Mueller matrix of targets can reflect the change in the polarization state of the light in the propagation process, and it contains the polarization characteristics of the target itself, such as polarizance and depolarization. In the analysis of the characteristics of the Mueller matrix, most studies analyze the polarizance and depolarization characteristics separately. But in the process of theoretical derivation, it turns out that the two characteristics are independent of each other. Therefore, it is necessary to define a new index that can comprehensively evaluate the two characteristics.

In view of the shortcomings of the existing Mueller matrix measurement systems, this paper, based on the working principle of a polarization analyzer, improves and builds a rotating Mueller matrix measurement system. Then, the linear operation of the change in the polarization state is realized by transforming the propagation process of the light into a correlation semi-positive definite quadratic function, and a novel index is proposed to comprehensively evaluate the polarizance and depolarization characteristics of the Mueller matrix. In addition, we use a polarizer to verify the derived index and test the effectiveness of its comprehensive representation of the polarizance and depolarization characteristics. According to Mueller matrices of different targets published in the literature, their ability to identify targets during target detection is verified. Finally, Mueller matrices of aluminum plates under different incident angles and roughness are measured. The effect of incident angles and roughness on the Mueller matrix is analyzed by defining the influencing factor Q of roughness on polarization characteristics and stability S of the polarization characteristics to incident angle.

From the analysis results, it can be concluded that leaves, sand, soil, and glass of natural objects have weak polarizance characteristics, strong depolarization characteristics, and strong retained depolarization characteristics, and their values are close to 1. Therefore, all of them can be approximated as a complete depolarizing system. Artificial target dielectric, smooth steel plate, rough steel plate, camouflage coating, and camouflage cloth have relatively strong polarizance characteristics but relatively weak retained depolarization characteristics, with 1<P_Δ<2. They belong to a retained depolarizing system, and the dielectric can be approximated as a nondepolarizing system. The camouflage coating is a complete polarizing system (Fig. 3 and Table 1). As the roughness increases, P_P, P_D, and P_M of the aluminum plates get smaller. In other words, weaker polarizance characteristics are accompanied by stronger depolarization characteristics. Theoretically, stronger retained depolarization characteristics of the aluminum plates can be obtained, and their values get smaller, which is consistent with the rule in Fig. 5 (d). Under different roughness, with 1<P_Δ<2, all aluminum plates are in the range of the retained depolarizing system. In view of other characteristics, as roughness gets smaller, aluminum plates tend to be a nondepolarizing system, and as the roughness increases, aluminum plates tend to be a complete depolarizing system (Fig. 5).

By converting the degree of polarization into a correlation semidefinite quadratic function, the linear calculation of the reflection process of incident light with different polarization states on the target surface is realized. In view of the problem that the traditional evaluation indexes of the Mueller matrix can only be used to evaluate the polarizance and depolarization characteristics, the retained depolarization characteristics and PΔ are defined, and the polarization characteristics of the target Mueller matrix in different definition ranges are analyzed, so as to realize the comprehensive evaluation of the polarizance and depolarization characteristics of the target by using one index. The proposed index is verified by using polarizers with different extinction ratios and published data. The results show that the index can not only define polarizers with arbitrary extinction ratios but also play a positive role in target recognition during target detection. Finally, the Mueller matrices of three groups of different roughness under different incident angles are measured experimentally. The influence factor Q of the roughness on different polarization characteristicsof the aluminum plates and the stability S of aluminum plate polarization characteristics with the increase in incident angle are defined, and the influence of roughness and incident angle on the target Mueller matrix elements and polarization characteristics is explored. The results show that when the roughness is small, the influence degree on the polarization characteristics of the target Mueller matrix is greater than that under a large roughness, and the influence factor decreases with the increase in the roughness. As the incident angle increases, the stability of the index related to the depolarization of the aluminum plates becomes worse.