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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 56, Iss. 6 — Jun. 1, 1966
  • pp: 739–740

Theorem in Coherence Theory

RICHARD BARAKAT  »View Author Affiliations

JOSA, Vol. 56, Issue 6, pp. 739-740 (1966)

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Parrent’s criterion for the complete coherence of an optical wave field is re-examined and a new proof is obtained using Fourier-Stieltjes integrals.

RICHARD BARAKAT, "Theorem in Coherence Theory," J. Opt. Soc. Am. 56, 739-740 (1966)

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  1. G. Parrent, Opt. Acta 6, 285 (1959). See also: M. Beran and G. Parrent, Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), p. 47.
  2. S. F. Edwards and G. Parrent, Opt. Acta 6, 367 (1959).
  3. Dr. Emil Wolf kindly informed the author that he has reached the same conclusion concerning Ref. 1. See: C. L. Metha, E. Wolf, and A. P. Balachandran, J. Math. Phys. 7, 133 (1966).
  4. The author prefers the use of real-valued functions, although the subsequent analysis can also be effectuated using complexvalued functions.
  5. The braces { } denote ensemble properties.
  6. M. S. Bartlett, Stochastic Processes, Methods and Applications (Cambridge University Press, Cambridge, England, 1956), p. 189.
  7. Actually there is a third component termed the singular continuous component; this component is continuous but is without a spectral density at every point. Such functions do not have any physical significance and are always omitted.
  8. H. Bohr, Almost Periodic Functions (Chelsea Publishing Co., New York, 1951).
  9. This theorem was first stated by Kampe de Feriet (in an almost completely unknown paper) for the case of an autocorrelation function; the extension to cross-correlation functions presented here is a straightforward extension of his proof. See: M. J. Kampe de Feriet, Ann. Soc. Sci. Bruxelles, Ser. 1 59, 145 (1939).
  10. E. T. Whittaker and G. N. Watson, Modern Analysis (Cambridge University Press, Cambridge, England, 1935), 4th ed., p. 172.

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