OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 10 — Oct. 1, 1967
  • pp: 1180–1189

Ambiguity of the Transfer Function with Partially Coherent Illumination

RICHARD E. SWING and JAMES R. CLAY  »View Author Affiliations

JOSA, Vol. 57, Issue 10, pp. 1180-1189 (1967)

View Full Text Article

Acrobat PDF (937 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The one-dimensional case of the image of a sinusoidal transmittance distribution in partially coherent illumination (with the quasimonochromatic approximation) is described analytically, and shown generally to bear a nonlinear relation to the object. It is shown that the significant parameter is the ratio of coherence interval to the diameter of the Airy disk (or diffraction spot) of the imaging lens. It is further shown that since the spatial frequency of the object is related to coherence interval, typical nonlinear effects can take place at low frequencies. Since the transfer function is defined only for the incoherent limit without ambiguity, an apparent transfer function, dealing only with the image component which existed in the object, is used for comparison. The harmonics generated by the nonlinear behavior are ignored, and the variation of transfer function is observed to be a function of coherence and input modulation. It becomes apparent that the transfer function, as currently defined and measured, is inadequate to describe optical-system performance under all conditions of illumination.

RICHARD E. SWING and JAMES R. CLAY, "Ambiguity of the Transfer Function with Partially Coherent Illumination," J. Opt. Soc. Am. 57, 1180-1189 (1967)

Sort:  Author  |  Journal  |  Reset


  1. G. Parrent, Jr., and R. Becherer, J. Opt. Soc. Am. 56, 548A (1966).
  2. R. Lamberts, J. Opt. Soc. Am. 51, 932 (1961).
  3. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon Press, N. Y., 1964), pp. 510, 532–533.
  4. G. Reynolds and J. Ward, J. Soc. Phot. Instr. Eng. 5, 3 (1966).
  5. J. Altman, J. Phot. Sci. Eng. 10, 156 (1966).
  6. D. Falconer, J. Phot. Sci. Eng. 10, 133 (1966).
  7. E. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1963), pp. 122–127.
  8. M. Beran and G. Parrent, Jr., Theory of Partial Cohzerelce (Prentice Hall, Englewood Cliffs, N. J., 1964), pp. 106–113.
  9. All integrals in this paper, unless otherwise noted, are evaluated between - ∞ and ∞.
  10. Reference 8, p. 111.
  11. Reference 3, pp. 528–530.
  12. Reference 3, Appendix IV, Eq. 12.
  13. This is based on the generalization that the larger the relative aperture (or the smaller the ƒ-number), the better the general image quality.
  14. K. Knopp, Theory and Application of Infinite Series (Blackie & Son, Ltd., London and Glasgow, 1947), p. 424.
  15. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Co., New York, 1965).

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