## 3 Results and Analysis of Ultraviolet Photon Counting
### Characteristics of Photon Count with Gain and Observation Distance Variations  
The experimental results indicate that the photon counts of the 2 mm, 3 mm, and 5 mm conductors have a consistent trend with the variations in the gain and observation distance of the ultraviolet imaging camera. Therefore, in this study, a conductor with a diameter of 5 mm was taken as an example to investigate the characteristics of photon count variations with changes in the gain and observation distance of the ultraviolet imaging camera. Figure 6 displays the ultraviolet photon count data obtained by varying the observation distance at different voltage levels while keeping the gain constant at 100%. An analysis of Figure 6 reveals that as the observation distance increased, the photon counts significantly decreased. When using ultraviolet detection to monitor corona discharge in electrical equipment, it is often considered that the discharge region of the equipment is much smaller compared to the detection distance. Therefore, the corona discharge source in the equipment being monitored is treated as a point source of light. As the detection distance increases, the energy emitted by the corona discharge source in the equipment gradually attenuates along the propagation path. Consequently, the photon counts obtained during detection decrease as the energy diminishes. These experimental results align with theoretical expectations. By using the least squares method to fit the data points in Figure 6, the fitted function expression for the relationship between ultraviolet photon count and observation distance was obtained, and it is shown in Table 4. In the table, \(P\) represents the ultraviolet photon count, and \(L\) represents the observation distance in meters. In Table 4, it can be observed that the fitted function expressions for photon count as a function of observation distance under different voltage levels have relatively high fitting coefficients. The relationship between the photon count and the observation distance follows an exponential function, with the exponent ranging from \(-0.2616\) to \(-0.2947\) and \begin{table}
\begin{tabular}{c c c} \hline
**Conductor Diameter (mm)** & **Fitting Function Expressions** & **Fit Coefficient** \\ \hline
2 & \(U=-8.1525\times 10^{-6}\times n^{2}+0.4856\times n+2.7028\times 10^{4}\) & 0.9936 \\
3 & \(U=-5.4202\times 10^{-6}\times n^{2}+0.5222\times n+3.8204\times 10^{4}\) & 0.9955 \\
5 & \(U=-3.9799\times 10^{-6}\times n^{2}+0.2592\times n+5.1455\times 10^{4}\) & 0.9966 \\ \hline \end{tabular}
\end{table} 
Table 3: Expression of fitting function between UV photon number and voltage of conductors of different specifications. Figure 6: The relationship between the photon count and the observation distance. with an average value of \(-0.2800\). Thus, the relationship between the ultraviolet photon count and the observation distance under different voltages satisfies Equation (3). \[P=ae^{bL} \tag{3}\]  
In the equation, \(P\) represents the ultraviolet photon count, \(L\) represents the detection distance, and \(a\) and \(b\) are constant coefficients. The value of coefficient \(a\) is related to the voltage magnitude (corona intensity) at the measured point, while coefficient \(b\) is set as the average of the exponent values from the fitted function expressions under different voltages in Table 4, which is \(-0.2800\).