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--- topic:optics:characterization:retardance [2020/09/03 16:14] – created samuel
+++ topic:optics:characterization:retardance [2020/09/03 16:31] (current) – [Mueller Matrix method] Some index errors. samuel
@@ Line 12: / Line 12: @@
 ==== Mueller Matrix method ====
+This is based on \cite{Hui.OSullivan:2009}. As a reminder, the Mueller matrix, applied to a normalized stokes vector $[s_{1,in}, s_{2,in}, s_{3,in}]$ looks like
 $$ \begin{bmatrix} s_1 \\ s_2 \\ s_3 \end{bmatrix}  = \begin{bmatrix} m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \\ m_{31} & m_{32} & m_{33} \end{bmatrix} \begin{bmatrix} s_{1,in} \\ s_{2,in} \\ s_{3,in} \end{bmatrix} $$
+If $\mathbf{s}_i$ is the basis vectors with a 1 on position $i$, all three output stokes vectors, will form the Mueller matrix.
+Also two independent input polarization states (no need to be orthogonal) allow determining the Mueller matrix as follows.
+Measure $\mathbf{s}_a$ and $\mathbf{s}_b$ for two independent input polarizations. $\mathbf{s_1} = \mathbf{s_a}$ and then we can find a orthogonal vector to $\mathbf{s_1}$ and $\mathbf{s_b}$ through the cross-product. $$ \mathbf{s_3} = \mathbf{s_1} \times \mathbf{s_b} $$
+The third vector can then be found by using the orthogonality through $$\mathbf{s_2} = \mathbf{s_3} \times \mathbf{s_1} $$.

Kollektanee - Samuel Gyger