## 2 Basic Principle of Polarization Imaging  
Polarization is a common natural phenomenon, and unlike traditional infrared imaging based on radiance representation, polarization imaging systems use the Stokes vector \(S=\left[I,Q,U,V\right]^{T}\) to represent polarized light [8], where \(I\) is the total intensity of the light wave; \(Q\) is the intensity difference between linearly polarized light in parallel and perpendicular directions; \(U\) is the intensity difference of linearly polarized light in the direction \(+\frac{\pi}{4}\) and \(-\frac{\pi}{4}\); and \(V\) is the difference between the right-hand circular polarization component and the left-hand circular polarization component. In general, most of the polarization phenomena in nature are linearly polarized, and the \(V\) component is negligible. The first three Stokes parameters can be derived using the different polarization directions of \(0^{\circ}\), \(60^{\circ}\), and \(120^{\circ}\):  
\[\left\{\begin{array}{l}I=\frac{2}{3}(I(0^{\circ})+I(60^{\circ})+I(120^{\circ }))\\ Q=\frac{2}{3}(2I(0^{\circ})-I(60^{\circ})-I(120^{\circ}))\\ U=\frac{2}{\sqrt{3}}(I(60^{\circ})-I(120^{\circ}))\end{array}\right. \tag{1}\]  
The degree of polarization can be represented by the Stokes vector as:  
\[P=\sqrt{\frac{Q^{2}+U^{2}}{I^{2}}} \tag{2}\]  
That is, it is the ratio of polarized light intensity to total light intensity. The polarization angle is denoted as:  
\[A=\frac{1}{2}\text{arctan}\bigg{(}\frac{U}{Q}\bigg{)} \tag{3}\]  
Reflection and radiation play an important role in polarization. This phenomenon can be described by [PERSON]'s formula [9; 10]:  
\[R_{P}=\frac{\left|E_{p}^{r}\right|^{2}}{\left|E_{p}^{i}\right|^{2}}=\left| \frac{n_{2}\cos\theta_{1}-n_{1}\cos\theta_{2}}{n_{2}\cos\theta_{1}+n_{1}\cos \theta_{2}}\right|^{2} \tag{4}\]  
\[R_{S}=\frac{\left|E_{s}^{r}\right|^{2}}{\left|E_{s}^{i}\right|^{2}}=\left| \frac{n_{1}\cos\theta_{1}-n_{2}\cos\theta_{2}}{n_{1}\cos\theta_{1}+n_{2}\cos \theta_{2}}\right|^{2} \tag{5}\]  
\(R_{p}\) and \(R_{s}\) represent the reflectance of parallel and vertical components, respectively. \(E_{p}^{i}\) and \(E_{s}^{i}\) are the electric field intensity of incident light in a parallel direction and vertical direction, respectively. Furthermore, \(E_{P}^{r}\) are \(E_{s}^{r}\) the electric field intensity of the reflected light in parallel and vertical directions, respectively. \(n_{1}\) is the refractive index of the incident medium, and \(n_{2}\) is the refractive index of the transmitted medium. In addition, \(\theta_{1}\) is the angle of incidence, and \(\theta_{2}\) is the angle of refraction. The degree of reflection polarization is defined as:  
\[P_{R}=\left|\frac{R_{P}-R_{S}}{R_{P}+R_{S}}\right| \tag{6}\]  
According to the law of conservation of energy and Kirchhoff's law, when the transmittance is negligible, the sum of the reflectance R and the emission rate \(\varepsilon\) equals 1 [11,12]:  
\[\left\{\begin{matrix}\varepsilon_{S}=1-R_{S}\\ \varepsilon_{P}=1-R_{P}\end{matrix}\right. \tag{7}\]  
\(\varepsilon_{P}\) and \(\varepsilon_{s}\) are represented as the parallel and vertical emission rates, respectively. The polarization degree \(P_{E}\) generated by the emission is defined as:  
\[P_{E}=\left|\frac{\varepsilon_{P}-\varepsilon_{S}}{\varepsilon_{P}+\varepsilon _{S}}\right|=\left|\frac{R_{P}-R_{S}}{2-R_{P}-R_{S}}\right| \tag{8}\]