Symmetries and Periodicities of Partially Coherent Fields

  • A. W. Lohmann
  • J. Ojeda-Casteneda
  • N. Streibl
Conference paper


The symmetries of wave fields are of practical interest in holography, phase conjugation and for automatic focusing. Periodicities of wavefields find practical applications in self-imaging, in interferometers based on the Talbot and on the Lau effect and in Fourier spectrometry. We show that if the operator form for the solution of the Helmholtz-equation is employed, it is possible to discuss in a simple fashion both the symmetry and the periodicity of the propagating field under coherent and under partially coherent illumination.


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  1. 1.
    M.D. Feit, J.A. Fleck, Light propagation in graded-index optical fibers, Appi. Opt. 17: 3990 (1978)ADSGoogle Scholar
  2. M.J. Bastiaans, Transport equations for the Wigner distribution function, Opt. Acta 26: 1265 (1979)ADSCrossRefMathSciNetGoogle Scholar
  3. It seems quite clear that the operator form has been employed elsewhere; however, the authors were only able to trace these two references.Google Scholar
  4. 2.
    M. Born, E. Wolf, Principles of Optics, Pergamon Press, OxfordGoogle Scholar
  5. 3.
    J. Ojeda-Castaneda, Focus error operator and related special functions, J. Opt. Soc. Am. (1983) (accepted)Google Scholar
  6. 4.
    W. Lukosz, Equivalent-lens theory of holographic imaging, J. Opt. Soc. Am. 58: 1084 (1968)ADSCrossRefGoogle Scholar
  7. 5.
    E. Wolf, Phase conjugacy and symmetries in spatially band-limited wavefield containing no evanescent components, J. Opt. Soc. Am. 70: 1311 (1980)CrossRefGoogle Scholar
  8. 6.
    W.D. Montgomery, Unitary operators in the homogeneous wavefield, Opt. Lett. 6: 314 (1981)ADSCrossRefGoogle Scholar
  9. 7.
    A.W. Lohmann, J. Ojeda-Castaneda, N. Streibl, Symmetries in coherent and in partially coherent fields, Opt. Acta 30: 399 (1983)ADSCrossRefGoogle Scholar
  10. 8.
    G. Häusler, E. Körner, A simple focusing criterion, Appl. Opt. (1983) (accepted)Google Scholar
  11. 9.
    W.D. Montgomery, Algebraic formulations of diffraction applied to self-imaging, J. Opt. Soc. Am. 58: 1112 (1968)ADSCrossRefGoogle Scholar
  12. 10.
    A.W. Lohmann, D.E. Silva, An interferometer based on the Talbot effect, Opt. Commun. 2: 413 (1971)ADSCrossRefGoogle Scholar
  13. 10.
    J. Jahns, A.W. Lohmann, The Lau effect (a diffraction experiment with incoherent illumination), Opt. Commun. 28: 263 (1979)ADSCrossRefGoogle Scholar
  14. 11.
    A.W. Lohmann, J. Ojeda-Castaneda, Spatial periodicities in partially coherent fields, Ont. Acta 30: 475 (1983)Google Scholar
  15. 12.
    A.W. Lohmann, J. Ojeda-Castaneda, W. Streibl, Spatial periodicities in coherent and in partially coherent fields, Opt. Acta (1983) (accepted)Google Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • A. W. Lohmann
    • 1
  • J. Ojeda-Casteneda
    • 1
    • 2
  • N. Streibl
    • 1
  1. 1.Physikalisches InstitutUniversität ErlangenErlangenGermany
  2. 2.INAOEPueblaMexico

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