Abstract

The passivity of the linear components in the main approaches for serial decompositions of depolarizing Mueller matrices [J. Opt. Soc. Am. A 13, 1106 (1996); J. Opt. Soc. Am. A 26, 1109 (2009)] is dealt with, and it is found that it is not always possible to perform such decompositions in terms of passive components. A compact form of Mueller matrix (“arrow matrix”) associated with any given Mueller matrix, which retains, in a condensed manner, the physical properties relative to transmittance, diattenuation, polarizance, and depolarization, is presented.

© 2013 Optical Society of America

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  1. R. C. Jones, “A new calculus for the treatment of optical systems. IV,” J. Opt. Soc Am. 32, 486–493 (1942).
    [CrossRef]
  2. R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–323 (1963).
    [CrossRef]
  3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  4. R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
    [CrossRef]
  5. C. Brosseau and R. Barakat, “Jones and Mueller polarization matrices for random media,” Opt. Commun. 84, 127–132 (1991).
    [CrossRef]
  6. A. B. Kostinski and R. C. Givens, “On the gain of a passive linear depolarizing system,” J. Mod. Opt. 39, 1947–1952 (1992).
    [CrossRef]
  7. J. J. Gil, “Characteristic properties of Mueller matrices,” J. Opt. Soc. Am. A 17, 328–334 (2000).
    [CrossRef]
  8. V. Devlaminck and P. Terrier, “Non-singular Mueller matrices characterizing passive systems,” Optik 121, 1994–1997 (2010).
    [CrossRef]
  9. Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod Opt. 39, 461–484 (1992).
    [CrossRef]
  10. 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]
  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. J. J. Gil and E. Bernabéu, “Depolarization and polarization indices of an optical system,” Optica Acta 33, 185–189 (1986).
    [CrossRef]
  13. J. J. Gil, “Components of purity of a Mueller matrix,” J. Opt. Soc. Am. A 28, 1578–1585 (2011).
    [CrossRef]
  14. J. J. Gil, “Determination of polarization parameters in matricial representation. Theoretical contribution and development of an automatic measurement device,” Ph.D. thesis (University of Zaragoza, 1983), available from http://www.pepegil.es/PhD-Thesis-JJ-Gil-English.pdf .
  15. E. Compain, S. Poirier, and B. Drévillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999).
    [CrossRef]
  16. A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004).
    [CrossRef]
  17. S. R. Cloude, “Group theory and polarisation algebra,” Optik 75, 26–36 (1986).
  18. J. J. Gil, “Procedimiento dinamico de medida de matrices de Mueller,” ES patent 8,800,025 (16July1989).
  19. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
    [CrossRef]
  20. D. H. Goldstein, Polarized Light, 3rd ed. (CRC, 2011).
  21. K. Dev and A. Asundi, “Mueller–Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
    [CrossRef]
  22. D. A. Ramsey and K. C. Ludema, “The influences of roughness on film thickness measurements by Mueller matrix ellipsometry,” Rev. Sci. Instrum. 65, 2874–2881 (1994).
    [CrossRef]
  23. B. J. Howell, “Measurement of the polarization effects of an instrument using partially polarized light,” Appl. Opt. 18, 809–812 (1979).
    [CrossRef]
  24. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
    [CrossRef]
  25. J. M. Correas, P. A. Melero, and J. J. Gil, “Decomposition of Mueller matrices into pure optical media,” Monografías del Seminario Matemático García de Galdeano 27, 233–240 (2003). Available from http://www.unizar.es/galdeano/actas_pau/PDF/233.pdf .
  26. J. J. Gil, “Parallel decompositions of Mueller matrices and polarimetric subtraction,” EPJ Web Conf. 5, 04002 (2010).
    [CrossRef]
  27. 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]
  28. 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]
  29. S.-Y. Lu and R. A. Chipman, “Homogeneous and inhomogeneous Jones matrices,” J. Opt. Soc. Am. A 11, 766–773 (1994).
    [CrossRef]
  30. 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]
  31. R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007).
    [CrossRef]
  32. M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” JEOS RP 2, 07018 (2007).
    [CrossRef]
  33. 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]
  34. R. A. Chipman, “Mueller matrices,” in The Handbook of Optics (McGraw-Hill, 2010), Chap. 14.
  35. S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–185 (1989).
    [CrossRef]
  36. R. Ossikovski, “Analysis of depolarizing Mueller matrices through a symmetric decomposition,” J. Opt. Soc. Am. A 26, 1109–1118 (2009).
    [CrossRef]
  37. R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod Opt. 41, 1903–1915 (1994).
    [CrossRef]
  38. C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5088 (1993).
    [CrossRef]
  39. 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]
  40. 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).
  41. R. Ossikovski, “Canonical forms of depolarizing Mueller matrices,” J. Opt. Soc. Am. A 27, 123–130 (2010).
    [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, “Mueller matrices,” in Light Scattering from Microstructures (Springer, 2000).
  44. R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990).
    [CrossRef]
  45. R. Ossikovski, “Alternative depolarization criteria for Mueller matrices,” J. Opt. Soc. Am. A 27, 808–814 (2010).
    [CrossRef]
  46. J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Seminario Matemático García de Galdeano 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .
  47. 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]

2013

2012

K. Dev and A. Asundi, “Mueller–Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

2011

J. J. Gil, “Components of purity of a Mueller matrix,” J. Opt. Soc. Am. A 28, 1578–1585 (2011).
[CrossRef]

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]

2010

R. Ossikovski, “Canonical forms of depolarizing Mueller matrices,” J. Opt. Soc. Am. A 27, 123–130 (2010).
[CrossRef]

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

V. Devlaminck and P. Terrier, “Non-singular Mueller matrices characterizing passive systems,” Optik 121, 1994–1997 (2010).
[CrossRef]

J. J. Gil, “Parallel decompositions of Mueller matrices and polarimetric subtraction,” EPJ Web Conf. 5, 04002 (2010).
[CrossRef]

2009

2007

R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007).
[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,” JEOS RP 2, 07018 (2007).
[CrossRef]

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
[CrossRef]

2004

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]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004).
[CrossRef]

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Seminario Matemático García de Galdeano 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .

2003

J. M. Correas, P. A. Melero, and J. J. Gil, “Decomposition of Mueller matrices into pure optical media,” Monografías del Seminario Matemático García de Galdeano 27, 233–240 (2003). Available from http://www.unizar.es/galdeano/actas_pau/PDF/233.pdf .

2000

1999

1998

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).

1996

1994

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

D. A. Ramsey and K. C. Ludema, “The influences of roughness on film thickness measurements by Mueller matrix ellipsometry,” Rev. Sci. Instrum. 65, 2874–2881 (1994).
[CrossRef]

S.-Y. Lu and R. A. Chipman, “Homogeneous and inhomogeneous Jones matrices,” J. Opt. Soc. Am. A 11, 766–773 (1994).
[CrossRef]

1993

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

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]

1992

D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
[CrossRef]

A. B. Kostinski and R. C. Givens, “On the gain of a passive linear depolarizing system,” J. Mod. Opt. 39, 1947–1952 (1992).
[CrossRef]

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

1991

C. Brosseau and R. Barakat, “Jones and Mueller polarization matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

1990

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990).
[CrossRef]

1989

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

1987

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

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).

1986

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

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

1979

1963

1942

R. C. Jones, “A new calculus for the treatment of optical systems. IV,” J. Opt. Soc Am. 32, 486–493 (1942).
[CrossRef]

Anastasiadou, M.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” JEOS RP 2, 07018 (2007).
[CrossRef]

Asundi, A.

K. Dev and A. Asundi, “Mueller–Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

Azzam, R. M. A.

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

Barakat, R.

C. Brosseau and R. Barakat, “Jones and Mueller polarization matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–323 (1963).
[CrossRef]

Bashara, N. M.

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

Ben Hatit, S.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” JEOS RP 2, 07018 (2007).
[CrossRef]

Bernabéu, E.

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).

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

Brosseau, C.

C. Brosseau and R. Barakat, “Jones and Mueller polarization matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

Chipman, R. A.

Cloude, S. R.

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

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

Compain, E.

Correas, J. M.

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Seminario Matemático García de Galdeano 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .

J. M. Correas, P. A. Melero, and J. J. Gil, “Decomposition of Mueller matrices into pure optical media,” Monografías del Seminario Matemático García de Galdeano 27, 233–240 (2003). Available from http://www.unizar.es/galdeano/actas_pau/PDF/233.pdf .

De Martino, A.

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]

R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32, 689–691 (2007).
[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,” JEOS RP 2, 07018 (2007).
[CrossRef]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004).
[CrossRef]

Dev, K.

K. Dev and A. Asundi, “Mueller–Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator,” Opt. Lasers Eng. 50, 599–607 (2012).
[CrossRef]

Devlaminck, V.

V. Devlaminck and P. Terrier, “Non-singular Mueller matrices characterizing passive systems,” Optik 121, 1994–1997 (2010).
[CrossRef]

Drévillon, B.

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004).
[CrossRef]

E. Compain, S. Poirier, and B. Drévillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999).
[CrossRef]

Ferreira, C.

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Seminario Matemático García de Galdeano 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .

Foldyna, M.

Garcia-Caurel, E.

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]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004).
[CrossRef]

Gil, J. J.

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]

J. J. Gil, “Components of purity of a Mueller matrix,” J. Opt. Soc. Am. A 28, 1578–1585 (2011).
[CrossRef]

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]

J. J. Gil, “Parallel decompositions of Mueller matrices and polarimetric subtraction,” EPJ Web Conf. 5, 04002 (2010).
[CrossRef]

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]

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
[CrossRef]

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Seminario Matemático García de Galdeano 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .

J. M. Correas, P. A. Melero, and J. J. Gil, “Decomposition of Mueller matrices into pure optical media,” Monografías del Seminario Matemático García de Galdeano 27, 233–240 (2003). Available from http://www.unizar.es/galdeano/actas_pau/PDF/233.pdf .

J. J. Gil, “Characteristic properties of Mueller matrices,” J. Opt. Soc. Am. A 17, 328–334 (2000).
[CrossRef]

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).

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

J. J. Gil, “Determination of polarization parameters in matricial representation. Theoretical contribution and development of an automatic measurement device,” Ph.D. thesis (University of Zaragoza, 1983), available from http://www.pepegil.es/PhD-Thesis-JJ-Gil-English.pdf .

J. J. Gil, “Procedimiento dinamico de medida de matrices de Mueller,” ES patent 8,800,025 (16July1989).

J. J. Gil, “Mueller matrices,” in Light Scattering from Microstructures (Springer, 2000).

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]

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]

Givens, R. C.

A. B. Kostinski and R. C. Givens, “On the gain of a passive linear depolarizing system,” J. Mod. Opt. 39, 1947–1952 (1992).
[CrossRef]

Goldstein, D. H.

Gopala Rao, A. V.

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).

Goudail, F.

Guyot, S.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” JEOS RP 2, 07018 (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]

Howell, B. J.

Jones, R. C.

R. C. Jones, “A new calculus for the treatment of optical systems. IV,” J. Opt. Soc Am. 32, 486–493 (1942).
[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]

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]

A. B. Kostinski and R. C. Givens, “On the gain of a passive linear depolarizing system,” J. Mod. Opt. 39, 1947–1952 (1992).
[CrossRef]

Laude, B.

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004).
[CrossRef]

Lu, S.-Y.

Ludema, K. C.

D. A. Ramsey and K. C. Ludema, “The influences of roughness on film thickness measurements by Mueller matrix ellipsometry,” Rev. Sci. Instrum. 65, 2874–2881 (1994).
[CrossRef]

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).

Melero, P. A.

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Generalized polarization algebra,” Monografías del Seminario Matemático García de Galdeano 31, 161–167 (2004). Available from http://www.unizar.es/galdeano/actas_pau/PDFVIII/pp161-167.pdf .

J. M. Correas, P. A. Melero, and J. J. Gil, “Decomposition of Mueller matrices into pure optical media,” Monografías del Seminario Matemático García de Galdeano 27, 233–240 (2003). Available from http://www.unizar.es/galdeano/actas_pau/PDF/233.pdf .

Morio, J.

Ossikovski, R.

Poirier, S.

Ramsey, D. A.

D. A. Ramsey and K. C. Ludema, “The influences of roughness on film thickness measurements by Mueller matrix ellipsometry,” Rev. Sci. Instrum. 65, 2874–2881 (1994).
[CrossRef]

San Jose, I.

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]

San José, I.

Simon, R.

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

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990).
[CrossRef]

Sridhar, R.

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

Sudha,

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[CrossRef]

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[CrossRef]

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[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).

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[CrossRef]

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Equations (39)

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M=m00(1DTPm);D1m00(m01,m02,m03,)T,P1m00(m10,m20,m30,)T,m1m00(m11m12m13m21m22m23m31m32m33).
PΔ=(D2+P2+m22)/3,
12{tr(TT)+[(tr(TT))24det(TT)]1/2}1,
m00(1+D)1,(P=D).
m00(1+D)1,m00(1+P)1.
Mm00(1DTPm)=m00M^ΔPMRM^D;M^ΔP(10TPΔPmΔP),MR(10T0mR),M^D(1DTDmD),
M^D=[1DTDmD],mD(1D2)1/2I+1D2[1(1D2)1/2]DDT,
MD=k(1+D)M^D,0<k1.
PΔP=(PmD)/(1D2).
(1+D)(1+PΔP)m001,
|PmD|(1D)[1/m00(1+D)].
MDPm00(1DTPPDT),0<D1,0<P1,PD<1,
MDP=m00M^ΔPM^D;M^ΔP=(10TPdiag(0,0,0)),M^D=(1DTDmD),
(1+D)(1+P)m001,
MI12[11001/21/20000000000]=12M^ΔPM^D;M^ΔP=[10001/200000000000],M^D=[1100110000(1D2)1/20000(1D2)1/2],
MI=34{12(1100110000000000)}+14{12(1100110000000000)},
M=MJOMΔMJI,
MΔd=diag(d0,d1,d2,εd3),di0,ε(detM)/|detM|,
MΔnd=2a0[1DΔndTDΔndmΔnd];DΔndT(1/2,0,0),mΔnddiag(0,a2,a2),0a2a0.
MJi=MDiMRi=MRiMDi(MDi=MRiTMDiMRi),i=I,O.
m001(1+DO)d01(1+DI),
MDP1(1+Dm)(1DTPPDT);Dmmax(D,P),0<D1,0<P1,PD<1,
MDP=m00MDOMΔMDI;m00=1(1+Dm),MDO=(1PTPmP),MΔ=(10T0diag(0,0,0)),MDI=(1DTDmD),
m001(1+D)(1+P);P0,D0,
MII=815(11/8007/82/80000000000),
MII=916{815(1100110000000000)}+616{815(1100110000000000)}+116{815(1100110000000000)},
MII=m00M^DM^ΔndM^D;m00=815,M^D=(11/2001/2100003/200003/2),M^Δnd=12(2100100000000000)
MS(M)MROTMMRIT=MDOMΔMDI.
M=QOΣQI,
G1(φ1)=[cosφ100sinφ101000010sinφ100cosφ1],G2(φ2)=[cosφ20sinφ200100sinφ20cosφ200001],G3(φ3)=[cosφ3sinφ300sinφ3cosφ30000100001]MG1(α1)=[1000010000cosα1sinα100sinα1cosα1],MG2(α2)=[10000cosα20sinα200100sinα20cosα2],MG3(α3)=[10000cosα3sinα300sinα3cosα300001].
QI=GIMGIQO=MGOGO,
MGIMG3T(α4)MG2T(α5)MG1T(α6);GIG3T(φ6)G2T(φ5)G1T(φ4)MGOMG1(α1)MG2(α2)MG3(α3);GOG1(φ1)G2(φ2)G3(φ3),
M=MGOMKMGI;MK[GOΣGI]=MGOTMMGIT.
m=mROmlmRI;mRi1=mRiT(i=I,O),mldiag(l1,l2,l3).
MRi=(10T0mRi),(i=I,O)
MA(M)MROTMMRIT=m00(1DATPAdiag(l1,l2,l3));DA=mRID,PA=mROTP.
PSm2/3,0PS1,
PΔ2=13P2+13D2+PS2.
PΔ2(M)=PΔ2(MA)=13(P2+D2+L2).

Metrics