Comparative study of 3 x 3 Mueller matrix transformation and polar decomposition

Abstract

Mueller matrix polarimetry (MMP) has evolved as a tool of paramount importance to study the polarization properties of biological tissues. The conventional 4 x 4 Mueller matrix M is constructed by sixteen measurements involving both linear and circularly polarized light. Alternatively, the concept of 3 ×3M has been introduced where M is constructed from linear polarization measurements alone, thus simplifying the experimental geometry and procedure significantly. The individual polarization properties of the sample are encrypted in M. Several methods have been proposed to extract the encrypted polarization parameters of the sample from its M; Mueller matrix polar decomposition (MMPD) and Mueller matrix transformation (MMT) are two broadly utilized methods for this purpose. Here, we compared these two methods (i.e., MMPD and MMT) in the regime of 3 x 3 M. In particular, we have compared two important polarization parameters, namely linear depolarization and linear retardance for both MMPD and MMT methods. The results showed no significant difference between the mean linear depolarization values (n=10) (74.64 ± 14.39% vs 73.01 ± 13.74%, p = 0.799), while the mean linear retardance values (1.79 ± 0.10 vs 0.18 ± 0.17 radian, p < 0.001) were significantly different for MMPD and MMT methods. However, a good correlation between the two methods was observed for both linear depolarization (R2=0.87) and linear retardance (R2=0.89). This preliminary study indicates that the optical variables of both MMPD and MMT methods are sensitively correlated to the microstructure of the tissue samples, and there is a good correlation between the two decomposition methods.