## 4 Results and Analysis of Spot Area Detection
### Characteristics of the Spot Area in Relation to Gain and Observation Distance Variations  
Figure 10 shows the variation of the spot area with changing observation distance while keeping the gain at 100%. Similar to the variation pattern of the UV photon count, the spot area decreased exponentially with increasing observation distance. Figure 10: The variation trend of the discharge region area at different detection distances. Figure 9: The relationship between the spot area and the voltage for a 5 mm diameter conductor. Using the least squares method, the data points in Figure 10 were fitted, and the fitted function expression for the spot area as a function of the observation distance is shown in Table 5. In the table, \(S\) represents the spot area in pixels, and \(L\) represents the observation distance in meters. From Table 5, it can be observed that the fitted function expressions for the discharge area as a function of the observation distance have high fitting coefficients for each voltage level. The spot area exhibited an exponential relationship with the observation distance. Similarly to the process of Equations (3)\(\sim\)(6), we can obtain the correction of the spot area, with \(S\) at the actual observation distance to the spot area and \(S_{0}\) at the reference observation distance. \[S_{0}=Se^{0.2504(L-L_{0})} \tag{9}\]  
In the above equation, \(L\) is the actual observation distance, \(S\) is the spot area obtained from the actual observation, \(L_{0}\) is the reference distance in this paper, which is taken as 2 m in this paper, and \(S_{0}\) is the corrected spot area. Keeping the observation distance constant at 2 m, and setting the gain of the UV detector between 50 and 100, the changed in the UV spot area with gain under different voltages could be observed, as shown in Figure 11.  
Comparing Figures 7 and 11, it can be observed that under the same experimental conditions, the effects of gain on the photon count and spot area were different. The spot area shows a monotonous increase with the increase in the instrument gain. However, the photon count does not follow the same trend. When the gain increased from low to high, it did not monotonously increase with the gain. Instead, it exhibited a pattern of initial increase, followed by a decrease, and then an increase again. By observing the different characteristics of the photon count and spot area with respect to the instrument gain, it can be concluded that when the corona discharge is relatively stable, if the spot area is used as the reference factor for detection, the detection results will correspond directly to the instrument gain. If the photon count is used as the reference fac  
Figure 11: The variation of the discharge area with respect to the gain under different applied voltages. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Voltage (kV)** & **Fitted Function Expression** & **Fit Coefficient** \\ \hline
51.5 & \(S(L)=3268e^{-0.2451L}\) & 0.9842 \\
52.5 & \(S(L)=7543e^{-0.2528L}\) & 0.9658 \\
53.5 & \(S(L)=8923e^{-0.2339L}\) & 0.9704 \\
54.5 & \(S(L)=17173e^{-0.2698L}\) & 0.9638 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The fitted relationship expression between the spot area and the observation distance at different voltages. possible to have similar detection results at different instrument gains. Therefore, more accurate results can be obtained by combining the two to detect discharge. By using the least squares method to fit the data points in Figure 11, the fitting function expression for the relationship between the spot area (\(S\)) and the gain (\(g\)) was obtained and is shown in Table 6.  
From Table 6, it can be seen that the fitting coefficients of the function expressions for the photon count with respect to the observation distance are relatively high for each voltage level. The photon count is related to the observation distance in a power function relationship.