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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 45, Iss. 34 — Dec. 1, 2006
  • pp: 8586–8595

Analysis of optical systems with extended depth of field using the Wigner distribution function

Qingguo Yang, Liren Liu, Jianfeng Sun, Yongjian Zhu, and Wei Lu  »View Author Affiliations


Applied Optics, Vol. 45, Issue 34, pp. 8586-8595 (2006)
http://dx.doi.org/10.1364/AO.45.008586


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Abstract

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase–space curve that formulates a joint phase–space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated.

© 2006 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(080.2740) Geometric optics : Geometric optical design
(110.2990) Imaging systems : Image formation theory

History
Original Manuscript: April 12, 2006
Revised Manuscript: July 17, 2006
Manuscript Accepted: July 17, 2006

Virtual Issues
Vol. 2, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Qingguo Yang, Liren Liu, Jianfeng Sun, Yongjian Zhu, and Wei Lu, "Analysis of optical systems with extended depth of field using the Wigner distribution function," Appl. Opt. 45, 8586-8595 (2006)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-34-8586


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References

  1. M. Mino and Y. Okano, "Improvement in the optical transfer function of a defocused optical system through the use of shaded aperture," Appl. Opt. 10, 2219-2225 (1971). [CrossRef] [PubMed]
  2. J. Ojeda-Castañeda, L. R. Berriel-Valdos, and E. L. Montes, "Spatial filter for increasing the depth of focus," Opt. Lett. 10, 520-522 (1985). [CrossRef] [PubMed]
  3. J. Ojeda-Castañeda, P. Andres, and A. Diaz, "Annular apodizers for low sensitivity to defocus and to spherical aberration," Opt. Lett. 11, 487-489 (1986). [CrossRef] [PubMed]
  4. J. Ojeda-Castañeda, E. Tepichin, and A. Diaz, "Arbitrary high focal depth with finite aperture," Opt. Lett. 13, 183-185 (1988). [CrossRef] [PubMed]
  5. J. Ojeda-Castañeda and L. R. Berriel-Valdos, "Zone plate for arbitrarily high focal depth," Appl. Opt. 29, 994-997 (1990). [CrossRef] [PubMed]
  6. Q. Yang, L. Liu, and H. Lang, "Enlarging the depth of focus by filtering in the phase-space domain," Appl. Opt. 44, 6833-6840 (2005). [CrossRef] [PubMed]
  7. J. N. Mait, R. Athale, and J. van der Gracht, "Evolutionary paths in imaging and recent trends," Opt. Express 11, 2093-2101 (2003). [CrossRef] [PubMed]
  8. W. T. Cathey and E. R. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002). [CrossRef] [PubMed]
  9. E. R. Dowski and W. T. Cathey, "Extended depth of field through wavefront coding," Appl. Opt. 34, 1859-1866 (1995). [CrossRef] [PubMed]
  10. A. Castro and J. Ojeda-Castañeda, "Asymmetric phase masks for extended depth of field," Appl. Opt. 43, 3474-3479 (2004). [CrossRef] [PubMed]
  11. S. S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004). [CrossRef] [PubMed]
  12. M. J. Bastiaans, "Application of the Wigner distribution function in optics," in The Wigner Distribution; Theory and Applications in Signal Processing, W.Mechlenbräuker and F.Hlawatsch, eds. (Elsevier, 1997), pp. 375-426. [PubMed]
  13. M. J. Bastianns, "The Wigner distribution function applied to optical signals and systems," Opt. Commun. 25, 26-30 (1978). [CrossRef]
  14. M. J. Bastiaans, "Wigner distribution function and its application to first-order optics," J. Opt. Soc. Am. 69, 1710-1716 (1979). [CrossRef]
  15. D. Zalvidea, M. Lehman, S. Granieri, and E. E. Sicre, "Analysis of the Strehl ratio using the Wigner distribution function," Opt. Commun. 118, 207-214 (1995). [CrossRef]
  16. D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998). [CrossRef]
  17. D. Zalvidea, C. Colautti, and E. E. Sicre, "Quality parameters analysis of optical imaging systems with enhanced focal depth using the Winger distribution function," J. Opt. Soc. Am. A 17, 867-873 (2000). [CrossRef]
  18. M. A. Alonso and G. W. Forbes, "Phase-space distributions for high-frequency fields," J. Opt. Soc. Am. A 17, 2288-2300 (2000). [CrossRef]
  19. A. W. Lohmann and B. H. Soffer, "Relationships between the Radon-Wigner and fractional Fourier transforms," J. Opt. Soc. Am. A 11, 1798-1801 (1994). [CrossRef]
  20. T. Alieva and M. J. Bastiaans, "Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform," J. Opt. Soc. Am. A 17, 2324-2329 (2000). [CrossRef]
  21. K. Brenner, A. W. Lohmann, and J. Ojeda-Castañeda, "The ambiguity function as a polar display of the OTF," Opt. Commun. 44, 323-326 (1983). [CrossRef]
  22. C. J. R. Sheppard and K. G. Larkin, "Wigner function and ambiguity function for nonparaxial wavefields," in Optical Processing and Computing: a Tribute to Adolf Lohmann, D.P.Casasent, H.J.Caulfield, W.J.Dallas, and H.H.Szu, eds., Proc. SPIE 4392,99-103 (2001).
  23. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001), pp. 883-891.
  24. N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals (Dover, 1986), pp. 252-320.

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