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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 3 — Mar. 1, 2011
  • pp: 448–454

Numerical experiment of the Shannon entropy in partially coherent imaging by Koehler illumination to show the relationship to degree of coherence

Kenji Yamazoe and Andrew R. Neureuther  »View Author Affiliations


JOSA A, Vol. 28, Issue 3, pp. 448-454 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000448


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Abstract

This paper describes the Shannon entropy in a partially coherent imaging system with Koehler illumination. Numerical simulation shows that the entropy has a one-to-one relationship with the normalized mutual intensity given by the van Cittert–Zernike theorem. Analytical evaluation shows that the entropy is consistent with the definition of coherence and incoherence, which is also verified by numerical simulations. Additional numerical experiments confirm that the entropy depends on the source intensity distribution, polarization state of the source, object, and pupil. Therefore, the entropy quantitatively measures the degree of coherence of the partially coherent imaging system.

© 2011 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(110.2990) Imaging systems : Image formation theory
(110.4980) Imaging systems : Partial coherence in imaging

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: September 10, 2010
Revised Manuscript: January 5, 2011
Manuscript Accepted: January 9, 2011
Published: February 28, 2011

Citation
Kenji Yamazoe and Andrew R. Neureuther, "Numerical experiment of the Shannon entropy in partially coherent imaging by Koehler illumination to show the relationship to degree of coherence," J. Opt. Soc. Am. A 28, 448-454 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-3-448


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References

  1. L. Mandel and E. Wolf, “Coherence Properties of Optical Fields,” Rev. Mod. Phys. 37, 231–287 (1965). [CrossRef]
  2. J. W. Goodman, Statistical Optics, (Wiley, 2000), Chap. 5.
  3. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Chap. 10.
  4. E. Hecht, Optics, 4th International ed. (Addison Wesley, 2002), Chap. 12.
  5. J. W. Goodman, Statistical Optics, (Wiley, 2000), Chap. 7.
  6. R. E. Swing, “Conditions for microdensitometer linearity,” J. Opt. Soc. Am. 62, 199–207 (1972). [CrossRef]
  7. R. E. Kinzly, “Partially coherent imaging in a microdensitometer,” J. Opt. Soc. Am. 62, 386–394 (1972). [CrossRef]
  8. H. Gamo, “Intensity matrix and degree of coherence,” J. Opt. Soc. Am. 47, 976–976 (1957). [CrossRef]
  9. H. H. Hopkins, “On the diffraction theory of optical image,” Proc. R. Soc. A 217, 408–432 (1953). [CrossRef]
  10. A. Luis, “An overview of coherence and polarization properties for multicomponent electromagnetic waves,” in Advances in Information Optics and Photonics, A.T.Friberg and R.Dändliker, eds. (SPIE, 2008), Chap. 9. [CrossRef]
  11. J. Perina, Coherence of light (Kluwer, 1985) Chap. 5.
  12. H. M. Ozaktas, S. Yüksel, and M. A. Kutay, “Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence,” J. Opt. Soc. Am. A 19, 1563–1571(2002). [CrossRef]
  13. H. Gamo, “Matrix treatment of partial coherence,” in Progress in Optics, Vol.  III, E.Wolf, ed. (North-Holland, 1964), Chap. 3. [CrossRef]
  14. E. L. O’Neill, Introduction to Statistical Optics (Dover, 2003), Chap. 8.
  15. K. Yamazoe, “Two matrix approaches for aerial image formation obtained by extending and modifying the transmission cross coefficients,” J. Opt. Soc. Am. A 27, 1311–1321(2010). [CrossRef]
  16. K. Yamazoe and A. R. Neureuther, “Aerial image calculation by eigenvalues and eigenfunctions of a matrix that includes source, pupil and mask,” Proc. SPIE-Int. Soc. Opt. Eng. 7640, 76400N (2010). [CrossRef]
  17. For entropy, the term Shannon entropy is used in this paper, although the term von Neumann entropy is used in .
  18. E. L. O’Neill, Introduction to Statistical Optics (Dover, 2003), Appendix B.
  19. J. Tervo, T. Seta¨la¨, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11, 1137–1143(2003). [CrossRef] [PubMed]
  20. E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources I. Field with a narrow spectral range,” Proc. R. Soc. A 225, 96–111 (1954). [CrossRef]
  21. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989). [CrossRef]
  22. M. Mansuripur, “Certain computational aspects of vector diffraction problems: erratum,” J. Opt. Soc. Am. A 10, 382–383(1993). [CrossRef]
  23. I. Moreno, M. J. Yzuel, J. Campos, and A. Vargas, “Jones matrix treatment for polarization Fourier optics,” J. Mod. Opt. 51, 2031–2038 (2004). [CrossRef]

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