Skip to main content

Symmetries and Periodicities of Partially Coherent Fields

  • Conference paper
  • 374 Accesses

Abstract

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.

Supported by the Humboldt-foundation

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.D. Feit, J.A. Fleck, Light propagation in graded-index optical fibers, Appi. Opt. 17: 3990 (1978)

    ADS  Google Scholar 

  2. M.J. Bastiaans, Transport equations for the Wigner distribution function, Opt. Acta 26: 1265 (1979)

    Article  ADS  MathSciNet  Google 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. M. Born, E. Wolf, Principles of Optics, Pergamon Press, Oxford

    Google Scholar 

  5. J. Ojeda-Castaneda, Focus error operator and related special functions, J. Opt. Soc. Am. (1983) (accepted)

    Google Scholar 

  6. W. Lukosz, Equivalent-lens theory of holographic imaging, J. Opt. Soc. Am. 58: 1084 (1968)

    Article  ADS  Google Scholar 

  7. E. Wolf, Phase conjugacy and symmetries in spatially band-limited wavefield containing no evanescent components, J. Opt. Soc. Am. 70: 1311 (1980)

    Article  Google Scholar 

  8. W.D. Montgomery, Unitary operators in the homogeneous wavefield, Opt. Lett. 6: 314 (1981)

    Article  ADS  Google Scholar 

  9. A.W. Lohmann, J. Ojeda-Castaneda, N. Streibl, Symmetries in coherent and in partially coherent fields, Opt. Acta 30: 399 (1983)

    Article  ADS  Google Scholar 

  10. G. Häusler, E. Körner, A simple focusing criterion, Appl. Opt. (1983) (accepted)

    Google Scholar 

  11. W.D. Montgomery, Algebraic formulations of diffraction applied to self-imaging, J. Opt. Soc. Am. 58: 1112 (1968)

    Article  ADS  Google Scholar 

  12. A.W. Lohmann, D.E. Silva, An interferometer based on the Talbot effect, Opt. Commun. 2: 413 (1971)

    Article  ADS  Google Scholar 

  13. J. Jahns, A.W. Lohmann, The Lau effect (a diffraction experiment with incoherent illumination), Opt. Commun. 28: 263 (1979)

    Article  ADS  Google Scholar 

  14. A.W. Lohmann, J. Ojeda-Castaneda, Spatial periodicities in partially coherent fields, Ont. Acta 30: 475 (1983)

    Google Scholar 

  15. A.W. Lohmann, J. Ojeda-Castaneda, W. Streibl, Spatial periodicities in coherent and in partially coherent fields, Opt. Acta (1983) (accepted)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer Science+Business Media New York

About this paper

Cite this paper

Lohmann, A.W., Ojeda-Casteneda, J., Streibl, N. (1984). Symmetries and Periodicities of Partially Coherent Fields. In: Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics V. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0605-5_58

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-0605-5_58

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0607-9

  • Online ISBN: 978-1-4757-0605-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics