OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 30 — Oct. 20, 2006
  • pp: 7878–7884

Bow-tie effect: differential operator

Albertina Castro, Jorge Ojeda-Castañeda, and Adolf W. Lohmann  »View Author Affiliations

Applied Optics, Vol. 45, Issue 30, pp. 7878-7884 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (1921 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose to use a differential operator for representing the influence of phase-only filters on the defocused modulation transfer function of the clear pupil aperture. We present a phase-only filter that implements optically Taylor's theorem in phase space. We show numerical simulations of the modulation transfer functions and the images that can be obtained by using the proposed filter.

© 2006 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(070.6110) Fourier optics and signal processing : Spatial filtering
(100.5090) Image processing : Phase-only filters
(110.4100) Imaging systems : Modulation transfer function
(110.4850) Imaging systems : Optical transfer functions
(110.6880) Imaging systems : Three-dimensional image acquisition

ToC Category:
Imaging Systems

Original Manuscript: January 27, 2006
Manuscript Accepted: April 21, 2006

Albertina Castro, Jorge Ojeda-Castañeda, and Adolf W. Lohmann, "Bow-tie effect: differential operator," Appl. Opt. 45, 7878-7884 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Häusler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972). [CrossRef]
  2. M. Minski, "Double focusing stage scanning microscope," U.S. patent 3,0130467 (19 December 1961).
  3. T. Wilson, Confocal Microscopy (Academic, 1990).
  4. J. Ojeda-Castañeda and A. Noyola-Isgleas, "High focal depth by apodization and digital restoration," Appl. Opt. 27, 2583-2586 (1988). [CrossRef] [PubMed]
  5. T. W. Cathey and E. R. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002). [CrossRef] [PubMed]
  6. E. B. Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A: Pure Appl. Opt. 5, S164-S163 (2003). [CrossRef]
  7. E. B. Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "Experimental realization of an imaging system with extended depth of field," Appl. Opt. 44, 2792-2798 (2005). [CrossRef]
  8. E. R. Dowski and T. W. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1865 (1995). [CrossRef] [PubMed]
  9. S. Mezouari and A. A. Harvey, "Phase pupil functions reduction of defocus and spherical aberrations," Opt. Lett. 28, 771-773 (2003). [CrossRef] [PubMed]
  10. N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A: Pure Appl. Opt. 5, S157-S163 (2003). [CrossRef]
  11. A. Sauceda and J. Ojeda-Castañeda, "High focal depth with fractional-power wave fronts," Opt. Lett. 29, 560-562 (2004). [CrossRef] [PubMed]
  12. A. Castro and J. Ojeda-Castañeda, "Asymmetric phase masks for extended depth of field," Appl. Opt. 43, 3474-3479 (2004). [CrossRef] [PubMed]
  13. S. Sanyal and A. Gosh, "High focal depth with a quasi-focus birefringent lens," Appl. Opt. 27, 4163-4165 (2000).
  14. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001). [CrossRef]
  15. S. S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging system," Appl. Opt. 43, 2709-2721 (2004). [CrossRef] [PubMed]
  16. 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]
  17. K. H. 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]
  18. J. Ojeda-Castañeda and L. R. Berriel-Valdos, "Ambiguity function as a design tool for high focal depth," Appl. Opt. 27, 790-795 (1988). [CrossRef] [PubMed]
  19. E. D. Rainville, Elementary Differential Equations, 3rd ed. (Macmillan, 1964) pp. 234-237.
  20. F. W. J. Olver, "Bessel functions of integer order," in Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, M.Abramowitz and I.A.Stegun, eds. (Dover, 1970), pp. 358-361.
  21. R. Gonzalez and R. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002) pp. 262-266.

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