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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 1 — Jan. 1, 2005
  • pp: 77–83

Focal shifts in diffracted converging electromagnetic waves. II. Rayleigh theory

Yajun Li  »View Author Affiliations


JOSA A, Vol. 22, Issue 1, pp. 77-83 (2005)
http://dx.doi.org/10.1364/JOSAA.22.000077


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Abstract

Part II of this study is an application of the Rayleigh vector diffraction integrals to an investigation of the effect of focal shifts in converging spherical waves diffracted in systems of arbitrary relative aperture. The results are compared numerically with those obtained in Part I [J. Opt. Soc. Am. A 22, 68 (2005)] from the Kirchhoff vector diffraction theory. The effect of the numerical aperture (NA) on focal shifts can be considered in two regions: When NA < or = 0.5 the system behaves like an paraxial system, and the Fresnel number is the dominant factor. When 0.5 < NA < or = 0.9 the absolute value of the relative focal shift decreases with increasing value of NA.

© 2005 Optical Society of America

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

Citation
Yajun Li, "Focal shifts in diffracted converging electromagnetic waves. II. Rayleigh theory," J. Opt. Soc. Am. A 22, 77-83 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-1-77


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References

  1. Y. Li, "Focal shifts in diffracted converging electromagnetic waves. I. Kirchhoff theory," J. Opt. Soc. Am. A 22, 68 (2005).
  2. R. K. Lunenberg, Mathematical Theory of Optics (University of California, Berkeley, California, 1964), Chap. 6.
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  10. H. Osterberg and L. W. Smith, "Close solution of Rayleigh diffraction integral for axial points," J. Opt. Soc. Am. 51, 1050-1054 (1961).
  11. C. J. R. Sheppard and P. Török, "Focal shift and axial coordinates for high-aperture systems of finite Fresnel number," J. Opt. Soc. Am. A 20, 2156-2162 (2003).

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