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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: 727–732

Generalized Source and the van Cittert—Zernike Theorem: A Study of the Spatial Coherence Required for Interferometry

C. W. McCUTCHEN  »View Author Affiliations


JOSA, Vol. 56, Issue 6, pp. 727-732 (1966)
http://dx.doi.org/10.1364/JOSA.56.000727


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Abstract

If two wavetrains are to exhibit interference at some point in space they must be at least partially coherent, one with the other, at this point. This partial coherence between the two interfering wavetrains can, in most interferometers, easily be related to the mutual coherence between separated points in the single wavetrain from which the two interfering wavetrains are derived. The mutual coherence in this wavetrain depends upon the distribution of the source which produces it in a manner given by the van Cittert-Zernike theorem, which in most practical cases can be economically stated in terms of source intensity as a function of direction from the point under consideration. The mutual intensity is the three-dimensional Fourier transform of this generalized source. Knowing this, we can, within the limits set by fact that the generalized source is a distribution spread upon the unit sphere, design to order source distributions to produce the mutual coherence necessary for different kinds of interferometry. Examples are given; the case of an infinitely thin annular source is worked out in detail.

Citation
C. W. McCUTCHEN, "Generalized Source and the van Cittert—Zernike Theorem: A Study of the Spatial Coherence Required for Interferometry," J. Opt. Soc. Am. 56, 727-732 (1966)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-56-6-727


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References

  1. G. Hansen, Zeiss Nachr., 109 (1942); Z. Angew. Phys. 6, 203 (1954); Optik 12, 5 (1955); Optik 15, 560 (1958).
  2. G. Schulz, Contributions to Interference Microscopy (Hilger & Watts, Ltd., London, England, 1964); p. 269 et seq. translated from Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, Germany 1961); Also Optica Acta 11, 43, 89, and 131 (1964).
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., Oxford, England, 1959).
  4. P. H. van Cittert, Physica 1, 201 (1934).
  5. F. Zernike, Physica 5, 785 (1938).
  6. C. W. McCutchen, J. Opt. Soc. Am. 54, 240 (1964).
  7. T. Merton, Proc. Roy. Soc. (London) 189A, 309 (1947).
  8. T. Merton, Proc. Roy. Soc. (London) 191A, 1 (1947).

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