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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 12 — Dec. 1, 1998
  • pp: 3016–3019

Dependence of Fresnel number on aperture stop position

C. J. R. Sheppard and P. Török  »View Author Affiliations

JOSA A, Vol. 15, Issue 12, pp. 3016-3019 (1998)

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The influence of aperture stop position on the focusing properties of a lens is investigated. Expressions are obtained for the optical coordinates in terms of the system geometry. If the aperture stop is placed in the front focal plane of the lens, the effective Fresnel number is infinite. For other positions, the effective Fresnel number can be made either positive or negative, corresponding to focal shift either toward or away from the lens and a resulting coordinate rescaling.

© 1998 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(260.1960) Physical optics : Diffraction theory

Original Manuscript: May 11, 1998
Manuscript Accepted: September 10, 1998
Published: December 1, 1998

C. J. R. Sheppard and P. Török, "Dependence of Fresnel number on aperture stop position," J. Opt. Soc. Am. A 15, 3016-3019 (1998)

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  1. G. Farnell, “Calculated intensity and phase distribution in the image space of a microwave lens,” Can. J. Phys. 35, 777–783 (1957). [CrossRef]
  2. A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Opt. Acta 23, 245–250 (1976). [CrossRef]
  3. J. Erkkila, M. Rogers, “Diffracted fields in the focal region of a convergent wave,” J. Opt. Soc. Am. 71, 904–905 (1981). [CrossRef]
  4. J. Stamnes, B. Spejelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981). [CrossRef]
  5. Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 1, 801–808 (1984). [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).
  7. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef] [PubMed]
  8. W. Hsu, R. Barakat, “Stratton–Chu vectorial diffraction of electromagnetic fields by apertures with application to small-Fresnel-number systems,” J. Opt. Soc. Am. A 11, 623–629 (1994). [CrossRef]
  9. V. Dhayalan, J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997). [CrossRef]
  10. H. Ling, S. Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. 59, 559–567 (1984).
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. R. G. Wenzel, “Effect of the aperture–lens separation on the focal shift in large-F-number systems,” J. Opt. Soc. Am. A 4, 340–345 (1987). [CrossRef]
  13. I. S. Gradstein, I. M. Ryshik, Tables of Series, Products, and Integrals (Deutsch, Frankfurt, Germany, 1981).

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