Abstract

It is shown that the Mueller matrix logarithm and the Mueller matrix roots decompositions used for the extraction of the elementary polarization properties of a depolarizing medium, although being computationally different, are formally equivalent, being both based upon the differential representation of a continuously depolarizing medium. The common set of six elementary polarization properties provided by these two decompositions is generally different from that obtained from the various product decompositions summarized by the G-polar decomposition whereby the depolarization phenomenon is treated as being concentrated, and not uniformly distributed, within the medium. However, if the medium is weakly depolarizing, the two sets of elementary properties coincide to the first order in the depolarization and tend to the set of properties of the nondepolarizing estimate of the measured Mueller matrix obtained from its Cloude sum decomposition.

© 2012 Optical Society of America

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References

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  1. J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
    [CrossRef]
  2. R. M. A. Azzam, J. Opt. Soc. Am. 68, 1756 (1978).
    [CrossRef]
  3. R. Ossikovski, Opt. Lett. 36, 2330 (2011).
    [CrossRef]
  4. N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011).
    [CrossRef]
  5. R. A. Chipman, in Handbook of Optics, 3rd ed. (McGraw Hill, 2009), Vol. 1.
  6. H. D. Noble and R. A. Chipman, Opt. Express 20, 17 (2012).
    [CrossRef]
  7. S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
    [CrossRef]
  8. R. Ossikovski, J. Opt. Soc. Am. A 26, 1109 (2009).
    [CrossRef]
  9. R. Ossikovski, A. De Martino, and S. Guyot, Opt. Lett. 32, 689 (2007).
    [CrossRef]
  10. R. Ossikovski, J. Opt. Soc. Am. A 27, 123 (2010).
    [CrossRef]
  11. S. R. Cloude, Optik 75, 26 (1986).
  12. N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
    [CrossRef]
  13. O. Arteaga and A. Canillas, Opt. Lett. 35, 559 (2010).
    [CrossRef]

2012 (1)

2011 (2)

2010 (2)

2009 (2)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

R. Ossikovski, J. Opt. Soc. Am. A 26, 1109 (2009).
[CrossRef]

2007 (2)

1996 (1)

1986 (1)

S. R. Cloude, Optik 75, 26 (1986).

1978 (1)

Arce-Diego, J. L.

Arteaga, O.

Azzam, R. M. A.

Canillas, A.

Chipman, R. A.

Cloude, S. R.

S. R. Cloude, Optik 75, 26 (1986).

De Martino, A.

Ghosh, N.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Gil, J. J.

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

Guyot, S.

Li, R.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Li, S.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Lu, S.-Y.

Noble, H. D.

Ortega-Quijano, N.

Ossikovski, R.

Vitkin, I. A.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Weisel, R. D.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Wilson, B. C.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

J. Biophoton. (1)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Express (1)

Opt. Lett. (4)

Optik (1)

S. R. Cloude, Optik 75, 26 (1986).

Other (1)

R. A. Chipman, in Handbook of Optics, 3rd ed. (McGraw Hill, 2009), Vol. 1.

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Equations (19)

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dM/dz=mM,
L=lnM,
Lm=12(LGLTG)=[0p¯1p¯2p¯3p¯10p¯4p¯5p¯2p¯40p¯6p¯3p¯5p¯60],
Lu=12(L+GLTG)=[0Δp1Δp2Δp3Δp1α1Δp4Δp5Δp2Δp4α2Δp6Δp3Δp5Δp6α3]
D=limqq(MqI),
D=[0D1+D7D2+D8D3+D9D1D7f13D6+D12D5+D11D2D8D6+D12f14D4+D10D3D9D5+D11D1+D10f15],
M=limq(I+1qD)q=exp(D),
M=UHorM=HU,
GUTG=U1andGHTG=H.
GLaTG=LaandGLsTG=Ls;
M=UH=exp(La)exp(Ls)=exp(La+Ls+12[La,Ls]+112[La,[La,Ls]]+112[[La,Ls],Ls]+),
M=exp(Lm+Lu),
Lm=La+112[[La,Ls],Ls]+,
Lu=Ls+12[La,Ls]+112[La,[La,Ls]]+,
M=exp(Lm+Lu)=exp(Lm)exp(Lm)exp(Lm+Lu)=exp(Lm)exp(Lu+12[Lu,Lm]+)=exp(Lm)(I+Lu+12[Lu,Lm]+),
M=Mnd+Md1+Md2+,
M=M1+M2+M3+M4,
C=i,jMij(σiσj*),
C=λ1v1v1++λ2v2v2++λ3v3v3++λ4v4v4+,

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