Abstract

Polarimetric optical techniques such as polarization microscopy or polarization-sensitive optical coherence tomography normally assume that light is perpendicular to the sample surface and that fibrils of a birefringent biological tissue are arranged in a plane parallel to this surface. The approaches that describe quantitatively polarimetric data from tissues with nonparallel fibril orientation and/or off-axis incidence usually lack a rigorous theoretical analysis. We present a polarimetric model with arbitrary fibril orientation and/or variable incidence angle by means of the extended Jones matrix theory, the polar decomposition, and Poincaré equivalence theorem. The model, suitable for diagnosis or tissue structure analysis, is applied to articular cartilage.

© 2010 Optical Society of America

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References

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2010

K. A. Athanasiou, E. M. Darling, and J. C. Hu, Articular Cartilage Tissue Engineering (Morgan & Claypool, 2010).

2009

M. C. van Turnhout, S. Kranenbarg, and J. L. van Leeuwen, J. Biomed. Opt.��14, 054018 (2009).
[CrossRef] [PubMed]

2008

P. Fratzl, Collagen: Structure and Mechanics (Springer, 2008).

N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage��17, 33 (2008).
[CrossRef] [PubMed]

2006

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

N. Ugryumova, S. V. Gangnus, and S. J. Matcher, Opt. Lett.��31, 2305 (2006).
[CrossRef] [PubMed]

2005

1997

1993

Athanasiou, K.?A.

K. A. Athanasiou, E. M. Darling, and J. C. Hu, Articular Cartilage Tissue Engineering (Morgan & Claypool, 2010).

Bonesi, M.

N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage��17, 33 (2008).
[CrossRef] [PubMed]

Chen, Z.

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

Darling, E.?M.

K. A. Athanasiou, E. M. Darling, and J. C. Hu, Articular Cartilage Tissue Engineering (Morgan & Claypool, 2010).

Farrell, R.?A.

Fratzl, P.

P. Fratzl, Collagen: Structure and Mechanics (Springer, 2008).

Gangnus, S.?V.

Gu, C.

Guo, S.

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

Hu, J.?C.

K. A. Athanasiou, E. M. Darling, and J. C. Hu, Articular Cartilage Tissue Engineering (Morgan & Claypool, 2010).

Jacobs, J.

N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage��17, 33 (2008).
[CrossRef] [PubMed]

Knighton, R.?W.

Kranenbarg, S.

M. C. van Turnhout, S. Kranenbarg, and J. L. van Leeuwen, J. Biomed. Opt.��14, 054018 (2009).
[CrossRef] [PubMed]

MacCally, R.?L.

Matcher, S.?J.

N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage��17, 33 (2008).
[CrossRef] [PubMed]

N. Ugryumova, S. V. Gangnus, and S. J. Matcher, Opt. Lett.��31, 2305 (2006).
[CrossRef] [PubMed]

Peavy, G.?M.

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

Rouseff, D.

Ugryumova, N.

N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage��17, 33 (2008).
[CrossRef] [PubMed]

N. Ugryumova, S. V. Gangnus, and S. J. Matcher, Opt. Lett.��31, 2305 (2006).
[CrossRef] [PubMed]

van Leeuwen, J.?L.

M. C. van Turnhout, S. Kranenbarg, and J. L. van Leeuwen, J. Biomed. Opt.��14, 054018 (2009).
[CrossRef] [PubMed]

van Turnhout, M.?C.

M. C. van Turnhout, S. Kranenbarg, and J. L. van Leeuwen, J. Biomed. Opt.��14, 054018 (2009).
[CrossRef] [PubMed]

Xie, T.

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

Yeh, P.

Zhang, J.

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

Zhou, Q.

Appl. Opt.

J. Biomed. Opt.

T. Xie, S. Guo, J. Zhang, Z. Chen, and G. M. Peavy, J. Biomed. Opt.��11, 064001 (2006).
[CrossRef]

M. C. van Turnhout, S. Kranenbarg, and J. L. van Leeuwen, J. Biomed. Opt.��14, 054018 (2009).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Lett.

Osteoarthritis Cartilage

N. Ugryumova, J. Jacobs, M. Bonesi, and S. J. Matcher, Osteoarthritis Cartilage��17, 33 (2008).
[CrossRef] [PubMed]

Other

P. Fratzl, Collagen: Structure and Mechanics (Springer, 2008).

K. A. Athanasiou, E. M. Darling, and J. C. Hu, Articular Cartilage Tissue Engineering (Morgan & Claypool, 2010).

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Figures (4)

Fig. 1
Fig. 1

Principal elements of the analysis. The layered birefringent material boundary is on the X Y plane. k is the incident propagation vector; k o and k e are the propagation vectors inside the birefringent structure, c is the optic axis (polar angle θ C , azimuthal angle ϕ C ), and s and p define the local polarization reference system.

Fig. 2
Fig. 2

Preferred collagen orientation of the articular cartilage. θ is the polar angle of the incident k vector. Representation reference system is X Y Z , where Z is coincident with the k vector and X is perpendicular to y vector.

Fig. 3
Fig. 3

Retardation (deg) as a function of depth for several incident radiation polar angles: (a) polar angles 0° (solid black) and 30° (dashed red), (b) 60° (dashed-dotted green) and 80° (dotted blue).

Fig. 4
Fig. 4

Slow-axis orientation (deg) as a function of depth for varying incident radiation polar angles: (a) polar angles 0° (solid black) and 30° (dashed red), (b) 60° (dashed-dotted green) and 80° (dotted blue).

Equations (3)

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J out = M T J in = D fin P N T N 1 , N P N 1 T N 2 , N 1 T 2 , 3 P 2 T 1 , 2 P 1 D ini J in = ( o s t s s e t s p o o t p p o e t p ) ( e j k o z d N 0 0 e j k e z d N ) ( o N 1 o N e N 1 o N o N 1 e N e N 1 e N ) ( s o t s p o o t p s e t s p o e t p ) J in .
M T = H T U T .
U T = R ( θ T ) D ( δ ) R ( θ T ) R ( θ R ) .

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