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Applied Optics

Applied Optics


  • Vol. 28, Iss. 13 — Jul. 1, 1989
  • pp: 2666–2670

Arbitrarily high focal depth with a quasioptimum real and positive transmittance apodizer

Jorge Ojeda-Castaneda, E. Tepichin, and A. Diaz  »View Author Affiliations

Applied Optics, Vol. 28, Issue 13, pp. 2666-2670 (1989)

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Focal depth is assessed by the average value of the square modulus of the slope associated with the complex amplitude along the optical axis. Then, the calculus of variations is used for identifying the optimum apodizer, characterized by a Strehl ratio vs defocus with high focal depth, for a specified light throughput. We show that a certain Lorentzian profile is a quasioptimum solution for the above requirements. This apodizer has real and positive transmittance, and it can be modified to achieve arbitrarily high focal depth. A closed formula relates focal depth to light throughput.

© 1989 Optical Society of America

Original Manuscript: July 11, 1988
Published: July 1, 1989

Jorge Ojeda-Castaneda, E. Tepichin, and A. Diaz, "Arbitrarily high focal depth with a quasioptimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2670 (1989)

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  1. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Line-Spread Function Relatively Insensitive to Defocus,” Opt. Lett. 8, 458–460 (1983). [CrossRef] [PubMed]
  2. G. Indebetouw, H. Bai, “Imaging with Fresnel Zone Pupils Masks: Extended Depth of Field,” Appl. Opt. 23, 4299–4302 (1984). [CrossRef] [PubMed]
  3. C. Varamit, G. Indebetouw, “Imaging Properties of Defocused Partitioned Pupils,” J. Opt. Soc. Am A 2, 799–807 (1985). [CrossRef]
  4. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Spatial Filter for Increasing the Depth of Focus,” Opt. Lett. 10, 520–522 (1985). [CrossRef] [PubMed]
  5. J. Ojeda-Castaneda, P. Andres, A. Diaz, “Annular Apodizers for Low Sensitivity to Defocus and to Spherical Aberration,” Opt. Lett. 11, 487–489 (1986). [CrossRef] [PubMed]
  6. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Bessel Annular Apodizers: Imaging Characteristics,” Appl. Opt. 26, 2770–2772 (1987). [CrossRef] [PubMed]
  7. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Ambiguity Function as a Design Tool for High Focal Depth,” Appl. Opt. 27, 790–794 (1988). [CrossRef] [PubMed]
  8. W. H. Steel, “Precision Focusing with Photoelectric Detection,” J. Opt. Soc. Am. 52, 1153–1155 (1962). [CrossRef]
  9. B. R. Frieden, “On Arbitrarily Perfect Imagery with a Finite Aperture,” Opt. Acta 16, 795–807 (1969). [CrossRef]
  10. J. Ojeda-Castaneda, L. R. Berriel-Valdos, “Arbitrarily High Focal Depth with Finite Apertures,” Opt. Lett. 13, 183–185 (1988). [CrossRef] [PubMed]
  11. R. K. Luneberg, Mathematical Theory of Optics (U. California Press, Berkeley, CA, 1964) 353.
  12. T. Asakura, T. Veno, “Apodization for Minimizing the Second Moment of the Intensity Distribution in the Fraunhofer Diffraction Pattern (I),” Nouv. Rev. d’Opt. 7, 199–203 (1976).

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