OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 55, Iss. 9 — Sep. 1, 1965
  • pp: 1110–1114

Analytic Solution of Two Apodization Problems

DAVID SLEPIAN  »View Author Affiliations

JOSA, Vol. 55, Issue 9, pp. 1110-1114 (1965)

View Full Text Article

Acrobat PDF (716 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Apodization theory is concerned with the determination of the distribution of light over the exit pupil of an optical system required in order to achieve a suppression of the side lobes of the diffraction pattern. Here analytic solutions are given to the problem of determining the distribution of light in the exit pupil to concentrate maximally the illuminance in a geometrically similar region of the image plane. Both slit and circular apertures are treated.

DAVID SLEPIAN, "Analytic Solution of Two Apodization Problems," J. Opt. Soc. Am. 55, 1110-1114 (1965)

Sort:  Author  |  Journal  |  Reset


  1. P. Jacquinot and B. Roizen-Dossier in Progress in Optics, E. Wolf, ed. (North-Holland Publishing Co., Amsterdam, 1964), Vol. III, p. 31.
  2. R. Straubel, Pieter Zeeman. Verhandelingen op 25 Mei 1935 Aangeboden aan Prof. Dr. P. Zeeman (Martinus Nijhoff, The Hague, Netherlands, 1935), p. 302.
  3. R . K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley, California, 1964), p. 353.
  4. G. Lansraux and G. Boivin, Can. J. Phys. 39, 158 (1961).
  5. R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).
  6. D. Slepian, Bell System Tech. J. 43, 3009 (1964).
  7. P. Jacquinot and B. Roizen-Dossier in Progress in Optics III edited by E. Wolf (North Holland Publishing Co., Amsterdam, 1964), pp. 47, 78.
  8. D. Slepian and H. O. Pollak, Bell System Tech. J. 40, 43 (1961).
  9. H. J. Landau and H. O. Pollak, Bell System Tech. J. 40, 65 (1961); 41, 1295 (1962).
  10. D. Slepian, IRE Trans. PGIT-3, 68 (1954).
  11. J. Meixner and F. W. Schäfke, Mathieusche Funktionen und Sphäroidfunktionen (Springer-Verlag, Berlin, 1954).
  12. C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford, California, 1957).
  13. J. A. Stratton, P. M. Morse, L. J. Chu, J. D. C. Little, and P. J. Corbató, Spheroidal Wave Functions (John Wiley & Sons, Inc., New York, 1956).
  14. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
  15. D. Slepian, J. Math. Phys. (MIT) 44, 99 (1965).
  16. W. Fuchs, J. Math. Anal. Appl. 9, 317 (1964).
  17. A. G. Fox and Tingye Li, Bell System Tech. J. 40, 453 (1961).
  18. J. C. Heurtley in Proc. Symposium on Quasi-Optics (Polytechnic Press, Brooklyn, New York, 1964), p. 367.
  19. H. Kogelnik, in Advances in Lasers, A. K. Levine, ed. (Dekker Publishers, New York, 1965).
  20. M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959).
  21. G. Szegö, Orthogonal Polynomials (Am. Math. Soc. Colloquium Publications, Vol. XXIII, New York, 1959), Chap. V.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited