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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 22 — Aug. 1, 2008
  • pp: E99–E105

Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field

Jorge Ojeda-Castañeda, J. E. A. Landgrave, and Cristina M. Gómez-Sarabia  »View Author Affiliations

Applied Optics, Vol. 47, Issue 22, pp. E99-E105 (2008)

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We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.

© 2008 Optical Society of America

OCIS Codes
(110.4100) Imaging systems : Modulation transfer function
(110.6880) Imaging systems : Three-dimensional image acquisition
(220.1230) Optical design and fabrication : Apodization
(080.5084) Geometric optics : Phase space methods of analysis

ToC Category:
Optical Design and Optical Synthesis

Original Manuscript: April 24, 2008
Manuscript Accepted: May 8, 2008
Published: June 24, 2008

Jorge Ojeda-Castañeda, J. E. A. Landgrave, and Cristina M. Gómez-Sarabia, "Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field," Appl. Opt. 47, E99-E105 (2008)

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  1. J. Ojeda-Castañeda, R. Ramos, and A. Noyola-Isgleas, “High focal depth by apodization and digital restoration,” Appl. Opt. 27, 2583-2586 (1988). [CrossRef] [PubMed]
  2. J. Ojeda-Castañeda and L. R. Berriel-Valdos, "Arbitrarily high focal depth with finite apertures," Opt. Lett. 13, 183-185(1988). [CrossRef] [PubMed]
  3. J. Ojeda-Castañeda and L. R. Berriel-Valdos, “Zone plate for arbitrarily high focal depth,” Appl. Opt. 29, 994-997 (1990). [CrossRef] [PubMed]
  4. E. R. Dowski, Jr., and T. W. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859-1865 (1995). [CrossRef] [PubMed]
  5. H. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40, 5658-5662 (2001). [CrossRef]
  6. W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26, 875-877 (2001). [CrossRef]
  7. A. Sauceda and J. Ojeda-Castañeda, “High focal depth with fractional-power wave fronts,” Opt. Lett. 29, 560-562 (2004). [CrossRef] [PubMed]
  8. A. Castro and J. Ojeda-Castañeda, “Asymmetric phase masks for extended depth of field,” Appl. Opt. 43, 3474-3479 (2004). [CrossRef] [PubMed]
  9. E. Ben-Eliezer, E. Maron, N. Konforti, and Z. Zalevsky, “Experimental realization of an imaging system with an extended depth of field,” Appl. Opt. 44, 2792-2798 (2005). [CrossRef] [PubMed]
  10. K. Brenner, A. Lohmann, and J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323-326 (1983). [CrossRef]
  11. J. Ojeda- Castañeda, L. R. Berriel-Valdos, and E. Montes, “Ambiguity function as a design tool for high focal depth,” Appl. Opt. 27, 790-795 (1988). [CrossRef]
  12. J. Ojeda-Castañeda, J. E. A. Landgrave, and H. M. Escamilla, “Annular phase-only mask for high focal depth,” Opt. Lett. 30, 1647-1649 (2005). [CrossRef] [PubMed]
  13. A. Castro, J. Ojeda-Castañeda, and A. W. Lohmann, “Bow-tie effect: differential operator,” Appl. Opt. 45, 7878-7884 (2006). [CrossRef] [PubMed]
  14. L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (3 December 1964).
  15. A. W. Lohmann, “Lente focale variabile,” Italian patent 727,848 (19 June 1964).
  16. A. W. Lohmann, “Improvements relating to lenses and to variable optical lens systems formed by such lenses,” Patent Specification 998,191, The Patent Office, London (1965).
  17. A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. 9, 1669-1671 (1970). [CrossRef] [PubMed]
  18. I. A. Palusinski, J. M. Sasián, and J. E. Greivenkamp, “Lateral shift variable aberrations generators,” Appl. Opt. 38, 86-90(1999). [CrossRef]
  19. A. W. Rihaczek, Principles of High Resolution Radar (McGraw-Hill, 1969), p. 120.
  20. M. Somayaji and M. P. Christensen, “Enhancing form factor and light collection of multiplex imaging systems by using a cubic phase mask,” Appl. Opt. 45, 2911-2923 (2006). [CrossRef] [PubMed]
  21. N. López-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, “Generation of third-order spherical and coma aberrations by the use of radially symmetrical fourth-order lenses,” J. Opt. Soc. Am. A 15, 2563-2571 (1998). [CrossRef]

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