Abstract

A product decomposition of a depolarizing Mueller matrix consisting in the sequence of five factors—a diagonal depolarizer stacked between two retarder and diattenuator pairs—is proposed. This novel “symmetric” decomposition allows for a straightforward interpretation and parameterization of an experimentally determined Mueller matrix in terms of an arrangement of polarization devices and their characteristic parameters: diattenuations, retardances, and axis azimuths. Its application is illustrated on experimentally determined Mueller matrices.

© 2009 Optical Society of America

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  1. E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
    [CrossRef]
  2. C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
    [CrossRef]
  3. 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]
  4. D. Lara and C. Dainty, “Axially resolved complete Mueller matrix confocal microscopy,” Appl. Opt. 45, 1917-1930 (2006).
    [CrossRef] [PubMed]
  5. N. A. Beaudry, Y. Zhao, and R. A. Chipman, “Dielectric tensor measurement from a single Mueller matrix image,” J. Opt. Soc. Am. A 24, 814-824 (2007).
    [CrossRef]
  6. J. E. Wolfe and R. A. Chipman, “Polarimetric characterization of liquid-crystal-on-silicon panels,” Appl. Opt. 45, 1688-1703 (2006).
    [CrossRef] [PubMed]
  7. F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
    [CrossRef]
  8. T. Novikova, A. De Martino, S. Ben Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45, 3688-3697 (2006).
    [CrossRef] [PubMed]
  9. R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
    [CrossRef]
  10. C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, 1998), Chap. 4.1, p. 235; Chap. 4.4, p. 277.
  11. 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]
  12. 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]
  13. 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 Publ. 2, 07018-1-07018-7 (2007).
    [CrossRef]
  14. P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), Chap.5, p. 192.
  15. Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461-484 (1992).
    [CrossRef]
  16. R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406-2410 (2008).
    [CrossRef]
  17. C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072-5088 (1993).
    [CrossRef]
  18. A. V. Gopala 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).
    [CrossRef]
  19. 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]
  20. The matrices under study in were actually GMTGM and GMGMT. However, these two matrices are similar, respectively, to MTGMG and MGMTG by G, and therefore share the same eigenvalue spectrum. Their respective eigenvectors are G times S1 and S2, the eigenvectors of MTGMG and MGMTG, and physically represent polarization states of the same nature (partially or totally polarized) as those represented by S1 and S2. Consequently, all results from are directly applicable to this work.
  21. A. V. Gopala 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).
    [CrossRef]
  22. Sudha and A. V. Gopala Rao, “Polarization elements: a group theoretical study,” J. Opt. Soc. Am. A 18, 3130-3134 (2001).
    [CrossRef]
  23. R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903-1915 (1994).
    [CrossRef]
  24. M. Renardy, “Singular value decomposition in Minkowski space,” Linear Algebra Appl. 236, 53-58 (1996).
    [CrossRef]
  25. S. R. Cloude, “Conditions for the physical realizability of matrix operators in polarimetry,” Proc. SPIE 1166, 177-185 (1989).
  26. R. Ossikovski, “Interpretation of nondepolarizing Mueller matrices based on the singular-value decomposition,” J. Opt. Soc. Am. A 25, 473-482 (2008).
    [CrossRef]
  27. J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).
  28. S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607-1-056607-8 (2006).
    [CrossRef]
  29. R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
    [CrossRef]
  30. 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] [PubMed]
  31. J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185-189 (1986).
    [CrossRef]
  32. 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]

2008 (4)

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406-2410 (2008).
[CrossRef]

R. Ossikovski, “Interpretation of nondepolarizing Mueller matrices based on the singular-value decomposition,” J. Opt. Soc. Am. A 25, 473-482 (2008).
[CrossRef]

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

2007 (3)

2006 (5)

2005 (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

2004 (3)

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

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]

2001 (1)

1998 (2)

A. V. Gopala 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).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

1997 (1)

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]

1996 (2)

M. Renardy, “Singular value decomposition in Minkowski space,” Linear Algebra Appl. 236, 53-58 (1996).
[CrossRef]

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]

1994 (1)

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903-1915 (1994).
[CrossRef]

1993 (2)

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]

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072-5088 (1993).
[CrossRef]

1992 (1)

Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461-484 (1992).
[CrossRef]

1989 (1)

S. R. Cloude, “Conditions for the physical realizability of matrix operators in polarimetry,” Proc. SPIE 1166, 177-185 (1989).

1987 (1)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

1986 (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185-189 (1986).
[CrossRef]

An, I.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Anastasiadou, M.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406-2410 (2008).
[CrossRef]

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 Publ. 2, 07018-1-07018-7 (2007).
[CrossRef]

Beaudry, N. A.

Ben Hatit, S.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

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 Publ. 2, 07018-1-07018-7 (2007).
[CrossRef]

T. Novikova, A. De Martino, S. Ben Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45, 3688-3697 (2006).
[CrossRef] [PubMed]

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185-189 (1986).
[CrossRef]

Boulbry, B.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Boulvert, F.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Brosseau, C.

C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, 1998), Chap. 4.1, p. 235; Chap. 4.4, p. 277.

Buddhiwant, P.

Cariou, J.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Chen, C.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Chipman, R. A.

Cloude, S. R.

S. R. Cloude, “Conditions for the physical realizability of matrix operators in polarimetry,” Proc. SPIE 1166, 177-185 (1989).

Collins, R. W.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Dainty, C.

De Martino, A.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406-2410 (2008).
[CrossRef]

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

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 Publ. 2, 07018-1-07018-7 (2007).
[CrossRef]

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]

T. Novikova, A. De Martino, S. Ben Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45, 3688-3697 (2006).
[CrossRef] [PubMed]

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]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Drévillon, B.

Ferreira, G. M.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Garcia-Caurel, E.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Gil, J. J.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185-189 (1986).
[CrossRef]

Givens, C. R.

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]

Gopala Rao, A. V.

Sudha and A. V. Gopala Rao, “Polarization elements: a group theoretical study,” J. Opt. Soc. Am. A 18, 3130-3134 (2001).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

Gupta, P. K.

Guyot, S.

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]

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 Publ. 2, 07018-1-07018-7 (2007).
[CrossRef]

Kostinski, A. B.

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]

Lancaster, P.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), Chap.5, p. 192.

Lara, D.

Laude-Boulesteix, B.

Le Brun, G.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Le Jeune, B.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

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]

Le Roy-Bréhonnet, F.

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]

Lu, S.-Y.

Mallesh, K. S.

A. V. Gopala 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).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

Manhas, S.

Marienko, V. V.

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607-1-056607-8 (2006).
[CrossRef]

Novikova, T.

Oberemok, E. A.

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607-1-056607-8 (2006).
[CrossRef]

Ossikovski, R.

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

R. Ossikovski, “Interpretation of nondepolarizing Mueller matrices based on the singular-value decomposition,” J. Opt. Soc. Am. A 25, 473-482 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406-2410 (2008).
[CrossRef]

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]

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 Publ. 2, 07018-1-07018-7 (2007).
[CrossRef]

Podraza, N. J.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Renardy, M.

M. Renardy, “Singular value decomposition in Minkowski space,” Linear Algebra Appl. 236, 53-58 (1996).
[CrossRef]

Rivet, S.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Savenkov, S. N.

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607-1-056607-8 (2006).
[CrossRef]

Schwartz, L.

Simon, R.

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903-1915 (1994).
[CrossRef]

Singh, K.

Sridhar, R.

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903-1915 (1994).
[CrossRef]

Sudha,

Sudha and A. V. Gopala Rao, “Polarization elements: a group theoretical study,” J. Opt. Soc. Am. A 18, 3130-3134 (2001).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

Swami, M. K.

Tismenetsky, M.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), Chap.5, p. 192.

van der Mee, C. V. M.

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072-5088 (1993).
[CrossRef]

Wolfe, J. E.

Xing, Z.-F.

Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461-484 (1992).
[CrossRef]

Zapien, J. A.

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Zhao, Y.

Appl. Opt. (4)

J. Eur. Opt. Soc. Rapid Publ. (1)

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 Publ. 2, 07018-1-07018-7 (2007).
[CrossRef]

J. Math. Phys. (1)

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072-5088 (1993).
[CrossRef]

J. Mod. Opt. (5)

A. V. Gopala 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).
[CrossRef]

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]

Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461-484 (1992).
[CrossRef]

A. V. Gopala 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).
[CrossRef]

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903-1915 (1994).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A, Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

J. Opt. Soc. Am. A (4)

Linear Algebra Appl. (1)

M. Renardy, “Singular value decomposition in Minkowski space,” Linear Algebra Appl. 236, 53-58 (1996).
[CrossRef]

Opt. Acta (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185-189 (1986).
[CrossRef]

Opt. Commun. (1)

R. Ossikovski, M. Anastasiadou, and A. De Martino, “Product decompositions of depolarizing Mueller matrices with negative determinants,” Opt. Commun. 281, 2406-2410 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (Stuttgart) (1)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

Phys. Rev. E (1)

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607-1-056607-8 (2006).
[CrossRef]

Phys. Status Solidi A (1)

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them,” Phys. Status Solidi A 205, 720-727 (2008).
[CrossRef]

Phys. Status Solidi C (1)

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

Proc. SPIE (1)

S. R. Cloude, “Conditions for the physical realizability of matrix operators in polarimetry,” Proc. SPIE 1166, 177-185 (1989).

Prog. Quantum Electron. (1)

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]

Thin Solid Films (2)

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

C. Chen, I. An, G. M. Ferreira, N. J. Podraza, J. A. Zapien, and R. W. Collins, “Multichannel Mueller matrix ellipsometer based on the dual rotating compensator principle,” Thin Solid Films 455-456, 14-23 (2004).
[CrossRef]

Other (3)

C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, 1998), Chap. 4.1, p. 235; Chap. 4.4, p. 277.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), Chap.5, p. 192.

The matrices under study in were actually GMTGM and GMGMT. However, these two matrices are similar, respectively, to MTGMG and MGMTG by G, and therefore share the same eigenvalue spectrum. Their respective eigenvectors are G times S1 and S2, the eigenvectors of MTGMG and MGMTG, and physically represent polarization states of the same nature (partially or totally polarized) as those represented by S1 and S2. Consequently, all results from are directly applicable to this work.

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Tables (1)

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Table 1 Correspondence between Mathematical Factorizations and Physical Decompositions for an Arbitrary Mueller Matrix M

Equations (57)

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M = M Δ M R M D ,
M Δ = [ 1 0 T P Δ m Δ ] ,
M = M D M R M Δ r .
M Δ r = [ 1 D Δ T 0 m Δ r ] ,
M Δ d = [ d 0 0 0 0 0 d 1 0 0 0 0 d 2 0 0 0 0 d 3 ] diag ( d 0 , d 1 , d 2 , d 3 ) .
M = M D 2 M R 2 M Δ d M R 1 T M D 1 ,
M = M 00 [ 1 D T P m ] ,
M D = T u [ 1 D T D m D ] ,
m D = 1 D 2 I + ( 1 1 D 2 ) D ̂ D ̂ T ,
M R = [ 1 0 0 m R ] ,
R = cos 1 [ 1 2 tr ( M R ) 1 ] ,
a i = 1 2 sin R j , k = 1 3 ε i j k ( m R ) j k , i = 1 , 2 , 3 ,
T u = 1 1 D 2
M D 1 = G M D G ,
M M D 1 1 = M ( G M D 1 G ) = M D 2 M R 2 M Δ d M R 1 T ,
( M G ) ( M D 1 G ) = M D 2 ( M R 2 M Δ d M R 1 T ) = M D 2 M ,
M = M R 2 M Δ d M R 1 T .
M = [ d 0 0 T 0 m ] .
( M G ) T u 1 ( 1 D 1 ) = d 0 T u 2 ( 1 D 2 ) .
( M T G ) T u 2 ( 1 D 2 ) = d 0 T u 1 ( 1 D 1 ) .
( M T G M G ) S 1 = d 0 2 S 1 , ( M G M T G ) S 2 = d 0 2 S 2
S 1 = ( 1 D 1 ) , S 2 = ( 1 D 2 ) .
M = M D 2 1 M M D 1 1 ,
m = m R 2 m Δ d m R 1 T ,
M = M 2 M Δ d M 1 T ,
M = M R 2 M D 2 M Δ d M D 1 M R 1 T ,
M = M D 2 M R 2 M Δ d M D 1 M R 1 T ,
M = M R 2 M D 2 M Δ d M R 1 T M D 1 .
M ( 1 ) = [ 1.000 0.115 0.066 0.023 0.111 0.759 0.061 0.001 0.018 0.151 0.435 0.139 0.046 0.006 0.128 0.334 ] ,
M ( 2 ) = [ 1.000 0.009 0.021 0.041 0.002 0.256 0.029 0.003 0.024 0.045 0.235 0.032 0.041 0.024 0.017 0.538 ]
M D 1 ( 1 ) = [ 1 0.0439 0.0899 0.0050 0.0439 0.9959 0.0020 0.0001 0.0899 0.0020 0.9990 0.0002 0.0050 0.0001 0.0002 0.9950 ] ,
M D 2 ( 1 ) = [ 1 0.0841 0.0503 0.0329 0.0841 0.9982 0.0021 0.0014 0.0503 0.0021 0.9959 0.0008 0.0329 0.0014 0.0008 0.9952 ] .
M ( 1 ) = [ 0.9989 0 0 0 0 0.7596 0.0695 0.0002 0 0.1493 0.4420 0.1398 0 0.0031 0.1262 0.3370 ] ;
m ( 1 ) = [ 0.9398 0.3414 0.0167 0.3413 0.9349 0.0972 0.0176 0.0971 0.9951 ] [ 0.7964 0 0 0 0.4307 0 0 0 0.3589 ] [ 0.9602 0.2788 0.0138 0.2742 0.9329 0.2333 0.0522 0.2278 0.9723 ] T ,
M R 1 ( 1 ) = [ 1 0 0 0 0 0.9602 0.2788 0.0138 0 0.2742 0.9329 0.2333 0 0.0522 0.2278 0.9723 ] ,
M R 2 ( 1 ) = [ 1 0 0 0 0 0.9398 0.3414 0.0167 0 0.3413 0.9349 0.0972 0 0.0176 0.0971 0.9951 ] ,
M Δ d ( 1 ) = diag ( 0.9989 , 0.7964 , 0.4307 , 0.3589 ) = 0.9989 diag ( 1 , 0.7973 , 0.4311 , 0.3593 ) ,
M D 1 ( 2 ) = [ 1 0.0125 0.0294 0.0889 0.0125 0.9956 0.0002 0.0006 0.0294 0.0002 0.9960 0.0013 0.0889 0.0006 0.0013 0.9995 ] ,
M D 2 ( 2 ) = [ 1 0.0001 0.0288 0.0900 0.0001 0.9955 0.0000 0.0000 0.0288 0.0000 0.9959 0.0013 0.0900 0.0000 0.0013 0.9996 ] ,
M R 1 ( 2 ) = [ 1 0 0 0 0 0.9577 0.2835 0.0495 0 0.2832 0.9590 0.0133 0 0.0513 0.0013 0.9987 ] ,
M R 2 ( 2 ) = [ 1 0 0 0 0 0.9047 0.4257 0.0170 0 0.4260 0.9035 0.0459 0 0.0042 0.0488 0.9988 ]
M Δ d ( 2 ) = diag ( 1.0046 , 0.2644 , 0.2380 , 0.5480 ) = 1.0046 diag ( 1 , 0.2632 , 0.2369 , 0.5455 ) .
M ( 3 ) = [ 1.0000 0.0045 0.0172 0.0085 0.0075 0.1146 0.0018 0.0035 0.0011 0.0031 0.1079 0.0036 0.0037 0.0008 0.0069 0.0309 ]
M R 1 ( 3 ) = [ 1 0 0 0 0 0.9943 0.1004 0.0358 0 0.0984 0.9936 0.0547 0 0.0411 0.0509 0.9979 ] ,
M R 2 ( 3 ) = [ 1 0 0 0 0 0.9924 0.1223 0.0144 0 0.1208 0.9894 0.0800 0 0.0241 0.0777 0.9967 ] ,
M Δ d ( 3 ) = diag ( 1.0000 , 0.1148 , 0.1083 , 0.0305 ) .
M R 2 ( 3 ) = [ 1 0 0 0 0 0.9924 0.1223 0.0144 0 0.1208 0.9894 0.0800 0 0.0241 0.0777 0.9967 ] ,
M Δ d ( 3 ) = diag ( 1.0000 , 0.1148 , 0.1083 , 0.0305 )
M ( 4 ) = [ 1.0000 0.0077 0.0247 0.0108 0.0006 1.0023 0.0207 0.0196 0.0259 0.0259 1.0014 0.0151 0.0115 0.0229 0.0159 0.9857 ] .
M f ( 4 ) = [ 1.0053 0.0052 0.0255 0.0109 0.0030 0.9972 0.0207 0.0204 0.0251 0.0256 0.9968 0.0153 0.0112 0.0221 0.0157 0.9902 ]
M f D 1 ( 4 ) = [ 1 0.2565 0.0646 0.0052 0.2565 0.9979 0.0084 0.0007 0.0646 0.0084 0.9665 0.0002 0.0052 0.007 0.0002 0.9644 ] ,
M f D 2 ( 4 ) = [ 1 0.2499 0.0954 0.0229 0.2499 0.9951 0.0121 0.0029 0.0954 0.0121 0.9679 0.0011 0.0229 0.0029 0.0011 0.9636 ] ,
M f R 1 ( 4 ) = [ 1 0 0 0 0 0.7884 0.6103 0.0765 0 0.6120 0.7908 0.0014 0 0.0613 0.0458 0.9971 ] ,
M f R 2 ( 4 ) = [ 1 0 0 0 0 0.7701 0.6301 0.0990 0 0.6316 0.7750 0.0195 0 0.0890 0.0475 0.9949 ] ,
M f Δ d ( 4 ) = diag ( 1.0813 , 1.0768 , 1.0707 , 1.0661 ) = 1.0813 diag ( 1 , 0.9958 , 0.9902 , 0.9859 ) .
M n d ( 4 ) = [ 1.0049 0.0037 0.0255 0.0110 0.0046 1.0040 0.0236 0.0213 0.0252 0.0231 1.0045 0.0158 0.0113 0.0216 0.0155 1.0042 ] .
M ( 5 ) = [ 1.2569 0.1756 0.2936 0.7239 0.1354 0.4770 0.3446 0.0246 0.6887 0.3827 0.4421 0.2252 0.7651 0.0792 0.1790 0.8953 ]

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