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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 2 — Feb. 1, 1978
  • pp: 175–185

Atmospheric propagation of partially coherent radiation

J. Carl Leader  »View Author Affiliations

JOSA, Vol. 68, Issue 2, pp. 175-185 (1978)

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An extended, Rayleigh-Sommerfeld integral method is used to derive expressions for the mutual coherence function and radiation intensity derived from a planar, partially coherent source propagating through the atmosphere. The derived results reduce to previous results for (i) coherent radiation propagation in the atmosphere and (ii) the relations relating the far-field intensity angular distribution and the source coherence for a partially coherent source in vacuo. A mathematical description of the predicted results in terms of the vacuum distribution and scattering functions (related to the Fourier-transformed two-source mutual coherence function) is permitted by this development. Analytical results are calculated for a homogeneous atmosphere and a source coherence that simulates a laser-illuminated rough surface. The effective far-field range is determined by the source size, wavelength, and source coherence length. The phase of the calculated mutual coherence function is determined by the field-point separation for off-axial propagation directions. Numerical results for the amplitude and phase coherence lengths are calculated and illustrated as a function of the source size, source coherence length, propagation angle, range, and refractive-index structure constant.

© 1978 Optical Society of America

J. Carl Leader, "Atmospheric propagation of partially coherent radiation," J. Opt. Soc. Am. 68, 175-185 (1978)

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  1. M. J. Beran, "Propagations of a finite beam in a random medium," J. Opt. Soc. Am. 60, 518–521 (1970).
  2. R. L. Fante, "Mutual coherence function and frequency spectrum of a laser beam propagating through atmospheric turbulence," J. Opt. Soc. Am. 64, 592–598 (1974).
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  8. R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomgeneous medium," Appl. Opt. 10, 1652–1658 (1971).
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  11. E. W. Marchand and E. Wolf, "Angular correlation and the far-zone behavior of partially coherent fields," J. Opt. Soc. Am. 62, 379–385 (1972).
  12. The vector problem can be treated using the technique described in this paper together with the formalism described in J. C. Leader, "The generalized partial coherence of a radiation source and its far-field" Optica Acta (to be published).
  13. A. Sommerfeld, "Optics," Lectures on Theoretical Physics (Academic, New York, 1954), Vol IV, pp. 197–201.
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  16. Use has been made of the fact that R- = (|p|2 + z2)1/2 - (|p′|2 + z2)1/2 ≅ (1/2z) × (|p|2 - |p′|2) = P+ · p-/z.
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  19. A. Kon and V. Feizulin, "Fluctuations in the parameters of spherical waves propagating in a turbulant atmosphere," Radiophys. Quantum Electron. (USSR) 13, 51–53 (1970).
  20. R. L. Fante, "Two-source spherical wave structure functions in atmospheric turbulence," J. Opt. Soc. Am. 66, 74 (1976).
  21. A. V. Artem'ev and A. S. Gurvich, "Experimental study of coherence function spectra," Radiophys. Quantum Electron. (USSR) 14, 580–583 (1971).
  22. D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).
  23. J. R. Dunphy and J. R. Kerr, "Turbulence effects on target illumination by laser sources: phenomonological analysis and experimental results," Appl. Opt. 16, 1345–1358 (1977).
  24. Ref 17, pp. 50–52.
  25. J. C. Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).
  26. J. C. Leader, "Incoherent backscatter from rough surfaces: the two scale model re-examined," Radio. Sci. (to be published June/July 1978).

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