Symmetric decomposition of experimental depolarizing Mueller matrices in the degenerate case

We propose a detailed procedure to determine the two retardance matrix factors entering the symmetric decomposition of Mueller matrices when the depolarizer matrix is partially degenerate (i.e., two out of three of its depolarization coefficients are equal), which is a common occurrence. Thanks to a relatively simple algebraic method, we show that linear retardance, as well as its eigenaxes orientation can be determined unambiguously from each retardance matrix factor. The method, applied on both experimental Mueller matrices of an ad hoc sample, as well as on that of a biological tissue, shows its efficiency for decoupling the different polarimetric effects of retardance that occur during the propagation of light throughout a complex medium.