## 3 Results and Analysis of Ultraviolet Photon Counting
### Characteristics of Photon Count with Gain and Observation Distance Variations
Therefore, the ultraviolet photon count measured at different observation distances under a reference gain can be corrected to the ultraviolet photon count measured at a distance of 2 m. The specific process is as follows: for the same corona discharge light source, the relationship between the actual measured photon count \(P\) and the distance \(L\) is given by Equation (4):  
\[P=ae^{-0.28L} \tag{4}\]  
The relationship between the corrected photon count \(P_{0}\) and the distance \(L_{0}\) can be expressed as follows:  
\[P_{0}=ae^{-0.28L_{0}} \tag{5}\]  
By combining Equations (4) and (5), we can obtain:  
\[P_{0}=Pe^{0.28(L-L_{0})} \tag{6}\]  
In the above equation, \(L\) is the actual observation distance, \(P\) is the photon count obtained from the actual observation, \(L_{0}\) is the reference distance, which is taken as 2 m in this paper, and \(P_{0}\) is the corrected photon count. Based on Equation (6), the ultraviolet photon count measured at any detection distance can be corrected to the reference detection distance. Using Equation (6) to correct the ultraviolet photon count to the reference detection distance, and then applying the fitted function relationship between the voltage and the ultraviolet photon count for the 5 mm conductor, we can determine the corresponding average ultraviolet photon count at the measured observation distance under the reference gain and the measurement distance, as well as the corresponding conductor voltage value, which provides a reference method for comparing the discharge intensity at different observation distances. By keeping the observation distance constant at 2 m and setting the gain of the ultraviolet detector within the range of 50 to 100, the variation in the ultraviolet photon count with respect to the gain at different voltages was obtained, as shown in Figure 7.  
Analyzing Figure 7, the following characteristics of the photon count as a function of gain can be observed. With the increase in gain, the photon count did not monotonically increase or decrease. Instead, it underwent a process of initially increasing, then decreasing, and finally increasing again. When the instrument gain was low, with the increase in the instrument gain, some corona discharge signals that were not easily detectable at a low gain became measurable. The bright spots at the corona discharge locations gradually increased, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Voltage (kV)** & **Fitting Function Expressions** & **Fit Coefficient** \\ \hline
51.5 & \(P=5857e^{-0.2769L}\) & 0.9891 \\
52.5 & \(P=8825e^{-0.2616L}\) & 0.9704 \\
53.5 & \(P=14322e^{-0.2867L}\) & 0.9786 \\
54.5 & \(P=18479e^{-0.2947L}\) & 0.9625 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The fitted relationship expression between the ultraviolet photon count and the observation distance at different voltages. leading to a certain increase in the photon count. The corresponding gain ranged from 50% to 60%. However, when the instrument gain was set high and further increased, the discrete corona discharge spots on the screen were enlarged and merged with each other, forming a larger light spot. This affected the identification of the photon counts, resulting in a decrease in the photon count rather than an increase. The corresponding gain ranged from 60% to 80%. Therefore, from the experimental results, it can be seen that the detection performance was best when the gain was set to 60%.