OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 7 — Jul. 1, 2009
  • pp: 1588–1597

Diffraction of paraxial partially coherent fields by planar obstacles in the Wigner representation

Miguel A. Alonso  »View Author Affiliations


JOSA A, Vol. 26, Issue 7, pp. 1588-1597 (2009)
http://dx.doi.org/10.1364/JOSAA.26.001588


View Full Text Article

Enhanced HTML    Acrobat PDF (364 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The free-space propagation of paraxial, partially coherent stationary fields can be described in a simple and intuitive way through the use of the Wigner function. In this context, this function plays the role of a generalized radiance that is constant along straight lines or rays. The effect of diffraction by transverse planar opaque obstacles or apertures is considered here for this representation, and a simple analytic approximate formula is given for the case when the incident field is quasi-homogeneous, at least in the neighborhood of the obstacle’s edges. In this result, diffraction is accounted for by including rays emanating from the obstacle’s edges.

© 2009 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(030.5630) Coherence and statistical optics : Radiometry
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: February 18, 2009
Revised Manuscript: May 6, 2009
Manuscript Accepted: May 25, 2009
Published: June 17, 2009

Citation
Miguel A. Alonso, "Diffraction of paraxial partially coherent fields by planar obstacles in the Wigner representation," J. Opt. Soc. Am. A 26, 1588-1597 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-7-1588


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, 1990). [CrossRef]
  2. Yu. A. Kravtsov and Yu. I. Orlov, Caustics, Catastrophes, and Wave Fields, 2nd ed. (Springer-Verlag, 1998).
  3. M. A. Alonso, “Rays and waves,” in Phase Space Optics: Fundamentals and Applications, B.Hennelly, J.Ojeda-Castañeda, and M.Testorf, eds. (McGraw-Hill, to be published in 2009), Chap. 8.
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, 1995), pp. 287-307.
  5. A.T.Friberg, vol. ed., Selected Papers on Coherence and Radiometry, Milestone Series Vol. MS69 (SPIE Press, 1993).
  6. Yu. A. Kravtsov and L. A. Apresyan, “Radiative transfer: new aspects of the old theory,” in Progress in Optics Vol. XXXVI, E.Wolf, ed. (North Holland, 1996) pp. 179-244. [CrossRef]
  7. L. A. Apresyan and Yu. A. Kravtsov, Radiative Transfer. Statistical and Wave Aspects (Gordon & Breach, 1996).
  8. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, 1983), p. 13.
  9. L. E. Vicent and M. A. Alonso, “Generalized radiometry as a tool for the propagation of partially coherent fields,” Opt. Commun. 207, 101-112 (2002). [CrossRef]
  10. E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932). [CrossRef]
  11. L. S. Dolin, “Beam description of weakly-inhomogeneous wave fields,” Izv. Vyssh. Uchebn. Zaved., Radiofiz. 7, 559-563 (1964).
  12. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710-1716 (1980). [CrossRef]
  13. M. J. Bastiaans, “Wigner function,” in Phase Space Optics: Fundamentals and Applications, B.Hennelly, J.Ojeda-Castañeda, and M.Testorf, eds. (McGraw-Hill, to be published in 2009), Chap. 1.
  14. A. Torre, Linear Ray and Wave Optics in Phase Space: Bridging Ray and Wave Optics via the Wigner Phase-Space Picture (Elsevier, 2005). [PubMed]
  15. A. T. Friberg, “On the generalized radiance associated with radiation from a quasihomogeneous planar source,” Opt. Acta 28, 261-277 (1981). [CrossRef]
  16. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007) pp. 90-95.
  17. G. I. Ovchinnikov and V. I. Tatarskii, “On the relation between coherence theory and the radiative transfer equation,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 15, 1419-1421 (1972).
  18. M. A. Alonso, “Radiometry and wide-angle wave fields. III. Partial coherence,” J. Opt. Soc. Am. A 18, 2502-2511 (2001), and references therein. [CrossRef]
  19. M. A. Alonso, “Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space,” J. Opt. Soc. Am. A 21, 2233-2243 (2004), and references therein. [CrossRef]
  20. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116-130 (1962). [CrossRef] [PubMed]
  21. R.C.Hansen, vol. ed., Geometric Theory of Diffraction (IEEE Press, New York, 1981).
  22. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves, 3rd ed. (Peter Peregrinus, 1986).
  23. R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE 62, 1448-1461 (1974). [CrossRef]
  24. R. Castañeda, J. Carrasquilla, and J. Herrera, “Radiometric analysis of diffraction of quasi-homogeneous optical fields,” Opt. Commun. 273, 8-20 (2007). [CrossRef]
  25. R. Castañeda and J. Carrasquilla, “Spatial coherence wavelets and phase-space representation of diffraction,” Appl. Opt. 47, E76-E87 (2008). [CrossRef] [PubMed]
  26. This follows from the Hermiticity of the cross-spectral density, i.e., W(r⃗1;r⃗2)=W*(r⃗2;r⃗1)4. The fact that B is real is then shown by considering the complex conjugate of both sides of Eq. and changing the variable of integration according to x″=−x′.
  27. E. Wolf, “Radiometric model for propagation of coherence,” Opt. Lett. 19, 2024-2026 (1994). [CrossRef] [PubMed]

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