## Abstract

Mueller matrices provide a complete characterization of the optical
polarization properties of biological tissue. A
polarization-sensitive optical coherence tomography (OCT) system
was built and used to investigate the optical polarization properties
of biological tissues and other turbid media. The apparent degree
of polarization (DOP) of the backscattered light was measured with
both liquid and solid scattering samples. The DOP maintains the
value of unity within the detectable depth for the solid sample,
whereas the DOP decreases with the optical depth for the liquid
sample. Two-dimensional depth-resolved images of both the Stokes
vectors of the backscattered light and the full Mueller matrices of
biological tissue were measured with this system. These
polarization measurements revealed some tissue structures that are not
perceptible with standard OCT.

© 2000 Optical Society of America

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### Equations (12)

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(1)
$$\mathbf{S}=\left(\begin{array}{c}{I}_{H}+{I}_{V}\\ {I}_{H}-{I}_{V}\\ {I}_{P}-{I}_{M}\\ {I}_{R}-{I}_{L}\end{array}\right),$$
(2)
$$\mathbf{S}=\left(\begin{array}{c}{S}_{0}\\ {S}_{1}\\ {S}_{2}\\ {S}_{3}\end{array}\right)=\left(\begin{array}{c}{I}_{H}+{I}_{V}\\ {I}_{H}-{I}_{V}\\ 2{I}_{P}-\left({I}_{H}+{I}_{V}\right)\\ 2{I}_{R}-\left({I}_{H}+{I}_{V}\right)\end{array}\right).$$
(3)
$$\mathrm{DOP}=\frac{{\left(S_{1}{}^{2}+S_{2}{}^{2}+S_{3}{}^{2}\right)}^{1/2}}{{S}_{0}},\mathrm{DOLP}=\frac{{\left(S_{1}{}^{2}+S_{2}{}^{2}\right)}^{1/2}}{{S}_{0}},\mathrm{DOCP}=\frac{{S}_{3}}{{S}_{0}}.$$
(4)
$${\mathbf{S}}_{\mathrm{out}}={\mathbf{MS}}_{\mathrm{in}},$$
(5)
$${\mathbf{S}}_{\mathit{Hi}}=\left(\begin{array}{c}1\\ 1\\ 0\\ 0\end{array}\right),{\mathbf{S}}_{\mathit{Vi}}=\left(\begin{array}{c}1\\ -1\\ 0\\ 0\end{array}\right),{\mathbf{S}}_{\mathit{Pi}}=\left(\begin{array}{c}1\\ 0\\ 1\\ 0\end{array}\right),{\mathbf{S}}_{\mathit{Ri}}=\left(\begin{array}{c}1\\ 0\\ 0\\ 1\end{array}\right),$$
(6)
$${\mathbf{S}}_{H}={\mathbf{MS}}_{\mathit{Hi}}={\mathbf{M}}_{0}+{\mathbf{M}}_{1},{\mathbf{S}}_{V}={\mathbf{MS}}_{\mathit{Vi}}={\mathbf{M}}_{0}-{\mathbf{M}}_{1},{\mathbf{S}}_{P}={\mathbf{MS}}_{\mathit{Pi}}={\mathbf{M}}_{0}+{\mathbf{M}}_{2},{\mathbf{S}}_{R}={\mathbf{MS}}_{\mathit{Ri}}={\mathbf{M}}_{0}+{\mathbf{M}}_{3}.$$
(7)
$$\mathbf{M}=\frac{1}{2}\left[{\mathbf{S}}_{H}+{\mathbf{S}}_{V},{\mathbf{S}}_{H}-{\mathbf{S}}_{V},2{\mathbf{S}}_{P}-\left({\mathbf{S}}_{H}+{\mathbf{S}}_{V}\right),2{\mathbf{S}}_{R}-\left({\mathbf{S}}_{H}+{\mathbf{S}}_{V}\right)\right].$$
(8)
$${I}_{\mathrm{OCT}}=2\mathit{Re}\left[\u3008{\mathbf{E}}_{s}\left({l}_{s}\right)\xb7{\mathbf{E}}_{r,A}*\left({l}_{r}\right)\u3009\right]=2{\left[{I}_{s,A}\left({l}_{s}\right){I}_{r,A}\right]}^{1/2}|V\left(\mathrm{\Delta}l\right)|cos\left({k}_{0}\mathrm{\Delta}l\right),$$
(9)
$${I}_{s,A}\propto {{I}_{\mathrm{OCT}}}^{2}/{I}_{r,A}.$$
(10)
$$\mathbf{S}\prime =\left(\begin{array}{c}{I}_{H}+{I}_{V}\\ {I}_{H}-{I}_{V}\\ 2{I}_{P}-\left({I}_{H}+{I}_{V}\right)\\ 2{I}_{R}-\left({I}_{H}+{I}_{V}\right)\end{array}\right)+\left(\begin{array}{c}2{I}_{n}\\ 0\\ 0\\ 0\end{array}\right)=\mathbf{S}+{\mathbf{S}}_{n}.$$
(11)
$$\mathrm{DOP}\left(\mathbf{S}\prime \right)=\mathrm{DOP}\left(\mathbf{S}\right)\frac{{S}_{0}}{{S}_{0}+2{I}_{n}}=\frac{{S}_{0}}{{S}_{0}+2{I}_{n}}.$$
(12)
$${\mathbf{M}}_{\mathrm{cal}}=\left[\begin{array}{cccc}1.000& -0.0420& -0.0028& -0.0479\\ -0.0405& 0.9975& -0.0591& -0.0306\\ -0.0095& -0.0004& 1.0671& 0.2089\\ -0.0134& -0.0182& 0.2008& 1.0999\end{array}\right].$$