OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 55, Iss. 8 — Aug. 1, 1965
  • pp: 1002–1007

Investigations of the Influence of the Degree of Coherence upon Images of Edge Objects

ROBERT E. KIEZLY  »View Author Affiliations


JOSA, Vol. 55, Issue 8, pp. 1002-1007 (1965)
http://dx.doi.org/10.1364/JOSA.55.001002


View Full Text Article

Acrobat PDF (594 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The theoretical irradiance is presented for the images of sharp-edged objects as a function of the coherence of the illumination of the object. These distributions are presented for optical systems possessing both square apertures and circular apertures. The irradiance for degraded edged objects is also determined for optical systems with square apertures. The influence of the degree of coherence upon contrast and edge gradient is considered in detail. Experimental results are given which show good agreement with the theoretical irradiance. In all cases the systems are assumed free from aberration and the quasimonochromatic assumption is employed.

Citation
ROBERT E. KIEZLY, "Investigations of the Influence of the Degree of Coherence upon Images of Edge Objects," J. Opt. Soc. Am. 55, 1002-1007 (1965)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-55-8-1002


Sort:  Author  |  Journal  |  Reset

References

  1. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964).
  2. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), Chap. X.
  3. D. Canals-Frau and M. Rousseau, Opt. Acta 5, 15 (1958).
  4. M. De and S. C. Som, Opt. Acta 4, 17 (1962).
  5. W. N. Charman, J. Opt. Soc. Am. 53, 410 (1963).
  6. W. T. Welford, Optics in Meteorology (Pergamon Press, Inc., New York, 1960), pp. 85–91.
  7. H. H. Hopkins, Proc. Roy. Soc. (London) A217, 408 (1953).
  8. The mutual intensity is found by setting τ equal to zero in the expression for the mutual-coherence function which is useful when investigating the imaging process employing quasimonochromatic light.
  9. One of the restrictions imposed by Hopkins, namely that the mutual-intensity function in the object plane is spatially stationary, can be removed by employing other expressions for the propagation of the mutual-intensity function. These are J(x1,x2)=K∫∫J12) exp[i(x2·ξ-x1·ξ1)]dξ1dξ2 for the propagation of the mutual intensity between planes sufficiently separated to allow the far-field approximation and J′(x1,x2)=J(x1,x2)T(x1)T*(x2) for propagation through diffracting objects or apertures having a transmittance function T(x). We note in the first expression that the "far-field approximation may be valid" in the near field as shown by the case when J12) represents an incoherent source and the first expression reduces to the Van Cittert–Zernike theorem, which Hopkins uses to describe the effective source.
  10. D. Canals-Frau and M. Rousseau, Ref. 3, report a similar analysis employing the Fourier transforms of the functions which wefuse. However, the normalization criteria are different.
  11. In this case the normalized mutual-intensity function or complex degree of coherence measured perpendicular to the edged object is given by Г0(u1-u2)=[sin(u2-u1)ε]/[u2-u1)ε]
  12. By coherence interval, we mean the minimum separation between points in the object plane (spatial separation) for which the mutual-intensity function vanishes.
  13. See Fig. 8 of Ref. 5. Private communication with W. N. Charman revealed that a typographical error resulted in the mislabeling of the "s" value at the low-intensity region of the curves in this figure.
  14. That is, the width of the image of the square effective source in the plane of the entrance aperture normalized by the width of the square entrance aperture.

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