We'll use a python library called sympy to do symbolic math and to log the result as latex in the notebook

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Because the given @@0@@ assumes that the orientation of the optical anisotropy is along the x,y direction, we need to create an @@1@@, based on the rotational matrix applied to a Mueller element, as described here.

To do this, I'll use the symbolic mathematics with the created matrices, using the .subs method to substitute @@2@@.

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Now that we built the Mueller Matrix for the sample with fibers at @@0@@ to see what the output intensity will look like.

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Great, now let's extract the intensity element, that is, the first element of the @@0@@ vector.

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To compare to the final form as mentioned by W. Goth in the prior psfdi article, shown below: We can multiply our eqn for @@0@@ by a constant of 2 and collect some terms, as completed below