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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 10, Iss. 12 — Dec. 1, 1971
  • pp: 2739–2742

Lens Design for Optical Fourier Transform Systems

K. von Bieren  »View Author Affiliations


Applied Optics, Vol. 10, Issue 12, pp. 2739-2742 (1971)
http://dx.doi.org/10.1364/AO.10.002739


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Abstract

In coherent optical filtering systems, the paraxial description of the imaging process represents the basis for the functional representation of the optical filter. With this approximation, the light amplitude in the secondary focal plane of an aberration-free lens appears as the Fourier transform of the light amplitude in the primary focal plane, as long as the field angles of all chief rays remain within the limits of Gaussian optics. The introduction of Abbe’s sine condition into the chief ray path allows the paraxial restriction to be dropped, and the Fourier transform relationship becomes valid for large as well as small field angles. The resulting Fourier transform lens designs are remarkably different from conventional imaging systems.

© 1971 Optical Society of America

History
Original Manuscript: January 18, 1971
Published: December 1, 1971

Citation
K. von Bieren, "Lens Design for Optical Fourier Transform Systems," Appl. Opt. 10, 2739-2742 (1971)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-10-12-2739


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References

  1. E. Abbe, Gesammelte Abhandlungen (G. Fischer, Jena, 1904), Band 1, p. 137.
  2. F. Zernike, Physica 1, 689 (1934). [CrossRef]
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1950).
  4. P. Elias, D. Grey, D. Robinson, J. Opt. Soc. Am. 42, 127 (1952). [CrossRef]
  5. J. E. Rhodes, Am. J. Phys. 21, 337 (1953). [CrossRef]
  6. E. L. O’Neil, IRE Trans. Inform. Theory IT-2, 56 (1965).
  7. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Inform. Theory IT-6, 386 (1960). [CrossRef]

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