## 2 Theory and Methods  
### Theoretical Basis of Stray Light Analysis  
In addition to the imaging rays in the optical system, other non-imaging rays distributed on the imaging surface and rays reaching the imaging surface via the abnormal optical path are called stray light. Stray light usually reduces the image plane contrast of the optical system, thereby reducing the optical transfer function and signal-to-noise ratio. In addition, the stray light formed by the abnormal light transmitted to the imaging surface through the lens and light shield is the main source of external stray light for the aerial camera system. Stray light caused by scratches, bubbles on the outer surface of the lens, notches around the outer edge of the lens, and unintentional fine fragments during the assembly of the camera lens are the main sources of external stray light in the aerial camera system.  
The basic energy transfer equation in radiant heat transfer theory is to transfer energy between any two surface elements in the optical system, which is the physical basis of the stray light analysis. Then, the related physical quantities in the transfer equation are connected to analyze the stray light in different ways.  
As shown in Figure 1, \(dA_{s}\) and \(dA_{c}\) represent the two arbitrary facets in the optical system. \(r\) represents the center distance. \(\theta_{s}\) and \(\theta_{c}\) represent the angle between the connection of the normal of any two facets and the center of the two facets, respectively. \(L_{s}(\phi_{0},\theta_{0})\) represents the amplitude of \(dA_{s}\). The radiant flux received by \(dA_{c}\) and the radiant flux emitted from \(dA_{s}\) are given by Equation (1):\[\begin{array}{ll}d\phi_{c}&=L_{s}(\phi_{0},\theta_{0})\cos\theta_{s}dA_{s}d\Omega_ {s}\\ &=\frac{L_{s}(\phi_{0},\theta_{0})\cos\theta_{s}dA_{s}\cos\theta_{s}dA_{c}}{2}\\ &=BRDF(\phi_{i},\theta_{i},\phi_{0},\theta_{0},\lambda)d\phi_{0}GCF(\theta_{s},\theta_{c})\end{array} \tag{1}\]  
where \(BRDF(\phi_{i},\theta_{i},\phi_{0},\lambda)\) represents the bidirectional reflection distribution function of the diffuse reflection characteristics. It is the ratio of the surface reflection amplitude brightness \(L_{s}(\phi_{0},\theta_{0},\lambda)\) and the incident amplitude brightness \(E_{s}(\phi_{i},\theta_{i},\lambda)\), as shown in the equation below:  
\[BRDF(\phi_{i},\theta_{i},\phi_{0},\lambda)=\frac{L_{s}(\phi_{0},\theta_{0}, \lambda)}{E_{s}(\phi_{i},\theta_{i},\lambda)} \tag{2}\]  
\(GCF(\theta_{s},\theta_{c})\) reflects the projection angle of \(dA_{s}\) to \(dA_{c}\) stereo, which can be obtained by:  
\[GCF(\theta_{s},\theta_{c})=\frac{\cos\theta_{s}dA_{c}\cos\theta_{c}}{r^{2}} \tag{3}\]  
It is clear that the luminous flux received by \(dA_{c}\) is directly related to \(d\phi_{s}\), \(BRDF\), and \(GCF(\theta_{s},\theta_{c})\) by Equation (3). Therefore, three methods are commonly used to reduce the stray light flux received by reducing the bidirectional reflection distribution function (BRDF) on the surface of the material, the incident light energy of stray light or the outgoing radiation flux \(d\theta_{s}\) of the upper surface, and the projection solid angle of the surface source \(dA_{s}\) and the receiving surface \(dA_{c}\).