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. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2636–2643

Definition of a parametric form of nonsingular Mueller matrices

Vincent Devlaminck and Patrick Terrier  »View Author Affiliations


JOSA A, Vol. 25, Issue 11, pp. 2636-2643 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002636


View Full Text Article

Enhanced HTML    Acrobat PDF (134 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The goal of this paper is to propose a mathematical framework to define and analyze a general parametric form of an arbitrary nonsingular Mueller matrix. Starting from previous results about nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrix. We address this problem in a six-dimensional space in order to introduce a transformation group with the same number of degrees of freedom and explain why subsets of O ( 5 , 1 ) , the orthogonal group associated with six-dimensional Minkowski space, is a physically admissible solution to this question. Generators of this group are used to define possible expressions of an arbitrary nonsingular Mueller matrix. Ultimately, the problem of decomposition of these matrices is addressed, and we point out that the “reverse” and “forward” decomposition concepts recently introduced may be inferred from the formalism we propose.

© 2008 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

History
Original Manuscript: February 20, 2008
Revised Manuscript: July 23, 2008
Manuscript Accepted: August 5, 2008
Published: October 7, 2008

Citation
Vincent Devlaminck and Patrick Terrier, "Definition of a parametric form of nonsingular Mueller matrices," J. Opt. Soc. Am. A 25, 2636-2643 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-11-2636


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903-1915 (1994). [CrossRef]
  2. Z. F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461-484 (1992). [CrossRef]
  3. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072-5088 (1993). [CrossRef]
  4. J. W. Hovenier, “Structure of a general pure Mueller matrix,” Appl. Opt. 33, 8318-8324 (1994). [CrossRef] [PubMed]
  5. A. V. Gopala, K. S. Mallesh, and J. Sudha, “On the algebraic characterization of a Mueller matrix in polarization optics. I. Identifying a Mueller matrix from its N matrix,” J. Mod. Opt. 45, 955-987 (1998). [CrossRef]
  6. M. S. Kumar and R. Simon, “Characterization of Mueller matrices in polarization optics,” Opt. Commun. 88, 464-470 (1992). [CrossRef]
  7. A. B. Kostinski, C. R. Given, and J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646-1651 (1993). [CrossRef] [PubMed]
  8. C. R. Givens and B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40, 471-481 (1993). [CrossRef]
  9. R. Espinosa-Luna, D. Rodrıguez-Carrera, E. Bernabeu, and S. Hinojosa-Ruız, “Transformation matrices for the Mueller-Jones formalism,” Optik (Stuttgart) (to be published).
  10. R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293-297 (1982). [CrossRef]
  11. D. G. M. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305-2319 (1994). [CrossRef]
  12. C. Brosseau, C. R. Givens, and A. B. Kotinski, “Generalized trace condition on the Mueller-Jones polarization matrix,” J. Opt. Soc. Am. A 10, 2248-2251 (1993). [CrossRef]
  13. S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttgart) 75, 26-36 (1986).
  14. K. Kim, L. Mandel, and E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. A 4, 433-437 (1987). [CrossRef]
  15. J. J. Gil, “Characteristic properties of Mueller matrices,” J. Opt. Soc. Am. A 17, 328-334 (2000). [CrossRef]
  16. J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).
  17. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106-1113 (1996). [CrossRef]
  18. R. Ossikovski, “Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition,” J. Opt. Soc. Am. A 25, 473-482 (2008). [CrossRef]
  19. B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824-2832 (2004). [CrossRef] [PubMed]
  20. J. E. Wolfe and R. A. Chipman, “Polarimetric characterization of liquid-crystal-on-silicon panels,” Appl. Opt. 45, 1688-1703 (2006). [CrossRef] [PubMed]
  21. P. Pellat Finet, “Geometrical approach to polarization optics: quaternionic representation of the polarized light,” Optik (Stuttgart) 87, 68-76 (1991).
  22. S. Baskal and Y. S. Kim, “De Sitter group as a symmetry for optical decoherence,” J. Phys. A 39, 7775-7788 (2006). [CrossRef]
  23. H. Takenaka, “A unified formalism for polarization optics by using group theory,” Nouv. Rev. Opt. 4, 37-41 (1973). [CrossRef]
  24. Sudha and A. V. Gopala Rao, “Polarization elements, a group theoretical study,” J. Opt. Soc. Am. A 18, 3130-3134 (2001). [CrossRef]
  25. D. Han, Y. S. Kim, and M. E. Noz, “Stokes parameters as Minkowskian four-vectors,” Phys. Rev. E 56, 6065-6076 (1997). [CrossRef]
  26. R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689-691 (2007). [CrossRef] [PubMed]
  27. S. Sternberg, Group Theory and Physics (Cambridge U. Press, 1994).
  28. J. Bognar, Indefinite Inner Product Spaces (Springer, 1974).
  29. I. Gohberg, P. Lancaster, and L. Rodman, Matrices and Indefinite Scalar Products (Biikhauser OT 8, 1983).
  30. D. H. Sattiger and O. L. Weaver, Lie Group and Algebras with Applications to Physics, Geometry and Mechanics (Springer, 1991).
  31. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1957).
  32. K. D. Abhyankar and A. L. Fymat, “Relations between the elements of the phase matrix for scattering,” J. Math. Phys. 10, 1935-1938 (1969). [CrossRef]
  33. R. Barakat, “Bilinear constraints between elements of the 4×4 Mueller-Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159-161 (1981). [CrossRef]
  34. W. A. Shurcliff, Polarized Light (Harvard U. Press, 1962).
  35. A. A. Sagle and R. E. Walde, Introduction to Lie Groups and Lie Algebras (Academic, 1973).
  36. J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. 29, 2234-2236 (2004). [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