OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 64, Iss. 9 — Sep. 1, 1974
  • pp: 1237–1243

Integral equations for incoherent imagery

F. Gori  »View Author Affiliations


JOSA, Vol. 64, Issue 9, pp. 1237-1243 (1974)
http://dx.doi.org/10.1364/JOSA.64.001237


View Full Text Article

Acrobat PDF (674 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The main features of eigenfunctions and eigenvalues of integral equations connected with incoherent imaging through clear pupils are studied. As in the coherent imaging, both the object and the image can be expanded in eigenfunction series. On the contrary, the eigenvalue-step-function behavior typical of coherent imaging is not preserved when passing to the incoherent case. Upper and lower bounds for the eigenvalues are established in the one-dimensional case. They show that the eigenvalues, roughly speaking, decrease almost linearly with respect to the order index.

Citation
F. Gori, "Integral equations for incoherent imagery," J. Opt. Soc. Am. 64, 1237-1243 (1974)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-64-9-1237


Sort:  Author  |  Journal  |  Reset

References

  1. B. R. Frieden, Opt. Acta 16, 795 (1969).
  2. A. Walther, J. Opt. Soc. Am. 57, 639 (1967).
  3. G. Toraldo di Francia, J. Opt. Soc. Am. 59, 799 (1969).
  4. F. Gori and G. Guattari, Opt. Commun. 7, 163 (1973).
  5. C. W. Barnes, J. Opt. Soc. Am. 56, 575 (1966).
  6. C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).
  7. D. Slepian, J. Opt. Soc. Am. 55, 1110 (1965).
  8. Y. Itoh, J. Opt. Soc. Am. 60, 10 (1970).
  9. M. L. Mehta and C. L. Mehta, J. Opt. Soc. Am. 63, 826 (1973).
  10. D. Slepian and H. O. Pollak, Bell System Tech. J. 40, 43 (1961).
  11. H. J. Landau and H. O. Pollak, Bell System Tech. J. 40, 65 (1961).
  12. H. J. Landau and H. O. Pollak, Bell System Tech. J. 41, 1295 (1962).
  13. D. Slepian, Bell System Tech. J. 43, 3009 (1964).
  14. B. R. Frieden, in Progress in Optics, Vol. IX, edited by E. Wolf (North-Holland, Amsterdam, 1971). This paper contains a review of the properties of the prolate spheroidal wave functions as well as a review of optical applications up to 1971.
  15. H. J. Landau, Acta Mathematica 117, 37 (1967).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Ch. 6.
  17. F. Riesz and B. Sz. Nagy, Functional Analysis (Ungar, New York, 1955), Ch. 6.
  18. This was already noted in a different connection byA. Walther, J. Opt. Soc. Am. 60, 141 (1970).
  19. For a rigorous treatment, see Ref. 15.
  20. J. W. Goodman, in Progress in Optics, Vol. VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).
  21. F. Gori and G. Guattari, J. Opt. Soc. Am. 64, 453 (1974).
  22. See first theorem on p. 238 of Ref. 17.
  23. H. J. Landau, Trans. Am. Math. Soc. 115, 242 (1965). Theorem 1 and the considerations that follow the proof of theorem 2.
  24. See, for example, Ref. 14.
  25. See Ref. 21, theorem 2 and the considerations that follow it.
  26. D. Slepian and E. Sonnenblick, Bell System Tech. J. 44, 1745 (1965).
  27. F. Gori and G. Guattari, J. Opt. Soc. Am. 61, 36 (1971).
  28. B. J. Thompson, in Progress in Optics, Vol. VII, edited by E. Wolf (North-Holland, Amsterdam, 1969).
  29. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964), Ch. 8.
  30. We refer to the analysis of Ref. 6 as being pertinent to the coherent case, because the main results of this analysis are based on the hypothesis that the pupil function equals rect(ν).
  31. H. Kogelnik, in Lasers, Vol. I, edited by A. K. Levine (Dekker, New York, 1966).

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