## 2 Introduction to the Aerial Camera
### Thermal Network Model of the Aerial Camera  
The physical model of the aerial camera is divided into 24 nodes. In order to simplify the thermal network model, structures such as screws, holes, and threads, which have minimal effect on the temperature, are disregarded. Components exhibiting high thermal conductivity, such as the lens barrel, inner frame, and outer frame, are sparsely divided into nodes. The lens is subject to significantly higher temperature differences in the radial direction relative to the axial direction. Consequently, the nodes of the lens are densely distributed along the radial direction. The nodes are identified based on their consolidated thermal characteristics, including temperature and heat capacity. The original thermal network of the aerial camera is structured by linking nodes through thermal resistances, representing conduction, contact, convection, or radiation, with parallel or series arrangements. By employing [PERSON]'s current law and [PERSON]'s law, the thermal balance equations for each node can be established as follows [30]:  
\[(mc)_{i}\frac{\mathrm{d}T_{i}}{\mathrm{d}\tau}=\sum_{j=1}D_{ij}(T_{j}-T_{i})+ \sum_{j}E_{ij}(T_{j}^{4}-T_{i}^{4})+\sum_{j}H_{ij}(T_{j}-T_{i})+q_{i} \tag{1}\]  
where \((mc)_{i}\) is the thermal capacity; \(T_{i}\) and \(T_{j}\) are the temperature of adjacent nodes, respectively; \(D_{ij}\), \(E_{ij}\), and \(H_{ij}\) are the thermal conduction, radiation, and convection coefficients; and \(q_{i}\) is the total heat source of the node, including the internal heat source and external heat flow into the node. For the heat conduction between two nodes with an interface, \(D_{ij}\) can be expressed as  
\[D_{ij}=\frac{1}{\frac{L_{i}}{\lambda_{i}A_{i}}+\frac{1}{h_{c}A_{h}}+\frac{L_{ j}}{\lambda_{j}A_{j}}} \tag{2}\]  
where \(\lambda_{i}\), \(\lambda_{j}\), \(L_{i}\), \(L_{j}\), and \(A_{i}\), \(A_{j}\) are the thermal conductivity, effective thermal conductivity distance, and effective thermal conductivity area of adjacent nodes, respectively, and \(h_{c}\) and \(A_{h}\) are the contact heat transfer coefficient and contact area of adjacent nodes, respectively. \(E_{ij}\) is calculated as follows:  
\[E_{ij}=\frac{F_{ij}A_{i}\sigma}{\frac{1}{\dot{\epsilon}_{i}}+\frac{1}{\dot{ \epsilon}_{j}}-1} \tag{3}\]  
where \(F_{ij}\) is the radiation angle coefficient between nodes \(i\) and \(j\), \(\sigma\) is the Stefan-Boltzmann constant (\(\sigma\) = 5.67 \(\times\) 10\({}^{-8}\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-4}\)), and \(\varepsilon\) is the emissivity. The expression for \(H_{ij}\) is  
\[H_{ij}=\frac{1}{h_{ij}A_{i}} \tag{4}\]  
where \(h_{ij}\) is the convective heat transfer coefficient between nodes \(i\) and \(j\), and \(A_{i}\) is the effective thermal conductivity area. \begin{table}
\begin{tabular}{c c} \hline Flight attitude & 9000 m \\ \hline Temperature of ambient air & \(-\)38.5 \({}^{\circ}\)C \\ \hline Cruising speed & 150 m/s \\ \hline Temperature requirement of optical system & (20 \(\pm\) 5) \({}^{\circ}\)C \\ \hline Radial and axial temperature gradients & \textless{5} \({}^{\circ}\)C \\ \hline Thermal control power & \textless{100 W} \\ \hline \end{tabular}
\end{table} 
Table 1: Thermal environment conditions and thermal control requirements. The total thermal resistance \(R_{\Sigma}\) of a parallel or series heat transfer between two or more nodes can be expressed as follows, respectively:  
\[\frac{1}{R_{\Sigma}}=\frac{1}{R_{ij}^{(1)}}+\frac{1}{R_{ij}^{(2)}}+\cdots\frac{1 }{R_{ij}^{(n)}} \tag{5}\]  
\[R_{\Sigma}=R_{ij}^{(1)}+R_{ij}^{(2)}+\cdots+R_{ij}^{(n)} \tag{6}\]  
where \(R_{ij}^{(n)}\) is the thermal resistance of the \(n\)-th heat transfer path between nodes \(i\) and \(j\). There are four distinct types of thermal resistance, namely \(R_{\mathrm{cd}}\), \(R_{\mathrm{ct}}\), \(R_{\mathrm{cv}}\), and \(R_{\mathrm{rad}}\). These correspond to the conductive, contact, convective, and radiation thermal resistances, respectively.