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: Franco Gori
  • Vol. 30, Iss. 11 — Nov. 1, 2013
  • pp: 2291–2305

Poincaré sphere mapping by Mueller matrices

Razvigor Ossikovski, José J. Gil, and Ignacio San José  »View Author Affiliations


JOSA A, Vol. 30, Issue 11, pp. 2291-2305 (2013)
http://dx.doi.org/10.1364/JOSAA.30.002291


View Full Text Article

Enhanced HTML    Acrobat PDF (2179 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

By using the symmetric serial decomposition of a normalized Mueller matrix M [J. Opt. Soc. Am. A 26, 1109 (2009)] as a starting point and by considering the reciprocity property of Mueller matrices, the geometrical features of the Poincaré sphere mapping by M are analyzed in order to obtain a new parameterization of M in which the 15 representative parameters have straightforward geometrical interpretations. This approach provides a new geometry-based framework, whereby any normalized Mueller matrix M is completely described by a set of three associated ellipsoids whose geometrical and topological properties are characteristic of M. The mapping analysis considers the cases of type-I and type-II, as well as singular and nonsingular Mueller matrices. The novel parameterization is applied to several illustrative examples of experimental Mueller matrices taken from the literature.

© 2013 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization
(290.5855) Scattering : Scattering, polarization

ToC Category:
Physical Optics

History
Original Manuscript: July 29, 2013
Manuscript Accepted: September 17, 2013
Published: October 17, 2013

Citation
Razvigor Ossikovski, José J. Gil, and Ignacio San José, "Poincaré sphere mapping by Mueller matrices," J. Opt. Soc. Am. A 30, 2291-2305 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-11-2291


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. M. Sylla, C. J. K. Richardson, M. van Leeuwen, M. Saylors, and J. Goldhar, “DOP ellipsoids for systems with frequency-dependent principal states,” IEEE Photon. Technol. Lett. 13, 1310–1312 (2001). [CrossRef]
  2. M. W. Williams, “Depolarization and cross polarization in ellipsometry of rough surfaces,” Appl. Opt. 25, 3616–3622 (1986). [CrossRef]
  3. F. Le Roy-Brehonnet, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, “Analysis of depolarizing optical targets by Mueller matrix formalism,” Pure Appl. Opt. 6, 385–404 (1997). [CrossRef]
  4. F. Le Roy-Bréhonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21, 109–151 (1997). [CrossRef]
  5. C. Brosseau, Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998).
  6. S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998). [CrossRef]
  7. B. DeBoo, J. Sasian, and R. A. Chipman, “Degree of polarization surfaces and maps for analysis of depolarization,” Opt. Express 12, 4941–4957 (2004). [CrossRef]
  8. C. Ferreira, I. San José, J. J. Gil, and J. M. Correas, “Geometric modeling of polarimetric transformations,” Monog. Sem. Mat. G. de Galdeano 33, 115–119 (2006), www.unizar.es/galdeano/actas_pau/PDFIX/FerSanGilCor05.pdf .
  9. T. Tudor and V. Manea, “Ellipsoid of the polarization degree: a vectorial, pure operatorial Pauli algebraic approach,” J. Opt. Soc. Am. B 28, 596–601 (2011). [CrossRef]
  10. R. Ossikovski, “Analysis of depolarizing Mueller matrices through a symmetric decomposition,” J. Opt. Soc. Am. A 26, 1109–1118 (2009). [CrossRef]
  11. Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461–484 (1992). [CrossRef]
  12. 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]
  13. 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]
  14. R. Ossikovski, “Canonical forms of depolarizing Mueller matrices,” J. Opt. Soc. Am. A 27, 123–130 (2010). [CrossRef]
  15. J. J. Gil, “Characteristic properties of Mueller matrices,” J. Opt. Soc. Am. A 17, 328–334 (2000). [CrossRef]
  16. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007). [CrossRef]
  17. J. J. Gil, “Components of purity of a Mueller matrix,” J. Opt. Soc. Am. A 28, 1578–1585 (2011). [CrossRef]
  18. 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, University Zaragoza, 1983), zaguan.unizar.es/record/10680/files/TESIS-2013-057.pdf .
  19. J. J. Gil and E. Bernabéu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986). [CrossRef]
  20. A. Kostinski, B. James, and W. M. Boerner, “Optimal reception of partially polarized waves,” J. Opt. Soc. Am. A 5, 58–64 (1988). [CrossRef]
  21. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).
  22. S.-Y. Lu and R. A. Chipman, “Homogeneous and inhomogeneous Jones matrices,” J. Opt. Soc. Am. A 11, 766–773 (1994). [CrossRef]
  23. T. Tudor, “Generalized observables in polarization optics,” J. Phys. A 36, 9577–9590 (2003). [CrossRef]
  24. Z. Sekera, “Scattering matrices and reciprocity relationships for various representations of the state of polarization,” J. Opt. Soc. Am. 56, 1732–1740 (1966). [CrossRef]
  25. R. Bhandari, “Transpose symmetry of the Jones matrix and topological phases,” Opt. Lett. 33, 854–856 (2008). [CrossRef]
  26. R. Bhandari, “Transpose symmetry of the Jones matrix and topological phases: erratum,” Opt. Lett. 33, 2985 (2008). [CrossRef]
  27. A. Schönhofer and H.-G. Kuball, “Symmetry properties of the Mueller matrix,” Chem. Phys. 115, 159–167 (1987). [CrossRef]
  28. S. R. Cloude, “Conditions for the physical realizability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–185 (1989).
  29. A. V. G. Rao, K. S. Mallesh, and 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).
  30. A. V. G. Rao, K. S. Mallesh, and Sudha, “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).
  31. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–493 (1941). [CrossRef]
  32. P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, 1979), Chap. 4.
  33. J. J. Gil, “Mueller matrices,” in Light Scattering from Microstructures, Vol. 534 of Lecture Notes in Physics (Springer, 2000), Chap 4.
  34. 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]
  35. R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007). [CrossRef]
  36. M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. Eur. Opt. Soc. Rapid Pub. 2, 07018 (2007). [CrossRef]
  37. R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406–2410 (2008). [CrossRef]
  38. 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]
  39. R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009). [CrossRef]
  40. R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903–1915 (1994). [CrossRef]
  41. C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming stokes parameters,” J. Math. Phys. 34, 5072–5088 (1993). [CrossRef]
  42. 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).
  43. J. J. Gil, “Transmittance constraints in serial decompositions of depolarizing Mueller matrices,” J. Opt. Soc. Am. A 30, 701–707 (2013). [CrossRef]
  44. I. San José 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]
  45. J. J. Gil and I. San José, “Polarimetric subtraction of Mueller matrices,” J. Opt. Soc. Am. A 30, 1078–1088 (2013). [CrossRef]
  46. S. Manhas, M. K. Swami, P. Buddhiwant, P. K. Gupta, and K. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express 14, 190–202 (2006). [CrossRef]
  47. D. P. Cubián, J. L. A. Diego, and R. Rentmeesters, “Characterization of depolarizing optical media by means of entropy factor: application to biological tissues,” Appl. Opt. 44, 358–364 (2005). [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