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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 6 — Jun. 1, 1980
  • pp: 745–747

Meaning of quadratic structure functions

Stephen M. Wandzura  »View Author Affiliations


JOSA, Vol. 70, Issue 6, pp. 745-747 (1980)
http://dx.doi.org/10.1364/JOSA.70.000745


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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

Citation
Stephen M. Wandzura, "Meaning of quadratic structure functions," J. Opt. Soc. Am. 70, 745-747 (1980)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-6-745


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References

  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).
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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.
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  12. D. L. Fried, "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures," J. Opt. Soc. Am. 56, 1372–1379 (1966).
  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).

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