OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 2 — Feb. 1, 2000
  • pp: 328–334

Characteristic properties of Mueller matrices

José J. Gil  »View Author Affiliations

JOSA A, Vol. 17, Issue 2, pp. 328-334 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (127 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A complete and minimum set of necessary and sufficient conditions for a real 4×4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely, the four conditions obtained from the nonnegativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the transmittance condition. Using the properties of H, a demonstration is also presented of Tr(MTM)=4m002 as being a necessary and sufficient condition for a physical Mueller matrix to be a pure Mueller matrix.

© 2000 Optical Society of America

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

Original Manuscript: March 31, 1999
Revised Manuscript: October 12, 1999
Manuscript Accepted: October 25, 1999
Published: February 1, 2000

José J. Gil, "Characteristic properties of Mueller matrices," J. Opt. Soc. Am. A 17, 328-334 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. R. Cloude, “Group theory and polarisation algebra,” Optik 75, 26–36 (1986).
  2. R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987). [CrossRef]
  3. C. R. Givens, A. B. Kostinski, “A simple necessary and sufficient condition for the physical realizability of Mueller matrices,” J. Mod. Opt. 40, 471–481 (1993). [CrossRef]
  4. C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5088 (1993). [CrossRef]
  5. A. V. Gopala, K. S. Mallesh, “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).
  6. A. V. Gopala, K. S. Mallesh, “On the algebraic characterization of a Mueller matrix in polarization optics. II. Necessary and sufficient conditions for Jones-derived Mueller matrices,” J. Mod. Opt. 45, 989–999 (1998).
  7. K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. A 4, 433–437 (1987). [CrossRef]
  8. J. J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985). [CrossRef]
  9. R. Simon, “Mueller matrices and depolarization criteria,” J. Mod. Opt. 34, 569–575 (1987). [CrossRef]
  10. C. Brosseau, C. R. Givens, A. B. Kostinski, “Generalized trace condition on the Mueller–Jones polarization matrix,” J. Opt. Soc. Am. A 10, 2248–2251 (1993). [CrossRef]
  11. R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990). [CrossRef]
  12. B. Chakraborty, “Depolarizing effect of propagation of a polarized polychromatic beam through an optically active medium: a generalized study,” J. Opt. Soc. Am. A 3, 1422–1427 (1986). [CrossRef]
  13. N. G. Parke, “Matrix optics,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1948).
  14. E. L. O’Neill, Statistical Optics (Addison-Wesley, Reading, Mass., 1963).
  15. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  16. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959). [CrossRef]
  17. R. Barakat, “The statistical properties of partially polarized light,” Opt. Acta 32, 295–312 (1985). [CrossRef]
  18. R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–323 (1963). [CrossRef]
  19. U. Fano, “A Stokes-parameter technique for the treatment of polarization in quantum mechanics,” Phys. Rev. 93, 121–123 (1953). [CrossRef]
  20. R. C. Jones, “A new calculus for the treatment of optical systems. IV,” J. Opt. Soc. Am. 32, 486–493 (1942). [CrossRef]
  21. C. Brosseau, R. Barakat, “Jones and Mueller polarization matrices for random media,” Opt. Commun. 84, 127–132 (1991). [CrossRef]
  22. S.-Y. Lu, R. A. Chipman, “Homogeneous and inhomogeneous Jones matrices,” J. Opt. Soc. Am. A 11, 766–773 (1994). [CrossRef]
  23. A. B. Kostinski, R. C. Givens, “On the gain of a passive linear depolarizing system,” J. Mod. Opt. 39, 1947–1952 (1992). [CrossRef]
  24. J. J. Gil, E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from its Mueller matrix,” Optik 76, 67–71 (1987).
  25. R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982). [CrossRef]
  26. D. G. M. Anderson, 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]
  27. S. R. Cloude, E. Pottier, “Concept of polarization entropy in optical scattering,” Opt. Eng. 34, 1599–1610 (1995). [CrossRef]
  28. R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, UK, 1985), p. 404.
  29. Z. Sekera, “Scattering matrices and reciprocity relationships for various representations of the state of polarization,” J. Opt. Soc. Am. 56, 1732–1740 (1966). [CrossRef]
  30. P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979), Chap. 4.
  31. K. D. Abhyankar, A. L. Fymat, “Relations between the elements of the phase matrix for scattering,” J. Math Phys. 10, 1935–1938 (1969). [CrossRef]
  32. E. S. Fry, G. W. Kattawar, “Relationships between the elements of the Stokes matrix,” Appl. Opt. 20, 3428–3435 (1981). [CrossRef]
  33. J. W. Hovenier, H. C. van de Hulst, C. V. M. Van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).
  34. J. W. Hovenier, “Structure of a general pure Mueller matrix,” Appl. Opt. 33, 8318–8324 (1994). [CrossRef] [PubMed]
  35. H. Takenaka, “A unified formalism for polarization optics by using group theory,” Nouv. Rev. Opt. 4, 37–41 (1973). [CrossRef]
  36. R. Barakat, “Bilinear constraints between elements of the 4×4 Mueller–Jones transfer matrix of polarization theory,” Opt. Commun. 38, 159–161 (1981). [CrossRef]
  37. A. B. Kostinski, C. R. Givens, J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646–1651 (1993). [CrossRef] [PubMed]
  38. C. Brosseau, “Mueller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996). [CrossRef]
  39. M. S. Kumar, R. Simon, “Characterization of Mueller matrices in polarization optics,” Opt. Commun. 11, 2305–2319 (1994).
  40. R. Sridhar, R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903–1915 (1994). [CrossRef]
  41. J. J. Gil, E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986). [CrossRef]

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