Hui and O'Sullivan \cite{Hui.OSullivan:2009} in section 4.5 discuss the measurement of polarization mode dispersion (PMD) of fibers. There are two types of birefringence in an optical fiber geometrical birefringence (inherited in the geometry of the drawn fiber) and stress birefringence due to non-symmetric stress. Then there is also external influences on the fiber, that lead to polarization dispersion.

Several methods for measuring the PMD, one of them being the Jones matrix method (4.5.6) and one the Mueller matrix method. (4.5.7)

The problem is similar to measuring a fiber, so chapter 4.5.6 and 4.5.7 are interesting.

$$ \begin{bmatrix} s_1 \\ s_2 \\ s_3 \end{bmatrix} = \begin{bmatrix} m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \\ m_{31} & m_{32} & m_{33} \end{bmatrix} \begin{bmatrix} s_{1,in} \\ s_{2,in} \\ s_{3,in} \end{bmatrix} $$