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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 13 — May. 1, 2002
  • pp: 2586–2588

Tolerance on defocus precisely locates the far field (exactly where is that far field anyway?)

James E. Harvey, Andrey Krywonos, and Dijana Bogunovic  »View Author Affiliations


Applied Optics, Vol. 41, Issue 13, pp. 2586-2588 (2002)
http://dx.doi.org/10.1364/AO.41.002586


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Abstract

The Fraunhofer criterion defines the location of the boundary between the Fresnel and the Fraunhofer diffraction regions and thus determines the location of that region commonly referred to as the far field. The Fraunhofer criterion is usually given as an axial distance much greater than some amount relative to the maximum dimension of the aperture. By recognizing that Fresnel diffraction patterns are merely defocused Fraunhofer diffraction patterns, we show that the Fraunhofer criterion can be written precisely in terms of an allowable tolerance on defocus. This new criterion provides insight that is useful to optical designers and engineers who routinely deal with such tolerances.

© 2002 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1940) Diffraction and gratings : Diffraction
(080.0080) Geometric optics : Geometric optics
(080.1010) Geometric optics : Aberrations (global)
(260.0260) Physical optics : Physical optics

History
Original Manuscript: November 5, 2001
Revised Manuscript: December 14, 2001
Published: May 1, 2002

Citation
James E. Harvey, Andrey Krywonos, and Dijana Bogunovic, "Tolerance on defocus precisely locates the far field (exactly where is that far field anyway?)," Appl. Opt. 41, 2586-2588 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-13-2586


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References

  1. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  2. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  3. J. E. Harvey, R. V. Shack, “Aberrations of diffracted wave fields,” Appl. Opt. 17, 3003–3009 (1978). [CrossRef] [PubMed]
  4. J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979). [CrossRef]
  5. V. N. Mahajan, “Aberrations of diffracted wave fields. I. Optical imaging,” J. Opt. Soc. Am. A 17, 2216–2222 (2000). [CrossRef]
  6. V. N. Mahajan, Optical Imaging and Aberrations: Part II (SPIE, Bellingham, Wash., 2001). [CrossRef]
  7. V. N. Mahajan, Optical Imaging and Aberrations: Part I (SPIE, Bellingham, Wash., 1998). [CrossRef]
  8. H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, UK, 1950).

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