Study on the validity of 3 × 3 Mueller matrix decomposition

Using Monte Carlo simulations based on previously developed scattering models consisting of spherical and cylindrical scatterers imbedded in birefringent interstitial medium, we compare the polarization parameters extracted from the 3×3 and 4×4 Mueller matrix decomposition methods in forward and backward scattering directions. The results show that the parameters derived from the 3×3 Mueller matrix decomposition are usually not the same as those from the 4×4 Mueller matrix decomposition but display similar qualitative relations to changes in the microstructure of the sample, such as the density, size, and orientation distributions of the scatterers, and birefringence of the interstitial medium. The simulations are backed up by experiments when suitable samples are available.