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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

History
Original Manuscript: November 30, 2000
Revised Manuscript: April 9, 2001
Manuscript Accepted: April 11, 2001
Published: October 1, 2001

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, G. W. Forbes, “Wigner functions for Helmholtz wave fields,” J. Opt. Soc. Am. A 16, 2476–2487 (1999). [CrossRef]
  2. K. G. Larkin, C. J. R. Sheppard, “Direct method for phase retrieval from the intensity of cylindrical wavefronts,” J. Opt. Soc. Am. A 16, 1838–1844 (1999). [CrossRef]
  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, M. Gu, “Scattering by a one-dimensional rough surface and surface reconstruction by confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993). [CrossRef] [PubMed]
  6. C. J. R. Sheppard, M. Gu, Y. Kawata, S. Kawata, “Three-dimensional transfer functions for high aperture systems obeying the sine condition,” J. Opt. Soc. Am. A 11, 593–598 (1994). [CrossRef]
  7. B. Richards, 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). [CrossRef]
  8. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–244 (1964). [CrossRef]
  9. B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57, 56–66 (1967). [CrossRef]
  10. A. Papoulis, “Ambiguity function in Fourier optics,” J. Opt. Soc. Am. 64, 779–788 (1974). [CrossRef]
  11. A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  12. M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1144 (1994). [CrossRef] [PubMed]
  13. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymes, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995). [CrossRef] [PubMed]

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