We propose an attempt of explanation for the improvement of the transmittance dynamic of nematic liquid crystals, combined with neutral dichroic dyes, by the addition of chiral dopants. It is based on a fine polarimetric analysis of the liquid crystal medium, using the Mueller matrix formalism. This enables us to determine the polarization mode propagation and the residual scattering in the bulk. To calibrate our measurements we analyse two asymptotic cases, that have been extensively studied: the pure nematic case (no chiral dopants) and the cholesteric one (with high concentration of chiral dopants) in a Bragg regime. The mixture of interest in our case exhibits intermediate dopant concentrations. We present some experimental results explaining the impact of the addition of these chiral dopants on both dichroic efficiency, and scattering. Finally, we discuss how the complete polarimetric analysis can be used efficiently to describe the medium complexity.