Abstract

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.

© 2011 Optical Society of America

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References

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2009 (3)

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

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]

2004 (1)

1996 (1)

1995 (1)

1978 (1)

Arce-Diego, J. L.

N. Ortega-Quijano and J. L. Arce-Diego, “Depolarizing differential Mueller matrices,” Opt. Lett. (to be published).

Azzam, R. M. A.

Boulvert, F.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

Brosseau, C.

Cariou, J.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

Chipman, R. 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]

Goudail, F.

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Le Brun, G.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

Le Jeune, B.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

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.

Martin, L.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

Morio, J.

Ortega-Quijano, N.

N. Ortega-Quijano and J. L. Arce-Diego, “Depolarizing differential Mueller matrices,” Opt. Lett. (to be published).

Ossikovski, R.

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

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]

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 (2)

Opt. Commun. (1)

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, Opt. Commun. 282, 692 (2009).
[CrossRef]

Opt. Lett. (2)

Other (2)

N. Ortega-Quijano and J. L. Arce-Diego, “Depolarizing differential Mueller matrices,” Opt. Lett. (to be published).

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

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Tables (1)

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Table 1 Accumulated Differential Parameters of the Tissue Phantom Characterized by the Matrix in Eq. (29)

Equations (29)

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d S / d z = m S ,
m = ( d M z / d z ) M z 1 .
M z = n = 0 { [ m n ( z z 0 ) n ] / n ! } M z ( z 0 ) .
M = exp ( m z ) .
m 1 = κ i K i = κ i I ,
m 2 = κ q K q = κ q [ 0 1 0 0 ; 1 0 0 0 ; 0 0 0 0 ; 0 0 0 0 ] ,
m 3 = κ u K u = κ u [ 0 0 1 0 ; 0 0 0 0 ; 1 0 0 0 ; 0 0 0 0 ] ,
m 4 = κ v K v = κ v [ 0 0 0 1 ; 0 0 0 0 ; 0 0 0 0 ; 1 0 0 0 ] ,
m 5 = η q H q = η q [ 0 0 0 0 ; 0 0 0 0 ; 0 0 0 1 ; 0 0 1 0 ] ,
m 6 = η u H u = η u [ 0 0 0 0 ; 0 0 0 1 ; 0 0 0 0 ; 0 1 0 0 ] ,
m 7 = η v H v = η v [ 0 0 0 0 ; 0 0 1 0 ; 0 1 0 0 ; 0 0 0 0 ] ,
m 8 = κ i , q D q = κ i , q · diag [ 0 , 1 , 0 , 0 ] ,
m 9 = κ i , u D u = κ i , u · diag [ 0 , 0 , 1 , 0 ] ,
m 10 = κ i , v D v = κ i , v · diag [ 0 , 0 , 0 , 1 ] ,
m 11 = κ q K q = κ q [ 0 1 0 0 ; 1 0 0 0 ; 0 0 0 0 ; 0 0 0 0 ] ,
m 12 = κ u K u = κ u [ 0 0 1 0 ; 0 0 0 0 ; 1 0 0 0 ; 0 0 0 0 ] ,
m 13 = κ v K v = κ v [ 0 0 0 1 ; 0 0 0 0 ; 0 0 0 0 ; 1 0 0 0 ] ,
m 14 = η q H q = η q [ 0 0 0 0 ; 0 0 0 0 ; 0 0 0 1 ; 0 0 1 0 ] ,
m 15 = η u H u = η u [ 0 0 0 0 ; 0 0 0 1 ; 0 0 0 0 ; 0 1 0 0 ] ,
m 16 = η v H v = η v [ 0 0 0 0 ; 0 0 1 0 ; 0 1 0 0 ; 0 0 0 0 ] .
m = n = 1 16 m n = [ κ i κ q + κ q κ u + κ u κ v + κ v κ q κ q κ i κ i , q η v + η v η u + η u κ u κ u η v + η v κ i κ i , u η q + η q κ v κ v η u + η u η q + η q κ i κ i , v ] .
λ m = ( d λ M / d z ) λ M 1 ,
λ m = ln ( λ M ) / z .
M = VM λ V 1 ,
m = Vm λ V 1 ,
M 1 = [ 1.0000 0.0622 0.0038 0.0023 0.0646 0.9888 0.1407 0.0468 0.0026 0.1227 0.5846 0.7988 0.0015 0.0829 0.7838 0.6029 ] .
m ¯ 1 = [ 0.0020 0.0625 0.0011 0.0006 0.0644 0.0022 0.0260 0.1843 0.0063 0.0255 0.0054 2.2264 0.0036 0.1824 2.1931 0.0158 ] .
M 2 = [ 1.0000 0.0056 0.0019 0.0064 0.0081 0.8461 0.0028 0.0169 0.0037 0.0002 0.7672 0.3358 0.0048 0.0216 0.3485 0.7728 ] .
M 3 = [ 1.0000 0.0185 0.0029 0.0042 0.0172 0.7569 0.0405 0.0462 0.0034 0.0524 0.5450 0.5466 0 . 0024 0 . 0070 0 . 6244 0 . 5967 ] .

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