OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 54, Iss. 5 — May. 1, 1964
  • pp: 606–609

Resolving Power and Decision Theory

J. L. HARRIS  »View Author Affiliations

JOSA, Vol. 54, Issue 5, pp. 606-609 (1964)

View Full Text Article

Acrobat PDF (686 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The fundamental resolving power of optical systems is defined by use of decision theory. For binary decisions in the presence of Gaussian noise, the probability of a correct decision is determined by the quadratic content of the difference image and the noise variance per unit of area. In the spatial frequency domain the probability of correct decision involves the integral of the power spectrum of the difference image and the noise variance per unit of area. The merit of a particular optical system for the performance of a specific binary decision task may be evaluated by use of a formula involving its modulation transfer function. The resolution of two monochromatic, incoherent point sources under conditions of high background radiation is discussed, as an illustrative example. The resolution of two point sources is limited only by the precision with which the flux density at all points in the image plane can be determined. The manner in which this increased precision can be obtained by increasing the period of observation is discussed, for the case of a photon-counting detector.

J. L. HARRIS, "Resolving Power and Decision Theory," J. Opt. Soc. Am. 54, 606-609 (1964)

Sort:  Author  |  Journal  |  Reset


  1. J. L. Harris, Scripps Inst. Oceanog. Ref. 58–56 (1958).
  2. J. L. Harris, Scripps Inst. Oceanog. Ref. 59–65 (1959).
  3. Hoel, Introduction to Mathematical Statistics (John Wiley & Sons, Inc., New York, 1955), p. 40.
  4. S. Goldman, Information Theory (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1954), pp. 67, 81.
  5. G. Toraldo di Francia, J. Opt. Soc. Am. 45, 497 (1955).
  6. J. L. Harris, Scripps Inst. Oceanog. Ref. 63–10 (1963).
  7. F. E. Washer and F. W. Rosberry, J. Opt. Soc. Am. 41, 597 (1951).

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