Abstract

We propose a novel model for the measurement of a Mueller matrix for biological tissues. Compared with earlier measurement methods, our method can reduce measurement times and can significantly improve measurement efficiency. Our model needs only six intensity measurements to derive all 16 Mueller matrix components of a biological sample in arbitrary pixels. We used the pellicle cell of magnolia as our sample, and the experimental results are identical with those obtained with other methods. We demonstrate that we can obtain Mueller matrix components to recognize different biological tissues in the same visual field rapidly and reliably.

© 2009 Optical Society of America

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  1. J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
    [CrossRef]
  2. A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
    [CrossRef] [PubMed]
  3. L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
    [CrossRef] [PubMed]
  4. V. Sankaran, J. T. Walsh , Jr., and D. J. Maitland, “Comparative study of polarized light propagation in biological tissues,” J. Biomed. Opt. 7, 300-306 (2002).
    [CrossRef] [PubMed]
  5. D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.
  6. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  7. A. H. Hielscher, A. Eick, J. Mourant, D. Shen, J. Freyer, and I. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Express 1, 441-453 (1997).
    [CrossRef] [PubMed]
  8. R. Espinosa-Luna, “Scattering by rough surfaces in a conical configuration: experimental Mueller matrix,” Opt. Lett. 27, 1510-1512 (2002).
    [CrossRef]
  9. M. Xu, “E1ectric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express 12, 6530-6539 (2004).
    [CrossRef] [PubMed]
  10. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 4420-4438(2005).
    [CrossRef] [PubMed]
  11. R. Shintani, A. Fa, and C. Kang, Polarized Light (Atomic Energy Press, 1994).
  12. 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]

2007

J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
[CrossRef]

2005

2004

2002

R. Espinosa-Luna, “Scattering by rough surfaces in a conical configuration: experimental Mueller matrix,” Opt. Lett. 27, 1510-1512 (2002).
[CrossRef]

V. Sankaran, J. T. Walsh , Jr., and D. J. Maitland, “Comparative study of polarized light propagation in biological tissues,” J. Biomed. Opt. 7, 300-306 (2002).
[CrossRef] [PubMed]

2001

D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.

1997

1996

1995

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1994

R. Shintani, A. Fa, and C. Kang, Polarized Light (Atomic Energy Press, 1994).

1977

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

Arce Diego, J. L.

D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.

Arce-Diego, J. L.

J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
[CrossRef]

Azzam, R. M. A.

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

Bashara, N. M.

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

Bigio, I.

Chipman, R. A.

Eick, A.

Espinosa-Luna, R.

Fa, A.

R. Shintani, A. Fa, and C. Kang, Polarized Light (Atomic Energy Press, 1994).

Fanjul-Vélez, F.

J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
[CrossRef]

Freyer, J.

Hielscher, A. H.

Jacques, S. L.

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 4420-4438(2005).
[CrossRef] [PubMed]

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Kang, C.

R. Shintani, A. Fa, and C. Kang, Polarized Light (Atomic Energy Press, 1994).

Kim, A. D.

A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
[CrossRef] [PubMed]

Lu, S.-Y.

Maitland, D. J.

V. Sankaran, J. T. Walsh , Jr., and D. J. Maitland, “Comparative study of polarized light propagation in biological tissues,” J. Biomed. Opt. 7, 300-306 (2002).
[CrossRef] [PubMed]

Moscoso, M.

A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
[CrossRef] [PubMed]

Mourant, J.

Pereda Cubián, D.

D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.

Pereda-Cubián, D.

J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
[CrossRef]

Prahl, S. A.

Ramella-Roman, J. C.

Samperio-García, D.

J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
[CrossRef]

Sankaran, V.

V. Sankaran, J. T. Walsh , Jr., and D. J. Maitland, “Comparative study of polarized light propagation in biological tissues,” J. Biomed. Opt. 7, 300-306 (2002).
[CrossRef] [PubMed]

Shen, D.

Shintani, R.

R. Shintani, A. Fa, and C. Kang, Polarized Light (Atomic Energy Press, 1994).

Vlcek, C.

D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.

Walsh , J. T.

V. Sankaran, J. T. Walsh , Jr., and D. J. Maitland, “Comparative study of polarized light propagation in biological tissues,” J. Biomed. Opt. 7, 300-306 (2002).
[CrossRef] [PubMed]

Wang, L. H.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Xu, M.

Zaoralek, Z.

D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.

Zheng, L. Q.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Comput. Methods Programs Biomed.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

J. Biomed. Opt.

V. Sankaran, J. T. Walsh , Jr., and D. J. Maitland, “Comparative study of polarized light propagation in biological tissues,” J. Biomed. Opt. 7, 300-306 (2002).
[CrossRef] [PubMed]

A. D. Kim and M. Moscoso, “Light transport in two-layer tissues,” J. Biomed. Opt. 10, 034015 (2005).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Proc. SPIE

J. L. Arce-Diego, F. Fanjul-Vélez, D. Samperio-García, and D. Pereda-Cubián, “Mueller coherency matrix method for contrast image in tissue polarimetry,” Proc. SPIE 6627, 66271T (2007).
[CrossRef]

Other

D. Pereda Cubián, ?. Vl?ek, J. L. Arce Diego, and Z. Zaoralek, “Variation of the Pauli matrices coefficients in Nd-doped fibers subjected to a magnetic field, ” in Proceedings of the 14th Annual Meeting of the IEEE, Vol. 2 (IEEE, 2001), pp. 823-824.

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

R. Shintani, A. Fa, and C. Kang, Polarized Light (Atomic Energy Press, 1994).

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Figures (3)

Fig. 1
Fig. 1

Measurement structure delineation.

Fig. 2
Fig. 2

Experimental setup for Mueller matrix measurements.

Fig. 3
Fig. 3

Simultaneous experimental results.

Equations (25)

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S = [ S 0 S 1 S 2 S 3 ] = [ | E x | 2 + | E y | 2 | E x | 2 | E y | 2 E x * E y + E x E y * i ( E x * E y E x E y * ) ] ,
M = [ M i j ] 4 × 4 ( i , j = 1 , 2 , 3 , 4 ) .
S = [ S 0 S 1 S 2 S 3 ] = [ a x 2 + a y 2 a x 2 a y 2 2 a x a y cos δ 2 a x a y sin δ ] .
a x 2 = 1 2 ( S 0 + S 1 ) ,     a y 2 = 1 2 ( S 0 S 1 ) ,
a x = a x exp ( β x L / 2 ) , a y = a y exp ( β y L / 2 ) , δ = δ Δ ,
S 0 = [ ( S 0 + S 1 ) exp ( β x L ) + ( S 0 S 1 ) exp ( β y L ) ] / 2 , S 1 = [ ( S 0 + S 1 ) exp ( β x L ) ( S 0 S 1 ) exp ( β y L ) ] / 2 , S 2 = exp ( β x + β y 2 L ) S 2 cos Δ + exp ( β x + β y 2 L ) S 3 sin Δ , S 3 = exp ( β x + β y 2 L ) S 2 sin Δ + exp ( β x + β y 2 L ) S 3 cos Δ ,
M Δ , β = 1 2 [ A 2 + B 2 A 2 B 2 0 0 A 2 B 2 A 2 + B 2 0 0 0 0 2 A B cos Δ 2 A B sin Δ 0 0 2 A B sin Δ 2 A B cos Δ ] ,
M Δ , β , θ = T θ M Δ , β T θ = 1 2 [ A 2 + B 2 ( A 2 B 2 ) C ( A 2 B 2 ) S 0 ( A 2 B 2 ) C ( A 2 + B 2 ) C 2 + 2 S 2 D F ( A 2 + B 2 ) C S 2 S C D F 2 S E F ( A 2 B 2 ) S ( A 2 + B 2 ) C S 2 S C D F ( A 2 + B 2 ) S 2 + 2 C 2 D F 2 C E F 0 2 S E F 2 C E F 2 D F ] ,
M d = [ 1 λ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] .
M cell = M d + λ M Δ , β , θ = [ 1 λ + A 2 + B 2 2 λ A 2 B 2 2 λ C A 2 B 2 2 λ S 0 A 2 B 2 2 λ C ( A 2 + B 2 ) C 2 + 2 S 2 D F 2 λ ( A 2 + B 2 ) C S 2 S C D F 2 λ λ S E F A 2 B 2 2 λ S ( A 2 + B 2 ) C S 2 S C D F 2 λ ( A 2 + B 2 ) S 2 + 2 C 2 D F 2 λ λ C E F 0 λ S E F λ C E F λ D F ] .
S out 1 = M cell S in 1 ,
S out 2 = M cell S in 2 ,
S out 3 = M cell S in 3 ,
S out i = M A M cell S in i ( i = 4 , 5 ) ,
M A = 1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] .
S out 4 = M A M cell S in 4 ,
S out 5 = M A M cell S in 5 ,
m 11 = I 1 + I 2 2 I , m 12 = m 21 = I 1 I 2 2 I , m 13 = 2 I 3 I 1 I 2 2 I , m 22 = 4 I 4 3 I 1 + I 2 2 I , m 23 = 4 I 5 2 I 3 + I 2 I 1 2 I .
S out 7 = M LC M cell S in 7 ,
M LC = 1 2 [ 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 ] .
S out 7 = M LC M cell S in 7 ,
θ = 1 2 arctan ( m 23 m 22 m 44 )
m 42 = λ sin ( 2 θ ) sin ( Δ ) A B = tan ( 2 θ ) m 43 ,
m 43 = ( 2 I 7 I 3 ) / I , m 24 = m 42 , m 34 = m 43 , m 31 = m 13 , m 32 = m 23 ,
m 33 = ( A 2 + B 2 ) sin 2 ( 2 θ ) 2 A B cos 2 ( 2 θ ) cos ( Δ ) 2 λ = ( A 2 + B 2 ) cos 2 ( 2 θ ) + 2 A B sin 2 ( 2 θ ) cos ( Δ ) 2 λ λ A B cos ( Δ ) sin 2 ( 2 θ ) + λ A B cos ( Δ ) cos 2 ( 2 θ ) = m 22 m 44 sin 2 ( 2 θ ) + m 44 cos 2 ( 2 θ ) .

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