Abstract

<p>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.</p><p>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.</p>

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  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 (1950โ€“51).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed.

Cowley, J. M.

J. M. Cowley and A. F. Moodie, Proc. Phys. Soc. (London) 71, 533 (1958).

Gabor, D.

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

Leith, E. N.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Mertz, L.

L. Mertz and N. O. Young, in Proceedings of the Conference on Optical Instruments and Techniques, London, 1961 (Chapman and Hall Ltd., London, 1962).

Moodie, A. F.

J. M. Cowley and A. F. Moodie, Proc. Phys. Soc. (London) 71, 533 (1958).

Parrent, G. B.

G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).

Rogers, G. L.

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A58, 193 (1950โ€“51).

Thompson, B. J.

G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).

Upatnieks, J.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Winthrop, J. T.

J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed.

Worthington, C. R.

J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).

Young, N. O.

L. Mertz and N. O. Young, in Proceedings of the Conference on Optical Instruments and Techniques, London, 1961 (Chapman and Hall Ltd., London, 1962).

Other

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1964), 2nd ed.

J. M. Cowley and A. F. Moodie, Proc. Phys. Soc. (London) 71, 533 (1958).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).

L. Mertz and N. O. Young, in Proceedings of the Conference on Optical Instruments and Techniques, London, 1961 (Chapman and Hall Ltd., London, 1962).

J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).

G. B. Parrent and B. J. Thompson, Opt. Acta 11, 183 (1964).

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A58, 193 (1950โ€“51).

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