Derivation of Mueller Calculus for PSFDI

#Derivation-of-Mueller-Calculus-for-PSFDI

For some background on this derivation, you will likely want to examine prior papers by Bin Yang and Will Goth using the technique called PSFDI. These prior papers can give you an idea of the system layout and the polarization components in a PSFDI system.

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:eqn We can multiply our eqn for @@0@@ by a constant of 2 and collect some terms, as completed below

DOA Brief Surface Plot investigation

#DOA-Brief-Surface-Plot-investigation