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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. 17, Iss. 12 — Dec. 1, 2000
  • pp: 2216–2222

Aberrations of diffracted wave fields. I. Optical imaging

Virendra N. Mahajan  »View Author Affiliations


JOSA A, Vol. 17, Issue 12, pp. 2216-2222 (2000)
http://dx.doi.org/10.1364/JOSAA.17.002216


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Abstract

The concept of aberrations of diffracted waves is revisited by using the Rayleigh–Sommerfeld theory of diffraction, and it is pointed out that these aberrations are in a class by themselves; they are only deceptively similar to the aberrations of a rotationally symmetric imaging system. Although an exact Fourier-transform expression can be written for the diffracted wave field, its numerical calculation is cumbersome because of the dependence of the aberrations of the diffracted wave on the observation point. This is true regardless of whether the diffracted wave field is observed on a plane or a hemisphere. It is shown that the Fresnel and Fraunhofer approximations, which neglect these aberrations and thereby simplify the calculations, are valid in imaging applications.

© 2000 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(080.1010) Geometric optics : Aberrations (global)
(110.2990) Imaging systems : Image formation theory
(230.1950) Optical devices : Diffraction gratings
(260.1960) Physical optics : Diffraction theory

History
Original Manuscript: April 24, 2000
Revised Manuscript: July 12, 2000
Manuscript Accepted: July 14, 2000
Published: December 1, 2000

Citation
Virendra N. Mahajan, "Aberrations of diffracted wave fields. I. Optical imaging," J. Opt. Soc. Am. A 17, 2216-2222 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2216


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References

  1. J. E. Harvey, R. V. Shack, “Aberrations of diffracted wave fields,” Appl. Opt. 17, 3003–3009 (1978). [CrossRef] [PubMed]
  2. J. E. Harvey, “Fourier treatment of near-field scalar theory,” Am. J. Phys. 47, 974–980 (1979). [CrossRef]
  3. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Sec. 10.5.
  4. J. E. Harvey, C. L. Vernold, A. Krywonos, P. L. Thompson, “Diffracted radiance: a fundamental quantity in non-paraxial scalar diffraction theory,” Appl. Opt. 38, 6469–6481 (1999). Only a short summary of the earlier work is given in this paper. [CrossRef]
  5. H. Osterberg, L. W. Smith, “Closed solutions of Rayleigh’s diffraction integrals for axial points,” J. Opt. Soc. Am. 51, 1050–1054 (1961). [CrossRef]
  6. V. N. Mahajan, “Axial irradiance and optimum focusing of laser beams,” Appl. Opt. 22, 3042–3053 (1983). [CrossRef] [PubMed]
  7. A. Sommerfeld, Optics (Academic, New York, 1972), Vol. 4, pp. 199–201; substitute Eq. (8) on p. 201 into Eq. (6) on p. 199.
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 43–44; substitute Eq. (3-23) on p. 44 into Eq. (3-15) on p. 43.
  9. V. N. Mahajan, Optical Imaging and Aberrations. Part I: Ray Geometrical Optics (SPIE, Bellingham, Wash., 1998), Sec. 3.5.
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1986, Sec. 5.1.
  11. V. N. Mahajan, Optical Imaging and Aberrations. Part I: Ray Geometrical Optics (SPIE, Bellingham, Wash., 1998), Chap. 7.
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 60.
  13. V. N. Mahajan, Optical Imaging and Aberrations. Part I: Ray Geoemtrical Optics (SPIE, Bellingham, Wash., 1998), Sec. 3.2.

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