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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 56, Iss. 11 — Nov. 1, 1966
  • pp: 1495–1501

Longitudinal Image Formation

B. ROY FRIEDEN  »View Author Affiliations

JOSA, Vol. 56, Issue 11, pp. 1495-1501 (1966)

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Optical transfer theory is not applicable to objects that have an extension parallel to the optical axis. In this paper a transfer theory is developed that applies to the “longitudinal object,” defined as a radiant line source that is directed in an arbitrary field direction θ. The “longitudinal image,” defined as the irradiance along the resulting gaussian image, is Fourier analyzed, resulting in a “longitudinal transfer theory.” This theory is predicated on the existence of a line of stationarity, along which the longitudinal object must lie. Stationarity is verified in the diffraction-limited case. One result of the theory is a new method for computing the depth of focus.

B. ROY FRIEDEN, "Longitudinal Image Formation," J. Opt. Soc. Am. 56, 1495-1501 (1966)

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  1. P. M. Duffieux, L'integrale de Fourier et ses applications a l'optique, Besançon, privately printed (1947).
  2. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Co., Inc., New York, 1957), p. 72.
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), p. 461.
  4. See, e.g., E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Mass., 1963), pp. 87, 105–108.
  5. Results of the lateral theory are presented without proof. They may be found, e.g., throughout Ref. 4.
  6. H. H. Hopkins, in Proceedings of the Conference on Optical Instruments and Techniques (John Wiley & Sons, Inc., New York, 1963), pp. 483, 484.
  7. Ref 3, p. 382.
  8. L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Co., Inc., New York, 1955), p. 51.
  9. W. T. Welford, J. Opt. Soc. Am. 50, 749 (1960).

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