Abstract

Because of the noncommutativity of the matrix product, the three factors into which a depolarizing Mueller matrix is decomposed, i.e., the diattenuator, the retarder, and the depolarizer, form six possible products grouped into two families, as already pointed out [J. Opt. Soc. Am. A 13, 1106 (1996) ; Opt. Lett. 29, 2234 (2004) ]. We show that, apart from the generalized polar decomposition generating the first family of products, there exists a dual decomposition belonging to the second family. The mathematical procedure for this dual decomposition is given, and the symmetry existing between the two decompositions is pointed out. The choice of the most appropriate decomposition for a given practical optical arrangement is likewise discussed and illustrated by simple examples.

© 2007 Optical Society of America

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References

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  1. S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
  2. J. E. Wolfe and R. A. Chipman, Appl. Opt. 45, 1688 (2006).
    [PubMed]
  3. B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, Appl. Opt. 43, 2824 (2004).
    [PubMed]
  4. S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).
  5. J. Morio and F. Goudail, Opt. Lett. 29, 2234 (2004).
    [PubMed]
  6. V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).
  7. A. S. Householder, J. Assoc. Comput. Mach. 5, 339 (1958).
  8. D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. 11, 2305 (1994).
  9. F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

2006 (1)

2004 (2)

2003 (1)

S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).

1996 (2)

S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

1994 (1)

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. 11, 2305 (1994).

1992 (1)

V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).

1958 (1)

A. S. Householder, J. Assoc. Comput. Mach. 5, 339 (1958).

Anderson, D. G. M.

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. 11, 2305 (1994).

Barakat, R.

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. 11, 2305 (1994).

Cariou, J.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

Chipman, R. A.

Clairac, B.

S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).

De Martino, A.

Drévillon, B.

Eliès, P.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

Fontas, B.

S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).

Goudail, F.

Guyot, S.

S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).

Householder, A. S.

A. S. Householder, J. Assoc. Comput. Mach. 5, 339 (1958).

Hovenier, J. W.

V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).

Laude-Boulesteix, B.

Le Jeune, B.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

Le Roy-Bréhonnet, F.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

Lotrian, J.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

Lu, S.-Y.

Morio, J.

Schwartz, L.

van der Mee, V. M.

V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).

Vézien, C.

S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).

Wolfe, J. E.

Appl. Opt. (2)

J. Assoc. Comput. Mach. (1)

A. S. Householder, J. Assoc. Comput. Mach. 5, 339 (1958).

J. Math. Phys. (1)

V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).

J. Opt. Soc. Am. (1)

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. 11, 2305 (1994).

J. Opt. Soc. Am. A (1)

J. Phys. D (1)

F. Le Roy-Bréhonnet, B. Le Jeune, P. Eliès, J. Cariou, and J. Lotrian, J. Phys. D 29, 34 (1996).

Opt. Lett. (1)

Optik (Stuttgart) (1)

S. Guyot, C. Vézien, B. Clairac, and B. Fontas, Optik (Stuttgart) 114, 289 (2003).

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Equations (21)

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M Δ = M R M Δ M R T ,
M D = M R T M D M R ,
M Δ = M R T M Δ M R ,
M D = M R M D M R T .
M = M Δ M R M D ,
M = M Δ M D M R ,
M = M R M Δ M D ,
M = M D M R M Δ ,
M = M R M D M Δ ,
M = M D M Δ M R ,
M D = T u [ 1 D T D m D ] ,
m D = 1 D 2 I + ( 1 1 D 2 ) D ̂ D ̂ T ,
M R = [ 1 0 T 0 m R ] , m R T = m R 1 ,
M Δ = [ 1 0 T P Δ m Δ ] , m Δ T = m Δ ,
M Δ 0 M D 0 [ 1 0 T 0 0 ] [ 1 D T D m D ] = [ 1 D T 0 0 ]
M Δ r = [ 1 D Δ r T 0 m Δ r ] , m Δ r T = m Δ r
M D = m 00 [ 1 P T P m P ] ,
D Δ r = D m P 1 P 2 ,
m Δ r = ± [ ( m ) T m + ( λ 1 λ 2 + λ 2 λ 3 + λ 3 λ 1 ) I ] 1 × [ ( λ 1 + λ 2 + λ 3 ) ( m ) T m + λ 1 λ 2 λ 3 I ] ,
M D 0 M Δ 0 [ 1 D T D m D ] [ 1 0 T 0 0 ] = [ 1 0 D 0 ] .
M D 0 M Δ a [ 1 D T D m D ] [ 1 0 T 0 a I ] = [ 1 a D T D a m D ] .

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