OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 6 — Jun. 1, 2013
  • pp: 1078–1088

Polarimetric subtraction of Mueller matrices

José J. Gil and Ignacio San José  »View Author Affiliations

JOSA A, Vol. 30, Issue 6, pp. 1078-1088 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (420 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A general formulation of the additive composition and decomposition of Mueller matrices is presented, which is expressed in adequate terms for properly performing the “polarimetric subtraction,” from a given depolarizing Mueller matrix M, of the Mueller matrix of a given nondepolarizing component that is incoherently embedded in the whole system represented by M. A general and comprehensive procedure for the polarimetric subtraction of depolarizing Mueller matrices is also developed.

© 2013 Optical Society of America

OCIS Codes
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization
(290.5855) Scattering : Scattering, polarization

ToC Category:

Original Manuscript: February 22, 2013
Manuscript Accepted: March 25, 2013
Published: May 8, 2013

José J. Gil and Ignacio San José, "Polarimetric subtraction of Mueller matrices," J. Opt. Soc. Am. A 30, 1078-1088 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. M. Correas, P. A. Melero, and J. J. Gil, “Decomposition of Mueller matrices into pure optical media,” VII Jornadas Zaragoza-Pau de Matemática Aplicada y estadística, Jaca, Spain, 17–18 September, 2001. Monografías del Semin. Matem. Garc a de Galdeano. 27, 233–240 (2003). Available from http://www.unizar.es/galdeano/actas_pau/PDF/233.pdf .
  2. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007). [CrossRef]
  3. J. J. Gil, I. San José, and R. Ossikovski, “Serial-parallel decompositions of Mueller matrices,” J. Opt. Soc. Am. A. 30, 32–50 (2013). [CrossRef]
  4. Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod Opt. 39, 461–484 (1992). [CrossRef]
  5. C. R. Givens and A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40, 471–481 (1993). [CrossRef]
  6. 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]
  7. J. J. Gil and E. Bernabéu, “Depolarization and polarization indices of an optical system,” Optica Acta 33, 185–189 (1986). [CrossRef]
  8. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University, 2012).
  9. N. Wiener, “Generalized harmonic analysis,” Acta Math. 55, 182–195 (1930). [CrossRef]
  10. N. G. Parke, “Matrix optics,” Ph.D. thesis (Massachusetts Institute of Technology, 1948).
  11. U. Fano, “A Stokes-parameter technique for the treatment of polarization in quantum mechanics,” Phys. Rev. 93, 121–123 (1954). [CrossRef]
  12. E. Wolf, “Optics in terms of observable quantities,” Nuovo Cimento 12, 884–888 (1954). [CrossRef]
  13. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 1165–1181 (1959). [CrossRef]
  14. G. B. Parrent and P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370–388 (1960). [CrossRef]
  15. R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–323 (1963). [CrossRef]
  16. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).
  17. J. J. Gil, “Characteristic properties of Mueller matrices,” J. Opt. Soc. Am. A 17, 328–334 (2000). [CrossRef]
  18. J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Semin. Matem. García de Galdeano. 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .
  19. J. J. Gil and I. San José, “3D polarimetric purity,” Opt. Commun. 283, 4430–4434 (2010). [CrossRef]
  20. I. San Jose and J. J. Gil, “Invariant indices of polarimetric purity. Generalized indices of purity for n×n covariance matrices,” Opt. Commun. 284, 38–47 (2011). [CrossRef]
  21. J. J. Gil, “Components of purity of a Mueller matrix,” J. Opt. Soc. Am. A 28, 1578–1585 (2011). [CrossRef]
  22. J. J. Gil, “Determination of polarization parameters in matricial representation. Theoretical contribution and development of an automatic measurement device,” Ph.D. thesis (Facultad de Ciencias, Univ. Zaragoza, Spain, 1983). Available from http://www.pepegil.es/PhD-Thesis-JJ-Gil-English.pdf .
  23. R. Ossikovski, “Analysis of depolarizing Mueller matrices through a symmetric decomposition,” J. Opt. Soc. Am. A 26, 1109–1118 (2009). [CrossRef]
  24. R. Ossikovski, “Canonical forms of depolarizing Mueller matrices,” J. Opt. Soc. Am. A 27, 123–130 (2010). [CrossRef]
  25. R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987). [CrossRef]
  26. 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]
  27. S. S. Girgel, “Structure of Mueller matrices of depolarized optical systems,” Sov. Phys. Crystallogr. 36, 890 (1991).
  28. J. J. Gil and J. Correas, “Polarimetric subtraction for obtaining the Mueller matrices of components which appear combined in a whole material sample under measurement,” Proceedings of ICO Topical Meeting on Polarization Optics (ICOPO), Polvijärvi, Finland, July 2, 2003. Available at http://www.pepegil.es/Polarimetric-subtraction-ICOPO-2003-.pdf .
  29. M. Foldyna, E. Garcia-Caurel, R. Ossikovski, A. De Martino, and J. J. Gil, “Retrieval of a non-depolarizing component of experimentally determined depolarizing Mueller matrices,” Opt. Express 17, 12794–12806 (2009). [CrossRef]
  30. A. Freeman and S. L. Durden, “A three component model for polarimetric SAR data,” IEEE Trans. Geosci. Remote Sens. 36, 963–973 (1998). [CrossRef]
  31. Y. Yamaguchi, T. Moriyama, M. Ishido, and H. Yamada, “Four-component scattering model for polarimetric SAR image decomposition,” IEEE Trans. Geosci. Remote Sens. 43, 1699–1706 (2005). [CrossRef]
  32. J. J. van Zyl, “Application of Cloude’s target decomposition theorem to polarimeric imaging radar,” Proc. SPIE 127, 184–212 (1992). [CrossRef]
  33. J. J. van Zyl, M. Arii, and Y. Kim, “Model-based decomposition of polarimetric SAR covariance matrices constrained for nonnegative eigenvalues,” IEEE Trans. Geosci. Remote Sens. 49, 3452–3459 (2011). [CrossRef]
  34. Y. Cui, Y. Yamaguchi, J. Yang, H. Kobayashi, S.-E. Park, and G. Singh, “On complete model based three component decomposition,” Proceedings of International Niigata Polarimetric SAR Workshop, University of Niigata, Niigata, Japan, 2012).
  35. J. H. M. Wedderburn, Lectures on Matrices (Dover, 1964).
  36. M. T. Chu, R. E. Funderlic, and G. H. Golub, “A rank-one reduction formula and its applications to matrix factorizations,” SIAM Rev. 37, 512–530 (1995). [CrossRef]
  37. J. J. Gil and E. Bernabéu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from its Mueller matrix,” Optik 76, 67–71 (1987).
  38. S. R. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2009).
  39. N. Gosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications and outlook,” J. Biomed. Opt. 16, 110801 (2011). [CrossRef]
  40. T. Novikova, A. Pierangelo, A. De Martino, A. Benali, and P. Validire, “Polarimetric imaging for cancer diagnosis and staging,” Opt. Photon. News 23(10), 26–33 (2012). [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.


Fig. 1. Fig. 2. Fig. 3.
Fig. 4.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited