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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 5 — May. 1, 1967
  • pp: 639–644

Gabor’s Theorem and Energy Transfer through Lenses

A. WALTHER  »View Author Affiliations

JOSA, Vol. 57, Issue 5, pp. 639-644 (1967)

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A theorem is proved which relates the number of degrees of freedom in the image space of any lens to the light-gathering effectiveness of the lens. Under appropriate approximations this theorem is equivalent to Gabor’s expansion theorem. If the number of degrees of freedom is small, these approximations are not warranted and true superresolution becomes a possibility.

A. WALTHER, "Gabor’s Theorem and Energy Transfer through Lenses," J. Opt. Soc. Am. 57, 639-644 (1967)

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  1. D. Gabor, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publishing Company, Amsterdam, 1961).
  2. K. Miyamoto, J. Opt. Soc. Am. 50, 865 (1960); 51, 910 (1961).
  3. H. J. Landau and H. O. Pollak, Bell System Tech. J. 41, 1295 (1962).
  4. L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965). At the request of the editor of J. Opt. Soc. Am., "light-gathering effectiveness" is used in this paper in place of the term "photometric throughput" used by Mertz.
  5. A. Walther, Am. J. Phys. 35, June (1967).
  6. E. Schmidt, Math Ann. 63, 433 (1907).
  7. Note that this also involves a Gabor-type theorem, which has been firmly established, however, by Landau and Pollak.3
  8. C. W. Barnes, J. Opt. Soc. Am. 56, 575 (1966).
  9. D. Slepian, J. Math. Phys. 44, 99 (1965).
  10. G. Lansraux, J. Opt. Soc. Am. 55, 595A (1965).
  11. M. Kline and E. Kay, Electromagnelic Theory and Geometrical Optics (Interscience Publishers, John Wiley & Sons, Inc., New York, 1965).

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