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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 10 — Oct. 1, 2001
  • pp: 2486–2490

Wigner function for nonparaxial wave fields

Colin J. R. Sheppard and Kieran G. Larkin  »View Author Affiliations


JOSA A, Vol. 18, Issue 10, pp. 2486-2490 (2001)
http://dx.doi.org/10.1364/JOSAA.18.002486


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Abstract

The generalized optical transfer function and the spectral correlation function are investigated for nonparaxial two-dimensional wave fields. The angle-impact marginal of the four-dimensional Wigner function is derived directly. For focused wave fields of semiangle greater than 90°, the spectral correlation function exhibits overlapping and interference. For focused wave fields for which the semiangle is known to be less than 180°, the magnitude and phase can be recovered directly from knowledge of the intensity in the focal region.

© 2001 Optical Society of America

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(350.7420) Other areas of optics : Waves

Citation
Colin J. R. Sheppard and Kieran G. Larkin, "Wigner function for nonparaxial wave fields," J. Opt. Soc. Am. A 18, 2486-2490 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-10-2486


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References

  1. K. B. Wolf, M. A. Alonso, and G. W. Forbes, “Wigner functions for Helmholtz wave fields,” J. Opt. Soc. Am. A 16, 2476–2487 (1999).
  2. K. G. Larkin and C. J. R. Sheppard, “Direct method for phase retrieval from the intensity of cylindrical wavefronts,” J. Opt. Soc. Am. A 16, 1838–1844 (1999).
  3. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  4. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik (Stuttgart) 72, 131–133 (1986).
  5. C. J. R. Sheppard, T. J. Connolly, and M. Gu, “Scattering by a one-dimensional rough surface and surface reconstruction by confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993).
  6. C. J. R. Sheppard, M. Gu, Y. Kawata, and S. Kawata, “Three-dimensional transfer functions for high aperture systems obeying the sine condition,” J. Opt. Soc. Am. A 11, 593–598 (1994).
  7. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
  8. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–244 (1964).
  9. B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57, 56–66 (1967).
  10. A. Papoulis, “Ambiguity function in Fourier optics,” J. Opt. Soc. Am. 64, 779–788 (1974).
  11. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  12. M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1144 (1994).
  13. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, and M. G. Raymes, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

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