OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 6 — Mar. 15, 2006
  • pp: 817–819

Maximum-likelihood estimation of Mueller matrices

A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman  »View Author Affiliations

Optics Letters, Vol. 31, Issue 6, pp. 817-819 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (82 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical optical systems. Contrary to linear reconstruction algorithms, the proposed method yields physically acceptable Mueller matrices even in the presence of uncontrolled experimental errors. We illustrate our method with the case of an unphysical measured Mueller matrix taken from the literature.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

Original Manuscript: November 3, 2005
Revised Manuscript: November 7, 2005
Manuscript Accepted: November 24, 2005

A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, "Maximum-likelihood estimation of Mueller matrices," Opt. Lett. 31, 817-819 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  2. R. P. Feynamn, F. L. Vernon Jr., and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957). [CrossRef]
  3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, reprinted 1st ed. (Cambridge U. Press, 2002).
  4. M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003). [CrossRef] [PubMed]
  5. N. Brunner, A. Acín, D. Collins, N. Gisin, and V. Scarani, Phys. Rev. Lett. 91, 180402 (2003). [CrossRef] [PubMed]
  6. J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O'Brien, M. A. Nielsen, and A. G. White, Phys. Rev. Lett. 90, 193601 (2003). [CrossRef] [PubMed]
  7. J. Fiurásek and Z. Hradil, Phys. Rev. A 63, 020101(R) (2001). [CrossRef]
  8. M. F. Sacchi, Phys. Rev. A 63, 054104 (2001). [CrossRef]
  9. R. L. Kosut, I. Walmsley, and H. Rabitz, arXiv.org e-print archive, quant-ph/0411093.
  10. F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997). [CrossRef]
  11. In the current literature there is some confusion in the use of terms such as "nominal" Mueller matrix, "physical" Mueller matrix, etc. Here we adopt the terminology of Ref. .
  12. D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. A 11, 2305 (1994). [CrossRef]
  13. A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
  14. A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).
  15. The literature on ML data analysis and its limitations is vast even in the classical optics context. Many pertinent papers may be found, e.g., by typing "maximum likelihood" on the web search engine of the Journal of the Optical Society of America A.
  16. D. L. Falkoff and J. E. McDonald, J. Opt. Soc. Am. 41, 862 (1951). [CrossRef]
  17. U. Fano, Phys. Rev. 93, 121 (1954). [CrossRef]
  18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, 1995).
  19. A. Aiello and J. P. Woerdman, arXiv.org e-print archive, math-ph/0412061 (2004).
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, 1994).
  21. B. J. Howell, Appl. Opt. 18, 1809 (1979). [CrossRef]
  22. A. Peres, Quantum Theory, Concepts and Methods (Kluwer Academic, 1998).

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.


Fig. 1

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited