Abstract

Mueller matrix differential decomposition is a novel method for retrieving the polarimetric properties of general depolarizing anisotropic media [N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011), R. Ossikovski, Opt. Lett. 36, 2330 (2011)]. The method has been verified for Mueller matrices available in the literature. We experimentally validate the decomposition for five different experimental setups with different commutation properties and controlled optical parameters, comparing the differential decomposition with the forward and reverse polar decompositions. The results enable to verify the method and to highlight its advantages for certain experimental applications of high interest.

© 2012 OSA

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References

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  1. D. Goldstein, Polarized Light (Marcel Dekker, 2003).
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    [CrossRef]
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  4. S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–185 (1989).
  5. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13(5), 1106–1113 (1996).
    [CrossRef]
  6. 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 (Stuttg.) 76, 67–71 (1987).
  7. J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. 29(19), 2234–2236 (2004).
    [CrossRef] [PubMed]
  8. R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32(6), 689–691 (2007).
    [CrossRef] [PubMed]
  9. 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, 070181–070187 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, “Comparative study of optical activity in chiral biological media by polar decomposition and differential Mueller matrices analysis,” Proc. SPIE 7906, 790612 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef] [PubMed]
  24. S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express 14(1), 190–202 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  28. 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(6), 1200–1208 (2010).
    [CrossRef]

2011

2010

C. Fallet, A. Pierangelo, R. Ossikovski, and A. De Martino, “Experimental validation of the symmetric decomposition of Mueller matrices,” Opt. Express 18(2), 831–842 (2010).
[CrossRef] [PubMed]

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(6), 1200–1208 (2010).
[CrossRef]

2009

2008

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(4), 720–727 (2008).
[CrossRef]

2007

R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32(6), 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, 070181–070187 (2007).

2006

2004

2000

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

1999

1997

1996

1995

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

1994

1989

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

1987

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 (Stuttg.) 76, 67–71 (1987).

1986

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

1978

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(4), 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, 070181–070187 (2007).

Ansari, R. R.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[CrossRef] [PubMed]

Arce-Diego, J. L.

Azzam, R. M. A.

Bashkatov, A. N.

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

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(4), 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, 070181–070187 (2007).

Berger, M.

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 (Stuttg.) 76, 67–71 (1987).

Böcker, D.

Böckle, S.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[CrossRef] [PubMed]

Bruulsema, J. T.

Buddhiwant, P.

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).

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

Compain, E.

De Martino, A.

C. Fallet, A. Pierangelo, R. Ossikovski, and A. De Martino, “Experimental validation of the symmetric decomposition of Mueller matrices,” Opt. Express 18(2), 831–842 (2010).
[CrossRef] [PubMed]

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(4), 720–727 (2008).
[CrossRef]

R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32(6), 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, 070181–070187 (2007).

B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43(14), 2824–2832 (2004).
[CrossRef] [PubMed]

Drevillon, B.

Drévillon, B.

Essenpreis, M.

Fallet, C.

Fanjul-Vélez, F.

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, “Comparative study of optical activity in chiral biological media by polar decomposition and differential Mueller matrices analysis,” Proc. SPIE 7906, 790612 (2011).
[CrossRef]

Fantini, S.

Farrell, T. J.

Franceschini, M. A.

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(4), 720–727 (2008).
[CrossRef]

Genina, E. A.

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

Ghosh, N.

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(6), 1200–1208 (2010).
[CrossRef]

S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express 14(1), 190–202 (2006).
[CrossRef] [PubMed]

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 (Stuttg.) 76, 67–71 (1987).

Goudail, F.

Gratton, E.

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(6), 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, 070181–070187 (2007).

Hayward, J. E.

Heinemann, L.

Joblin, A. J.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

Kochubey, V. I.

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

Koschinsky, T.

Lakodina, N. A.

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

Laude-Boulesteix, B.

Lu, S. Y.

Maier, J. S.

Manhas, S.

Morio, J.

Niesler, H. E.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

Orskov, H.

Ortega-Quijano, N.

Ossikovski, R.

Patterson, M. S.

Pierangelo, A.

Poirier, S.

Rovati, L.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[CrossRef] [PubMed]

Salas-García, I.

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, “Comparative study of optical activity in chiral biological media by polar decomposition and differential Mueller matrices analysis,” Proc. SPIE 7906, 790612 (2011).
[CrossRef]

Sandahl-Christiansen, J.

Schmelzeisen-Redeker, G.

Schwartz, L.

Simon, R.

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41(10), 1903–1915 (1994).
[CrossRef]

Singh, J.

Sinichkin, Y. P.

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

Sridhar, R.

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41(10), 1903–1915 (1994).
[CrossRef]

Swami, M. K.

Tarte, B. J.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

Tuchin, V. V.

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

van Doorn, T.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

Vitkin, I. A.

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(6), 1200–1208 (2010).
[CrossRef]

Walker, S. A.

Waterworth, M. D.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

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(6), 1200–1208 (2010).
[CrossRef]

Appl. Opt.

Australas. Phys. Eng. Sci. Med.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, and H. E. Niesler, “Optical transmission properties of homogenised milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18(1), 39–44 (1995).
[PubMed]

J. Biomed. Opt.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9(1), 103–115 (2004).
[CrossRef] [PubMed]

J. Eur. Opt. Soc. Rapid Publ.

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, 070181–070187 (2007).

J. Mod. Opt.

R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41(10), 1903–1915 (1994).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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(6), 1200–1208 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Stuttg.)

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 (Stuttg.) 76, 67–71 (1987).

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

Phys. Status Solidi (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(4), 720–727 (2008).
[CrossRef]

Proc. SPIE

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

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, “Comparative study of optical activity in chiral biological media by polar decomposition and differential Mueller matrices analysis,” Proc. SPIE 7906, 790612 (2011).
[CrossRef]

A. N. Bashkatov, E. A. Genina, Y. P. Sinichkin, N. A. Lakodina, V. I. Kochubey, and V. V. Tuchin, “Estimation of glucose diffusion coefficient in scleral tissue,” Proc. SPIE 4001, 345–355 (2000).
[CrossRef]

Other

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

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Figures (9)

Fig. 1
Fig. 1

Optical scheme of the microscopic Mueller imaging polarimeter in transmission.

Fig. 2
Fig. 2

Experimental samples scheme corresponding to a cuvette filled with a) glucose and milk dilution in distilled water, and milk dilution in distilled water with b) a linear polarizer at the bottom, c) a linear polarizer at the top, d) a linear polarizer symmetrically fixed inside the container, and e) a linear polarizer asymmetrically fixed inside the container. Dimensions are given in the text. The small arrow on the left indicates the light propagation direction.

Fig. 3
Fig. 3

Optical rotation as a function of the scatterer concentration for a milk dilution in distilled water without glucose. The theoretical value (zero) is depicted as a reference. The inset at the bottom shows the Cloude entropy for each value of milk volume fraction. Error bars represent the standard deviation, which overlaps for the three decompositions.

Fig. 4
Fig. 4

Optical rotation as a function of the scatterer concentration for a milk dilution in distilled water with a glucose molar concentration of 1.15M. The theoretical value (zero) is depicted as a reference. The inset at the bottom shows the Cloude entropy for each value of milk volume fraction. Error bars represent the standard deviation, which overlaps for the three decompositions.

Fig. 5
Fig. 5

Variation of the Cloude entropy as a function of the glucose concentration for a milk volume fraction of 12%.

Fig. 6
Fig. 6

Diattenuation coefficient as a function of the milk volume fraction for the configuration diattenuator-depolarizer (Fig. 2b). The inset at the bottom shows the Cloude entropy for each value of milk volume fraction.

Fig. 7
Fig. 7

Diattenuation coefficient as a function of the milk volume fraction for the configuration depolarizer-diattenuator (Fig. 2c). The inset at the bottom shows the Cloude entropy for each value of milk volume fraction.

Fig. 8
Fig. 8

Diattenuation coefficient as a function of the milk volume fraction for the polarizer symmetrically placed inside the turbid medium (Fig. 2d).

Fig. 9
Fig. 9

Diattenuation coefficient as a function of the milk volume fraction for the polarizer asymmetrically placed inside the turbid medium (Fig. 2e).

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

M turbid =[ 1 0 0 0 0 d l 0 0 0 0 d l 0 0 0 0 d c ],
M oa M turbid = M turbid M oa =[ 1 0 0 0 0 d l cos2θ d l sin2θ 0 0 d l sin2θ d l cos2θ 0 0 0 0 d c ],
M d ( p )=[ 1 p 0 0 p 1 0 0 0 0 ( 1 p 2 ) 1/2 0 0 0 0 ( 1 p 2 ) 1/2 ],
M turbid M d ( p )=[ 1 p 0 0 d l p d l 0 0 0 0 d l ( 1 p 2 ) 1/2 0 0 0 0 d c ( 1 p 2 ) 1/2 ],
M d ( p ) M turbid =[ 1 d l p 0 0 p d l 0 0 0 0 d l ( 1 p 2 ) 1/2 0 0 0 0 d c ( 1 p 2 ) 1/2 ].
M turbid2 M d ( p ) M turbid1 =[ 1 d l1 p 0 0 d l2 p d l1 d l2 0 0 0 0 d l1 d l2 ( 1 p 2 ) 1/2 0 0 0 0 d c1 d c2 ( 1 p 2 ) 1/2 ].
C= i,j=1 4 M ij ( σ i σ j * ) ,
M= M Δ f M R f M D f ,
M= M R r M D r M Δ r .
m ¯ =logm(M),
Ψ lc = 1 2 atan[ M R ( 3,2 ) M R ( 2,3 ) M R ( 2,2 )+ M R ( 3,3 ) ],
Ψ dd = η ¯ v /2 ,
D lc = 1 M D ( 1,1 ) [ M D ( 1,2 ) 2 + M D ( 1,3 ) 2 + M D ( 1,4 ) 2 ] 1/2 .
D dd =tanh[ ( κ ¯ q 2 + κ ¯ u 2 + κ ¯ v 2 ) 1/2 ],
H= i=1 4 x i log 4 x i , x i = λ Ci / j=1 4 λ Ci .

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