomirski, R. F.

Ouyang, C. F.

Plonus, M. A.

Sreenivasiah, I.

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci. 11, 775–778 (1976).

Tatarskii, V. I.

A. I. Kon and V. I. Tatarskii, "On the theory of the propagation of partially coherent light beams in a turbulent atmosphere," Radiophys. Quantum Electron. 15, 1187–1192 (1972).

Valley, G. C.

Wandzura, S. M.

Wang, S. C. H.

Wolf, E.

W. H. Carter and E. Wolf, "Coherence and radiometry with quasihomogeneous planar sources," J. Opt. Soc. Am. 66, 785–796 (1977).

Yura, H. T.

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

R. L. Fante, "Intensity scintillations of an EM wave in extremely strong turbulence," IEEE Trans. Antennas Propag. AP-25, 266–268 (1977).

J. Math. Phys. (1)

R. Dashen, "Path integrals for waves in random media," J. Math. Phys. 20, 894–922 (1979).

J. Opt. Soc. Am. (7)

Radio Sci. (1)

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytic solution to the plane wave case," Radio Sci. 11, 775–778 (1976).

Radiophys. Quantum Electron. (1)

A. I. Kon and V. I. Tatarskii, "On the theory of the propagation of partially coherent light beams in a turbulent atmosphere," Radiophys. Quantum Electron. 15, 1187–1192 (1972).

Other (3)

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

S. F. Clifford, "The classical theory of wave propagation in a turbulent medium," in Laser Beam Propagation in the Atmosphere, edited by J. W. Strobehn (Springer-Verlag, Berlin, Heidelberg, 1978), pp. 9–43.

The editor has suggested that it be made clear that "through tilts" does not necessarily mean "only a tilt." An example would be the optical transfer and point-spread functions (both second moments) of an imaging system whose performance is degraded by deep phase fluctuations across the receiving aperture. It can be shown that in this limit these functions depend only on the variance of local tilts (first partial derivatives) of the phase error, even if the overall tilt is removed (short-exposure case). Higher moments (intensity correlations) depend, however, on tilt-tilt correlations [see point (iii) in the conclusions]. Thus, in the strong phase fluctuation case, an "effective short-exposure quadratic structure function" can be used, but only for calculation of second moments. However, it is necessary to know the original tilt-tilt correlation length (information not contained in a QSF) in order to determine this effective structure function.

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