OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 43, Iss. 13 — May. 1, 2004
  • pp: 2709–2721

Phase plate to extend the depth of field of incoherent hybrid imaging systems

Sherif S. Sherif, W. Thomas Cathey, and Ed R. Dowski  »View Author Affiliations

Applied Optics, Vol. 43, Issue 13, pp. 2709-2721 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (1166 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A hybrid imaging system combines a modified optical imaging system and a digital postprocessing step. We describe a spatial-domain method for designing a pupil phase plate to extend the depth of field of an incoherent hybrid imaging system with a rectangular aperture. We use this method to obtain a pupil phase plate to extend the depth of field, which we refer to as a logarithmic phase plate. Introducing a logarithmic phase plate at the exit pupil of a simulated diffraction-limited system and digitally processing the detector’s output extend the depth of field by an order of magnitude more than the Hopkins defocus criterion. We also examine the effect of using a charge-coupled device optical detector, instead of an ideal optical detector, on the extension of the depth of field. Finally, we compare the performance of the logarithmic phase plate with that of a cubic phase plate in extending the depth of field of a hybrid imaging system with a rectangular aperture.

© 2004 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(110.0110) Imaging systems : Imaging systems
(110.6880) Imaging systems : Three-dimensional image acquisition

Original Manuscript: July 22, 2003
Revised Manuscript: January 20, 2004
Published: May 1, 2004

Sherif S. Sherif, W. Thomas Cathey, and Ed R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. T. Welford, “Use of annular apertures to increase focal depth,” J. Opt. Soc. Am. 50, 749–753 (1960). [CrossRef]
  2. M. Mino, Y. Okano, “Improvement in the optical transfer function of a defocused optical system through the use of shaded apertures,” Appl. Opt. 10, 2219–2225 (1971). [CrossRef] [PubMed]
  3. J. Ojeda-Castenada, P. Andres, A. Diaz, “Annular apodizers for low sensitivity to defocus and to spherical aberration,” Opt. Lett. 11, 487–489 (1986). [CrossRef]
  4. J. Ojeda-Castenada, E. Tepichin, A. Diaz, “Arbitrary high focal depth with a quasi-optimum real and positive transmittance apodizer,” Appl. Opt. 28, 2666–2670 (1989). [CrossRef]
  5. J. Ojeda-Castenada, L. R. Berriel-Valdos, “Zone plate for arbitrarily high focal depth,” Appl. Opt. 29, 994–997 (1990). [CrossRef]
  6. G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972). [CrossRef]
  7. W. T. Cathey, B. R. Frieden, W. T. Rhodes, C. K. Rushford, “Image gathering and processing for enhanced resolution,” J. Opt. Soc. Am. A 1, 241–250 (1984). [CrossRef]
  8. J. Ojeda-Castenada, R. Ramos, A. Noyola-Isgleas, “High focal depth by apodization and digital restoration,” Appl. Opt. 27, 2583–2586 (1988). [CrossRef]
  9. E. R. Dowski, W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995). [CrossRef] [PubMed]
  10. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955). [CrossRef]
  11. W.-L. Chi, N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26, 875–877 (2001). [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1997).
  13. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6, pp. 126–171.
  14. E. T. Copson, Asymptotic Expansions (Cambridge U. Press, Cambridge, 1967).
  15. E. L. Key, E. N. Fowle, R. D. Haggarty, “A method for designing signals of large time-bandwidth product,” IRE Int. Conv. Rec. 4, 146–155 (1961).
  16. E. N. Fowle, “The design of FM pulse compression signals,” IEEE Trans. Inf. Theory IT-10, 61–67 (1964). [CrossRef]
  17. Focus Software Inc., “Zemax optical design program: user’s guide,” (Focus Software, Tucson, Ariz., 2000).
  18. S. S. Sherif, W. T. Cathey, “Reduced depth of field in incoherent hybrid imaging systems,” Appl. Opt. 41, 6062–6074 (2002). [CrossRef] [PubMed]
  19. L. E. Franks, Signal Theory, rev. ed. (Dowden Culver, Stroudsburg, Pa., 1981).
  20. K. Brenner, A. Lohmann, J. Ojeda-Castenada, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983). [CrossRef]
  21. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  22. S. Bradburn, W. T. Cathey, E. R. Dowski, “Realizations of focus invariance in optical-digital systems with wavefront coding,” Appl. Opt. 36, 9157–9166 (1997). [CrossRef]
  23. J. E. Greivenkamp, A. E. Lowman, “Modulation transfer function measurement of sparse-array sensors using a self-calibrating fringe pattern,” Appl. Opt. 33, 5029–5036 (1994). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited