## 3 Results and Discussion
In summary, we can see from the comparative analyzing results presented in Sections 3.1 and 3.2 that the modified MMT parameter \(t_{121314}\) shows a better accordance with the MMPD parameter \(D\) in both the transmission and backscattering measurements than the original parameter \(t_{1213}\), which only reflects the linear diattenuation of the samples. Though the circular diattenuation effects of the tissue samples are often very limited, taking  
Figure 2: Comparison of backward measured MMT and MMPD diattenuation parameters of bulk tissue samples. **(a)** MMPD parameter \(D\) plotted against its counterpart MMT parameter \(t_{1213}\) for correlation analysis with all five kinds of bulk tissue samples. **(b)** Statistical analysis bar chart of MMPD parameter \(D\) and MMT parameter \(t_{1213}\) for each kind of bulk tissue samples. **(c)** MMPD parameter \(D\) plotted against its counterpart modified MMT parameter \(t_{121314}\) for correlation analysis with all five kinds of bulk tissue samples. **(d)** Statistical analysis bar chart of MMPD parameter \(D\) and modified MMT parameter \(t_{121314}\) for each kind of bulk tissue samples. the element \(m_{14}\) (encoded the circular diattenuation property) [42] into account for tissue polarimetric calculations can produce more accurate results. Quantitative Comparison of Linear Retardance Related MMPD and MMT Parameters for Transmission Imaging of Thin Tissue Samples  
Linear retardance is viewed as one of the most important polarization properties of tissue samples in terms of revealing the location and density of the birefringent fibrous structures [15; 16; 17; 18; 19; 20]. Our previous studies showed that the MMT parameters \(t_{2434}\) and \(t_{2423}\) can be used to reflect the linear retardance of the tissues [14; 29]. However, both of the parameters may slightly deviate from each other when measuring complicated tissue samples containing layered anisotropic structures, reducing the accuracy of Mueller matrix polarimetry for quantitative tissue evaluation. To deal with this problem, we proposed a modified MMT parameter \(t_{qr}\) based on the elements from both the fourth column and fourth row shown in Equation (15) to describe the linear retardance property. To verify its effectiveness, we conducted the comparisons among the linear retardance related MMPD and MMT parameters in three groups: (\(\delta\), \(t_{2434}\)), (\(\delta\), \(t_{4243}\)), and (\(\delta\), \(t_{qr}\)). The correlation and statistical analysis values of MMT and MMPD parameters groups for each kind of thin tissue samples are shown in Table 4 and Figure 3. For more intuitive comparisons, all the parameters are normalized to the [0, 1] value range. For the correlation analysis, Figure 3a,c,e show that, compared with the parameter groups (\(\delta\), \(t_{2434}\)) and (\(\delta\), \(t_{243}\)), the group (\(\delta\), \(t_{qr}\)) for all the samples have higher correlation coefficient values. We can also see the differences more clearly in Table 4, where the correlation coefficient values of (\(\delta\), \(t_{2434}\)) and (\(\delta\), \(t_{243}\)) deviate from each other ranging between 0.90 to 0.99, while the correlation coefficients of (\(\delta\), \(t_{qr}\)) are more stable with higher values for all the samples. Moreover, for the statistical analysis, all kinds of thin tissue samples show statistically significant differences with \(p<0.01\) among the parameter groups according to Table 4 and Figure 3b,d,f, meaning that the MMT linear retardance parameters cannot be substituted for MMPD parameter \(\delta\) directly without linear fitting. However, the modified MMT linear retardance parameter \(t_{qr}\) shows a good accordance with the MMPD parameter \(\delta\), indicating that it can be used to well present linear retardance distributions of tissues by linear fitting with MMPD parameter \(\delta\).