Abstract

Singular values of the arbitrary Mueller matrix are determined to be indicators of some polarization properties of the medium such as depolarization and diattenuation. Whereas eigenvalue analysis of the coherency matrix may wrongly characterize media with simultaneous strong depolarization and diattenuation effects. The comparison between the patterns of changes in singular-value and eigenvalue trends of the coherency matrix in experimental Mueller matrices, shows that singular values of the Mueller matrix are more capable of discriminating media with close degrees of depolarization.

© 2013 Optical Society of America

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  3. F. Fanjul Velez, N. Ortega Quijano, and J. L. Arce Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix,” Opt. Commun. 283, 4525–4530 (2010).
    [CrossRef]
  4. M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
    [CrossRef]
  5. S. Firdous, M. Atif, and M. Nawaz, “Study of blood malignancy in vitro for the diagnosis and treatment of blood diseases using polarimetery and microscopy,” Lasers Eng. 19, 291–305 (2010).
  6. N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
    [CrossRef]
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    [CrossRef]
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  13. A. Zakeri, M. H. Miran Baygi, and K. Madanipour, “Polarization characterization of biological tissues using Stokes vector decomposition,” J. Mod. Opt. 60, 987–992 (2013).
    [CrossRef]
  14. N. Ortega Quijano and J. L. Arce Diego, “Mueller matrix differential decomposition,” Opt. Lett. 36, 1942–1944 (2011).
    [CrossRef]
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    [CrossRef]
  23. C. Brosseau, “Polarization transfer and entropy transformation,” Optik 88, 109–117 (1991).
  24. F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular value decomposition and its applications to pure states of three qubits,” Phys. Rev. A 65, 032308 (2002).
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    [CrossRef]
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  32. N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13, 044036 (2008).
    [CrossRef]
  33. N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105, 102023 (2009).
    [CrossRef]
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2013

A. Zakeri, M. H. Miran Baygi, and K. Madanipour, “Polarization characterization of biological tissues using Stokes vector decomposition,” J. Mod. Opt. 60, 987–992 (2013).
[CrossRef]

J. J. Gil, I. S. Jose, and R. Ossikovski, “Serial–parallel decompositions of Mueller matrices,” J. Opt. Soc. Am. A 30, 32–50 (2013).
[CrossRef]

2012

2011

2010

F. Fanjul Velez, N. Ortega Quijano, and J. L. Arce Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix,” Opt. Commun. 283, 4525–4530 (2010).
[CrossRef]

S. Firdous, M. Atif, and M. Nawaz, “Study of blood malignancy in vitro for the diagnosis and treatment of blood diseases using polarimetery and microscopy,” Lasers Eng. 19, 291–305 (2010).

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

R. Ossikovski, “Alternative depolarization criteria for Mueller matrices,” J. Opt. Soc. Am. A 27, 808–814 (2010).
[CrossRef]

2009

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105, 102023 (2009).
[CrossRef]

R. Ossikovski, “Analysis of depolarizing Mueller matrices through a symmetric decomposition,” J. Opt. Soc. Am. A 26, 1109–1118 (2009).
[CrossRef]

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

2008

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13, 044036 (2008).
[CrossRef]

2007

2006

2002

F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular value decomposition and its applications to pure states of three qubits,” Phys. Rev. A 65, 032308 (2002).
[CrossRef]

2000

1996

1995

S. R. Cloude and E. Pottier, “Concept of polarization entropy in optical scattering,” Opt. Eng. 34, 1599–1610 (1995).
[CrossRef]

1994

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

1992

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

1991

C. Brosseau, “Polarization transfer and entropy transformation,” Optik 88, 109–117 (1991).

1989

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

1988

C. Brosseau, “Entropy and polarization optics: degree of polarization of a mixture of partially polarized plane waves,” Optik 79, 117–122 (1988).

1986

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

1978

Arce Diego, J. L.

N. Ortega Quijano and J. L. Arce Diego, “Depolarizing differential Mueller matrices,” Opt. Lett. 36, 2429–2431 (2011).
[CrossRef]

N. Ortega Quijano and J. L. Arce Diego, “Mueller matrix differential decomposition,” Opt. Lett. 36, 1942–1944 (2011).
[CrossRef]

F. Fanjul Velez, N. Ortega Quijano, and J. L. Arce Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix,” Opt. Commun. 283, 4525–4530 (2010).
[CrossRef]

Atif, M.

S. Firdous, M. Atif, and M. Nawaz, “Study of blood malignancy in vitro for the diagnosis and treatment of blood diseases using polarimetery and microscopy,” Lasers Eng. 19, 291–305 (2010).

Azzam, R. M. A.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Boulvert, F.

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

Brosseau, C.

C. Brosseau, “Polarization transfer and entropy transformation,” Optik 88, 109–117 (1991).

C. Brosseau, “Entropy and polarization optics: degree of polarization of a mixture of partially polarized plane waves,” Optik 79, 117–122 (1988).

Buddhiwant, P.

Cariou, J.

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

Chipman, R. A.

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]

R. A. Chipman, “Polarimetry,” in Handbook of Optics Vol II, Devices, Measurements, and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Part 3, Chap. 15, pp. 22.1–22.37.

Cloude, S. R.

S. R. Cloude and E. Pottier, “Concept of polarization entropy in optical scattering,” Opt. Eng. 34, 1599–1610 (1995).
[CrossRef]

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

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

De Martino, A.

De Moor, B.

F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular value decomposition and its applications to pure states of three qubits,” Phys. Rev. A 65, 032308 (2002).
[CrossRef]

Dehaene, J.

F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular value decomposition and its applications to pure states of three qubits,” Phys. Rev. A 65, 032308 (2002).
[CrossRef]

Fanjul Velez, F.

F. Fanjul Velez, N. Ortega Quijano, and J. L. Arce Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix,” Opt. Commun. 283, 4525–4530 (2010).
[CrossRef]

Firdous, S.

S. Firdous, M. Atif, and M. Nawaz, “Study of blood malignancy in vitro for the diagnosis and treatment of blood diseases using polarimetery and microscopy,” Lasers Eng. 19, 291–305 (2010).

Germer, T. A.

Ghosh, N.

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105, 102023 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13, 044036 (2008).
[CrossRef]

S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, 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]

Gil, J. J.

Gupta, P. K.

Guyot, S.

Jeune, B. L.

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

Jose, I. S.

Lancaster, P.

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

Le Brun, G.

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

Leon, S. J.

S. J. Leon, Linear Algebra with Applications (Macmillan, 1996).

Li, R.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

Li, S.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

Lu, S. Y.

Madanipour, K.

A. Zakeri, M. H. Miran Baygi, and K. Madanipour, “Polarization characterization of biological tissues using Stokes vector decomposition,” J. Mod. Opt. 60, 987–992 (2013).
[CrossRef]

Manhas, S.

Martin, L.

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

Miran Baygi, M. H.

A. Zakeri, M. H. Miran Baygi, and K. Madanipour, “Polarization characterization of biological tissues using Stokes vector decomposition,” J. Mod. Opt. 60, 987–992 (2013).
[CrossRef]

Moriyama, E. H.

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

Nawaz, M.

S. Firdous, M. Atif, and M. Nawaz, “Study of blood malignancy in vitro for the diagnosis and treatment of blood diseases using polarimetery and microscopy,” Lasers Eng. 19, 291–305 (2010).

Ortega Quijano, N.

N. Ortega Quijano and J. L. Arce Diego, “Depolarizing differential Mueller matrices,” Opt. Lett. 36, 2429–2431 (2011).
[CrossRef]

N. Ortega Quijano and J. L. Arce Diego, “Mueller matrix differential decomposition,” Opt. Lett. 36, 1942–1944 (2011).
[CrossRef]

F. Fanjul Velez, N. Ortega Quijano, and J. L. Arce Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix,” Opt. Commun. 283, 4525–4530 (2010).
[CrossRef]

Ossikovski, R.

Pottier, E.

S. R. Cloude and E. Pottier, “Concept of polarization entropy in optical scattering,” Opt. Eng. 34, 1599–1610 (1995).
[CrossRef]

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]

Swami, M. K.

Tismenetsky, M.

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

Verstraete, F.

F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular value decomposition and its applications to pure states of three qubits,” Phys. Rev. A 65, 032308 (2002).
[CrossRef]

Vitkin, I. A.

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105, 102023 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13, 044036 (2008).
[CrossRef]

Weisel, R. D.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

Wilson, B. C.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105, 102023 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13, 044036 (2008).
[CrossRef]

Xing, Z. F.

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

Zakeri, A.

A. Zakeri, M. H. Miran Baygi, and K. Madanipour, “Polarization characterization of biological tissues using Stokes vector decomposition,” J. Mod. Opt. 60, 987–992 (2013).
[CrossRef]

EPJ Appl. Phys.

J. J. Gil, “Polarimetric characterization of light and media,” EPJ Appl. Phys. 40, 1–47 (2007).

J. Appl. Phys.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105, 102023 (2009).
[CrossRef]

J. Biomed. Opt.

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14, 014029 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13, 044036 (2008).
[CrossRef]

J. Biophoton.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton. 2, 145–156 (2009).

J. Mod. Opt.

A. Zakeri, M. H. Miran Baygi, and K. Madanipour, “Polarization characterization of biological tissues using Stokes vector decomposition,” J. Mod. Opt. 60, 987–992 (2013).
[CrossRef]

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

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Lasers Eng.

S. Firdous, M. Atif, and M. Nawaz, “Study of blood malignancy in vitro for the diagnosis and treatment of blood diseases using polarimetery and microscopy,” Lasers Eng. 19, 291–305 (2010).

Opt. Commun.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

F. Fanjul Velez, N. Ortega Quijano, and J. L. Arce Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix,” Opt. Commun. 283, 4525–4530 (2010).
[CrossRef]

F. Boulvert, G. Le Brun, B. L. Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692–704 (2009).
[CrossRef]

Opt. Eng.

S. R. Cloude and E. Pottier, “Concept of polarization entropy in optical scattering,” Opt. Eng. 34, 1599–1610 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

C. Brosseau, “Polarization transfer and entropy transformation,” Optik 88, 109–117 (1991).

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

C. Brosseau, “Entropy and polarization optics: degree of polarization of a mixture of partially polarized plane waves,” Optik 79, 117–122 (1988).

Phys. Rev. A

F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular value decomposition and its applications to pure states of three qubits,” Phys. Rev. A 65, 032308 (2002).
[CrossRef]

Proc. SPIE

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

Other

S. J. Leon, Linear Algebra with Applications (Macmillan, 1996).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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

R. A. Chipman, “Polarimetry,” in Handbook of Optics Vol II, Devices, Measurements, and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Part 3, Chap. 15, pp. 22.1–22.37.

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Figures (8)

Fig. 1.
Fig. 1.

Singular values of the diagonal depolarizers with the variable depolarization index of 0.23Δ0.77. X axis, n, denotes the number of the singular values.

Fig. 2.
Fig. 2.

Singular values of the pure horizontal diattenuators with the variable diattenuation coefficients of 0d0.9 and zero depolarization effect. X axis, n, denotes the number of the singular values.

Fig. 3.
Fig. 3.

Singular values of the Mueller matrices in Table 1 with the depolarization index of Δ<0.05. Presented d=0.06 is determined by the polar decomposition method. X axis, n, denotes the number of the singular values.

Fig. 4.
Fig. 4.

Eigenvalues of the coherency matrix of samples in Table 1 with the depolarization index of Δ<0.05. X axis, n, denotes the number of the eigenvalues.

Fig. 5.
Fig. 5.

Singular values of the Mueller matrices in Table 1 with the depolarization index of 0.15Δ0.47. Presented d=0.13 is determined by the polar decomposition method. X axis, n, denotes the number of the singular values.

Fig. 6.
Fig. 6.

Eigenvalues of the coherency matrix of samples in Table 1 with the depolarization index of 0.15Δ0.47. X axis, n, denotes the number of the eigenvalues.

Fig. 7.
Fig. 7.

Singular values of the Mueller matrices in Table 1 with the depolarization index of 0.58Δ0.79. X axis, n, denotes the number of the singular values.

Fig. 8.
Fig. 8.

Eigenvalues of the coherency matrix of samples in Table 1 with the depolarization index of 0.58Δ0.79. X axis, n, denotes the number of the eigenvalues.

Tables (1)

Tables Icon

Table 1. Characteristics of the Analyzed Samples

Equations (21)

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H=i=14xilog4(xi),
M=M2MΔdM1T,
MΔd=diag(d1,d2,d3,d4),
M=MD2MR2MΔdMR1TMD1.
L1=[tr(N)ρmax(N)3ρmax(N)]1/2
L2=[4i=14ρi2(i=14ρi)23(i=14ρi)2]1/2=[4tr(N2)tr2(N)3tr2(N)]1/2,
PΔ=[4i=14λi2(i=14λi)23(i=14λi)2]1/2.
ΔL=1ρ2+ρ3+ρ43ρ1=1d2+d3+d43d1.
M=USVT,
MΔd=diag(a0,a1,a2,a3)ai>0,
MΔd=diag(1,0.5,a,a),
Δ=1tr(MΔ)13,
DP=1(σ1+σ2+σ3+σ41)3=1tr(S)13,
MLR=[10000cos22θ+sin22θcosδsin2θcos2θ(1cosδ)sin2θsinδ0sin2θcos2θ(1cosδ)sin22θ+cos22θcosδcos2θsinδ0sin2θsinδcos2θsinδcosδ],
MCR=[10000cosδsinδ00sinδcosδ00001].
MR.Δ=MRMΔ=[10000100000.50.87000.870.5][10000100000.100000.1],
MD=[1d00d10000(1d2)1/20000(1d2)1/2],
MR.Δ.D=MR.ΔMD,
dσ11.
MR.D.Δ=MRMDMΔ,
M1=[1.00000.38380.17970.88430.39250.19320.10200.31930.18550.09560.00490.17070.87410.30820.14620.8007].

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