In this article, we address the question of significance of the parameters of differential Mueller matrix formalism. We show how the concept of mean value and uncertainty of the optical properties recently introduced to depict this differential matrix can be related to the random fluctuations of these optical properties. From the layered-medium interpretation introduced by Jones [J. Opt. Soc. Am. 38, 671 (1948)] and extended to Mueller–Jones matrix by Azzam [J. Opt. Soc. Am. 68, 1756 (1978)], a generalization to depolarizing Mueller matrices is proposed. Based on the random Mueller–Jones matrix approach, the obtained parameterization perfectly fits the previous results from the literature. Necessary conditions of positivity on specific coefficients imposed in order to have physical Mueller matrix are introduced in a natural way and not inferred a posteriori. Interpretations of the underlying physical processes are also presented. An illustrative experimental example is provided from literature data.
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