In this paper, we address the issue of the existence of a solution of depolarizing differential Mueller matrix for a homogeneous medium. Such a medium is characterized by linear changes of its differential optical properties with the thickness of the medium. We show that, under a short correlation distance assumption, it is possible to derive such linear solution, and we clarify this solution in the particular case where the random fluctuation processes associated to the optical properties are Gaussian white noise-like. A solution to the problem of noncommutativity of a previously proposed model [J. Opt. Soc. Am. 30, 2196 (2013) [CrossRef] ] is given by assuming a random permutation of the order of the layers and by averaging all the differential matrices resulting from these permutations. It is shown that the underlying assumption in this case is exactly the Gaussian white noise assumption. Finally, a recently proposed approach [Opt. Lett. 39, 4470 (2014) [CrossRef] ] for analysis of the statistical properties related to changes in optical properties is revisited, and the experimental conditions of application of these results are specified.
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