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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 4, Iss. 8 — Aug. 1, 1987
  • pp: 1349–1353

Three-dimensional intensity distribution in low-Fresnel-number focusing systems

Yajun Li  »View Author Affiliations

JOSA A, Vol. 4, Issue 8, pp. 1349-1353 (1987)

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Investigations of the three-dimensional intensity distribution near the focus are extended here to systems with Fresnel numbers N < 0.5. Isophotes (contours of equal intensity) are presented that demonstrate the structure of the field deep within the region of Fresnel diffraction.

© 1987 Optical Society of America

Original Manuscript: November 4, 1986
Manuscript Accepted: March 24, 1987
Published: August 1, 1987

Yajun Li, "Three-dimensional intensity distribution in low-Fresnel-number focusing systems," J. Opt. Soc. Am. A 4, 1349-1353 (1987)

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  1. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Sec. 8.8, pp. 435–449.
  2. D. A. Holmes, J. E. Korka, P. V. Avizonis, “Parametric study of apertured focused Gaussian beams,” Appl. Opt. 11, 565–574 (1972). [CrossRef] [PubMed]
  3. J. H. Erkkila, M. E. Rogers, “Diffracted fields in the focal volume of a converging wave,”J. Opt. Soc. Am. 71, 904–905.
  4. J. J. Stamnes, H. Spjelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981). [CrossRef]
  5. Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981). [CrossRef]
  6. Y. Li, “Dependence of the focal shift on Fresnel number and f number,”J. Opt. Soc. Am. 72, 770–774 (1982). [CrossRef]
  7. V. N. Mahajan, “Uniform versus Gaussian beams: a comparison of the effects of diffraction, obscuration, and aberrations,” J. Opt. Soc. Am. A 3, 470–485 (1986). [CrossRef]
  8. B. N. Gorbachev, “Three-dimensional energy distribution of a converging spherical wave for arbitrary Fresnel numbers,” Opt. Spectrosc. (USSR) 44, 204–206 (1978).
  9. E. Wolf, Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun. 39, 205–210 (1981). [CrossRef]
  10. Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,”J. Opt. Am. A 1, 801–808 (1984). [CrossRef]
  11. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, London, 1962), Sec. 16.5, pp. 537–550. In this book the definition of Lommel’s V functions differs by a factor (−1) from that given in Refs. 1 and 10.
  12. Y. Li, “Focal shift formulae,” Optik 69, 41–42 (1984).
  13. Y. Li, “Encircled energy for systems of different Fresnel numbers,” Optik 66, 207–218 (1983).
  14. A. Sommerfeld, Optics, Vol. IV of Lectures on Theoretical Physics (Academic, New York, 1954), p. 217. Under the condition of an incident plane wave, Sommerfeld’s Eq. (19) on p. 217 should read as J=J0 sin2(ka2/4ρ),which is in agreement with Eq. (3.6) of this paper.

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