The differential Mueller matrix expresses the local action of an optical medium on the evolution of a propagating electromagnetic field, including partially coherent and partially polarized waves. Here, we present a derivation of the differential Mueller matrix from the canonical form of Type I Mueller matrices without making use of the exponential generators of uniform media. We demonstrate how to practically obtain this parameterization numerically using an eigenvalue decomposition and find validity criteria to ensure that the matrix satisfies the constraints of a physical system. This provides a convenient tool-set to investigate depolarization effects and extends previous treatments of the differential Mueller matrix formalism.
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