## 3 Results and Discussion  
### Test Experiment of True-Color Vectorial Retardance Imaging by a Vortex Retarder  
To demonstrate the performance of the true-color vectorial retardance imaging technique, we use the homemade MMIP system to detect a half-wave vortex retarder (m = 2, center wavelengths available from 405 nm to 1550 nm, Thorlabs). Figure 4 shows the imaging results of the half-wave vortex retarder. Figure 4a-c are the horizontal, 45\({}^{\circ}\)-linear, and circle retardance, respectively. Theoretically, the horizontally and 45\({}^{\circ}\)-linearly arranged anisotropic microstructures may display a great value in horizontal retardance and 45\({}^{\circ}\)-linear retardance, respectively [69, 70]. The results in Figure 4a,b are consistent with the previous conclusion. Figure 4c shows the circle retardance with the mean value of 0.0050 \(\pm\) 0.2866 rad, resulting from the linear birefringence property of the vortex retarder. Each retardance component can highlight the details of anisotropic structures with different orientations, which together can provide a complete description of the birefringence property. However, interpreting the three components simultaneously is complex and challenging. Figure 4d demonstrates the scalar retardance of the half-wave vortex retarder with a mean value of 3.0390 \(\pm\) 0.0216 rad. It is proved that our MMIP has high measurement accuracy for scalar retardance. Although the scalar retardance reflects the distribution of the anisotropic structures, Figure 4d shows the lack of fast axis orientation information of the vortex retarder. This is due to the superposition algorithm (the square root of the sum of squares) of the three components. Figure 4e shows the orientation of linear retardance for the half-wave vortex retarder. Figure 4f shows the true-color vectorial retardance image of the half-wave vortex retarder using the color-encoded algorithm. The brightness in Figure 4f is uniform, representing the scalar retardance of the vortex retarder is close to the same (\(\sim\)\(\pi\)). This is consistent with Figure 4d. On the other hand, each color of the vectorial retardance image corresponds to an independent fast-axis orientation. In contrast to Figure 4e, the vectorial retardance imaging method can enhance the contrast.  
Figure 3: Demonstration of the color-encoded vectorial retardance: (**a**,**b**) the front side and back side of the color-encoded sphere, which map all possible states of vectorial retardance; (**c**) the relationship between several typical vectorial retardance states and the colors; (**d**–**f**) each color on the cross-sections has characteristics of \(R_{H}=0\), \(R_{45}=0\), and \(R_{C}=0\), respectively; (**g**–**i**) each color on the cross-sections has characteristics of \(R_{H}=R_{45}\), \(R_{H}=R_{C}\), and \(R_{45}=R_{C}\), respectively.  
Different from the scalar retardance and the orientation of linear retardance, true-color vectorial retardance imaging can visualize the distribution and orientation of birefringent structures in one resultant image. We found that the orientation of linear retardance along +45\({}^{\circ}\) and \(-\)45\({}^{\circ}\) can be distinguished by different colors in Figure 4f, while they are not distinguishable in Figure 4e. The true-color vectorial retardance images can directly reflect the orientation with enhanced contrast. The measurement results are consistent with the theory shown in Figure 3. Therefore, the vectorial retardance imaging technology might be a vital tool in assessing the birefringence properties of anisotropic microstructures.