## 2 Relevant Theoretical Basis  
### Principles of Polarization Imaging in Electroluminescence  
Crystal silicon solar photovoltaic cells typically exhibit an N+P homojunction structure, characterized by the addition of a heavily doped N-type semiconductor layer atop a P-type silicon substrate. In this configuration, the cell's reverse side functions as the positive electrode, while the front side serves as the negative electrode. The outermost layer of the cell is an anti-reflective coating, designed to minimize energy losses resulting from light reflection during operational conditions. According to the composition of the photovoltaic cell depicted in Figure 1, it can be discerned as a PN junction structure. When a forward voltage bias is applied to photovoltaic cells, the electrons and holes in the P-N junction within the cell undergo radiative recombination, emitting near-infrared light. Should there be defects such as impurities, deposition or dislocations present in the silicon material, electrons and holes will preferentially recombine at these sites, consequently reducing or preventing near-infrared light emission. Similarly, if there are issues with the fabrication process of photovoltaic cells, such as silicon wafer fractures or other detrimental conditions, these may lead to problems with electrical injection, subsequently diminishing the electroluminescence intensity of the affected areas. In the electroluminescence image, these areas will manifest as darker regions. Light is a transverse wave whose vibration plane is perpendicular to its propagation direction. It exhibits several characteristics, including propagation direction, intensity and wavelength. Moreover, it possesses polarization characteristics. Polarized light can be categorized into fully polarized and partially polarized varieties, with fully polarized light further subdivided into circular and linear polarization types. Figure 2 shows the difference between unpolarized natural light and linearly polarized light: the light emanating from the source in the figure exhibits arbitrary vibration directions, thus classifying it as unpolarized light. Upon passage through a polarization filter, since only light oscillating along a specific direction is permitted to transmit, light with other vibration orientations is either absorbed or reflected. Consequently, the transmitted light becomes completely linearly polarized. The Stokes vector is usually used to describe the polarization of light. It is assumed that the Stokes vector of the optical signal entering the imaging observation system with the polarization azimuth of \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\) and \(135^{\circ}\) is S [18]. Then there is:  
\[S= \begin{pmatrix}S_{0}\\ S_{1}\\ S_{2}\\ S_{3}\end{pmatrix} = \begin{pmatrix}I_{0}+I_{45}\\ I_{0}-I_{90}\\ I_{45}-I_{135}\\ 0\end{pmatrix} = \begin{pmatrix}I_{90}+I_{135}\\ I_{0}-I_{90}\\ I_{45}-I_{135}\\ 0\end{pmatrix}  \tag{1}\]  
Figure 1: Structure of photovoltaic cells. Figure 2: Polarized light imaging schematic diagram. In the formula, \(S_{0}\) represents the total intensity of light, \(S_{1}\) represents the intensity of horizontal polarized light, \(S_{2}\) represents the intensity of diagonal polarized light, and \(S_{3}\) represents the intensity of circular polarized light. In general, the circular polarization component is very small and can be ignored. \(I_{0}\), \(I_{45}\), \(I_{90}\), and \(I_{135}\) represent the intensity of the light detected by a polarization observation system with a polarization azimuth of \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), or \(135^{\circ}\), respectively. According to Formula (1), the polarization degree of the incident light can be determined as [18]:  
\[DOP=\sqrt{S_{1}^{2}+S_{2}^{2}}/S_{0}^{2} \tag{2}\]  
Figure 3 presents the intensity and polarization degree images obtained through electro-luminescence polarization imaging analysis of scratch defects on photovoltaic cells.