# Mueller Matrix Decomposition and Image for Non-Destructive Testing of UAVs Skin
## 3 Experiments
### NDT of the UAV Skin  
In this section, UMMMD is used for the NDT of UAV skin. Figure 4 shows eigenvalue images obtained from the corresponding coherency matrices of each pixel. Figure 4a shows the image \(\lambda_{1}\) related to the reflection, and Figure 4b-d reflects the depolarization caused by the scattering of the UAV skin under different polarization states. Figure 4b-d are blurred since the detected signals under different polarized states are weak. In Figure 4d, the value of \(\lambda_{4}\) is close to 0, so the structure information is nearly lost. From Figure 4, the depolarization under the polarized, elliptical, and circular polarized light is different because of different light-matter interactions. The sharpness of the \(\lambda_{i}(i=1,2,3,4)\) images in Figure 4 is in agreement with the eigenvalues in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{\(M\)} & \multicolumn{2}{c}{\(\lambda_{i}(i=1,2,3,4)\)} & \(E\) \\ \hline \(\left[\begin{array}{cccc}1.0000&-0.3719&0.0892&-0.0671\\ -0.4652&0.7768&-0.1405&0.2109\\ -0.0151&-0.1275&-0.6098&0.1563\\ -0.0349&-0.0075&-0.1557&-0.6273\end{array}\right]\) & \(\left\{1.6774\right.\) 0.2111 0.0882 0.0233\(\left\}\right.\) & 0.3822 \\ \hline \end{tabular}
\end{table} 
Table 1: The decomposition results. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Methods**} & \(M_{J}\) & \(M_{d}\) &
\begin{tabular}{c} **Non-Uniform** \\ **Multiple Scattering** \\ \end{tabular} \\ \hline Brosseau method [10] & \(M-M_{d}\) & \(diag(0.2151,0,0,0)\) & No \\ PCM [14] & OM & \(diag(0.2151,0,0,0)\) & No \\ LRB [24] & \(\lambda_{1}e_{1}e_{1}{}^{\dagger}\) & \(diag(0.2151,0,0,0)\) & No \\ [PERSON] method [22] & \(\lambda_{1}e_{1}e_{1}{}^{\dagger}\) & \(diag(0.2669,0.1554,0.0325,-0.0325)\) & Yes \\ UMMMD & \(\lambda_{1}e_{1}e_{1}{}^{\dagger}\) & \(diag(0.2151,0.1036,-0.0193,-0.0842)\) & Yes \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison between UMMMD and some methods. In order to characterize the features of the UAV skin, it is necessary to improve the clarity and contrast of the images. Figure 5 shows the images calculated with the elements in the depolarization matrix. As shown in Figure 5a, the depolarization at the edge of the sample is larger than that in the center since the scattering at the edge is messier. In Figure 5b, most of the knots are hollow because the warp and weft yarns at different knots are not evenly stressed during manufacture and use, and then the yarns are distributed to the edge of the node. Accordingly, the edge position becomes tighter than the center position. The different friction force at the knots results in different sizes of the gaps in the knots since the tension distribution of the yarns is non-uniform. The lattice structure is formed by the bright areas reflected by the nodes and the dark areas corresponding to the gaps. Figure 5c,d are similar to Figure 5b. However, their contrast is significantly different. Figure 5d is the image obtained from the absolute value operation of \(\eta_{4}\). The polarization responses of the UAV skin are non-uniform since the properties and structures of different areas are different. Table 3 shows the contrast of Figures 3-5. As shown in Table 3, the contrast of the original intensity image is very low since the multiple scattered photons decrease the imaging resolution and contrast. The contrast of the \(\lambda_{i}(i=2,3,4)\) images is low since multiple scattering is serious under different polarization states. Although the values of \(\lambda_{i}(i=2,3,4)\) are small, their relative errors are large due to the dispersion of the three values. Accordingly, the contrast of the \(\eta_{i}(i=2,3,4)\) images is improved, especially the contrast of the \(abs(\eta_{4})\) image. In Table 3, the contrast of the \(\eta_{2}\) image is improved by about 13 times than that of the intensity image in Figure 3.