Abstract

It is shown that when a lens produces an image of a point source the three-dimensional diffraction pattern which results is the three-dimensional Fourier transform of a generalization of the lens aperture. This implies similar Fourier relations in one and two dimensions. An explicit form of the former is derived which demonstrates that the amplitude distribution on an arbitrarily directed line through the focus is the Fourier transform of the projection of the generalized aperture onto that line. These relations hold in aberrant as well as in ideal systems. Some examples are worked out by using the one-dimensional relation.

PDF Article

References

  • View by:
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., Oxford, England, 1959).
  2. I. N. Sneddon, Fourier Transforms (McGraw-Hill I Company, Inc., New York, 1951).
  3. D. Gabor, Progress in Optics, edited by E. Wolf (North- Holland Publishing Company, Amsterdam, The Netherlands, 1961), p. 117.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., Oxford, England, 1959).

Gabor, D.

D. Gabor, Progress in Optics, edited by E. Wolf (North- Holland Publishing Company, Amsterdam, The Netherlands, 1961), p. 117.

Sneddon, I. N.

I. N. Sneddon, Fourier Transforms (McGraw-Hill I Company, Inc., New York, 1951).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., Oxford, England, 1959).

Other

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., Oxford, England, 1959).

I. N. Sneddon, Fourier Transforms (McGraw-Hill I Company, Inc., New York, 1951).

D. Gabor, Progress in Optics, edited by E. Wolf (North- Holland Publishing Company, Amsterdam, The Netherlands, 1961), p. 117.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.