Mueller calculus

Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller. In this technique, the effect of a particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix.

Disregarding coherent wave superposition, any fully polarized, partially polarized, or unpolarized state of light can be represented by a Stokes vector (${\displaystyle {\vec {S}}}$); and any optical element can be represented by a Mueller matrix (M).

If a beam of light is initially in the state ${\displaystyle {\vec {S}}_{i}}$ and then passes through an optical element M and comes out in a state ${\displaystyle {\vec {S}}_{o}}$, then it is written

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