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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 56, Iss. 5 — May. 1, 1966
  • pp: 588–591

Convolution Formulation of Fresnel Diffraction

JOHN T. WINTHROP and C. R. WORTHINGTON  »View Author Affiliations


JOSA, Vol. 56, Issue 5, pp. 588-591 (1966)
http://dx.doi.org/10.1364/JOSA.56.000588


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Abstract

A convolution formulation of Fresnel diffraction is presented. The diffracted amplitude is expressed as a convolution in either direct or reciprocal space. Approximations involve the use of parabolic wavefronts and the omission of the obliquity factor. The formulation is readily applied to many optical phenomena.

A theory of Fresnel transforms is given. The Fresnel transforms are expressed as a convolution in either direct or reciprocal space. Two examples of their use are given.

Citation
JOHN T. WINTHROP and C. R. WORTHINGTON, "Convolution Formulation of Fresnel Diffraction," J. Opt. Soc. Am. 56, 588-591 (1966)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-56-5-588


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References

  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed.
  2. J. M. Cowley and A. F. Moodie, Proc. Phys. Soc. (London) 71, 533 (1958).
  3. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
  4. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
  5. L. Mertz and N. O. Young, in Proceedings of the Conference on Optical Instruments and Techniques, London, 1961 (Chapman and Hall Ltd., London, 1962).
  6. J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).
  7. G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).
  8. G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A58, 193 (1950–51).

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