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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 26 — Sep. 10, 2009
  • pp: 4893–4898

Fourier transform pupil functions for modifying the depth of focus of optical imaging systems

Jeffrey A. Davis, B. Melvin L. Pascoguin, C. Stewart Tuvey, and Don M. Cottrell  »View Author Affiliations

Applied Optics, Vol. 48, Issue 26, pp. 4893-4898 (2009)

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We use a Fourier transform approach to design pupil functions that modify the axial depth of focus for an optical system. We extend previous research in several ways. We first extend the depth of focus to 4 cm for a 38 cm focal length lens. We show that the transverse size of the focused beam is the same as for an open pupil. We then multiply the pupil function by a circular harmonic window function. The entire depth of focus is now characterized by a vortex beam. Finally we multiply our original pupil function by an edge-enhancing window function. Now the pupil function produces two sharp focus spots at the locations corresponding to the edges of the rectangle function.

© 2009 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(110.2990) Imaging systems : Image formation theory
(230.6120) Optical devices : Spatial light modulators
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Imaging Systems

Original Manuscript: May 18, 2009
Manuscript Accepted: August 12, 2009
Published: September 1, 2009

Jeffrey A. Davis, B. Melvin L. Pascoguin, C. Stewart Tuvey, and Don M. Cottrell, "Fourier transform pupil functions for modifying the depth of focus of optical imaging systems," Appl. Opt. 48, 4893-4898 (2009)

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  1. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240-244(1964). [CrossRef]
  2. C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43, 525- 536 (1996) [CrossRef]
  3. M. V. Klein, Optics (Wiley, 1970), Chap. 9.3.
  4. S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761-769 (1993). [CrossRef]
  5. J. A. Davis, C. S. Tuvey, O. López-Coronado, J. Campos, M. J. Yzuel, and C. Iemmi, “Tailoring the depth of focus for optical imaging systems using a Fourier transform approach,” Opt. Lett. 32, 844-846 (2007). [CrossRef] [PubMed]
  6. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051-1057 (1999). [CrossRef]
  7. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004-5013 (1999). [CrossRef]
  8. J. B. BentleyJ. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, “Generation of helical Ince-Gaussian beams with a liquid-crystal display,” Opt. Lett. 31, 649-651(2006). [CrossRef] [PubMed]
  9. P. A. M. Dirac, “Quantized singularities in the electromagnetic field,” Proc. R. Soc. London Ser. A 133, 60-72 (1931). [CrossRef]
  10. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165-190 (1974). [CrossRef]
  11. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995). [CrossRef] [PubMed]
  12. K. T. Gahagan and G. A. Swartzlander, Jr., “Optical vortex trapping of particles,” Opt. Lett. 21, 827-829 (1996). [CrossRef] [PubMed]
  13. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221-223 (1992). [CrossRef] [PubMed]
  14. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608-610 (1999). [CrossRef]
  15. B. Spektor, R. Piestun, and J. Shamir, “Dark beams with a constant notch,” Opt. Lett. 21, 456-458 (1996). [CrossRef] [PubMed]
  16. V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, and V. A. Soifer, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31, 1597-1599 (2006). [CrossRef] [PubMed]
  17. J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Analysis of the fractional Hilbert transform,” Appl. Opt. 37, 6911-6913(1998). [CrossRef]
  18. J. A. Davis, D. A. Smith, D. E. McNamara, D. M. Cottrell, and J. Campos, “Fractional derivatives: analysis and experimental implementation,” Appl. Opt. 40, 5943-5948 (2001). [CrossRef]

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