## 5 Experimental Results
### Digital Images of the Discharges  
Long exposure photographs of the discharges (32 s) were taken to increase the number of photons reaching the sensitive elements of the image sensors and thus the sensitivity of the method. Figure 5 summarizes some of the photographs of the discharges acquired under different experimental conditions, that is, under variable pressures within the range of 100-10 kPa and different applied voltages. It is seen that, for a fixed pressure, the intensity of the discharge increases with the applied voltage. From the photographs shown in Figure 5, it is deduced that the intensity of the images of the discharges increases with the applied voltage, that is, with the electric energy dissipated by the discharges. However, this correlation must be validated using experimental data acquired with the voltage and current probes and by calculating the intensity of the discharges acquired by the CMOS image sensor. This section shows that the electric energy dissipated by the discharges is related to the intensity of the digital images. The relationship between the intensity of the images and the electric energy dissipated by the discharges assumed and evaluated in this section is as follows:  
\[\underbrace{\sqrt{\sum\limits_{j=1}^{discharges}P_{discharges}(j)\cdot N\cdot \Delta t}}_{\sqrt{E_{discharges}}}\sim\underbrace{\frac{\sum\limits_{i=1}^{m* }\sum\limits_{j=1}^{n*}[I_{g_{g_{g_{g}}}(i,j)-B_{g_{g_{g}}}(i,j)]}}{n*m*255}100} _{INT_{normalized}}, \tag{9}\]  
The adequacy of (9) is assessed in the next paragraphs. According to (9), the square root of the energy dissipated by the discharges must be proportional to the normalized intensity of the images. It is based on the fact that the amplitude of the signal detected by any individual sensitive element of the CMOS sensor is directly related to the intensity of the light spreading over the sensor. In addition, \(INT_{normalized}\) can be used as a discharge severity indicator, providing values from 0 to 100, indicating the degree of severity. Figure 5(a) summarizes the experimental relationships between \(INT_{normalized}\) and the applied voltage, while Figure 5(b) shows the experimental measurements obtained with the photometric (\(INT_{normalized}\)) and electric (\(E_{discharges}\)[0.5]) methods and their linear fittings at different operating pressures characteristic of aeronautical environments. The experimental results presented in Figure 6a show a linear behavior between \(\mathit{INT}_{\mathit{normalized}}\) and the applied voltage. Since the intensity of the discharges increases with the applied voltage, these results show that \(\mathit{INT}_{\mathit{normalized}}\) is related to the severity of the discharges. The results presented in Figure 6b show a linear behavior between \(\mathit{INT}_{\mathit{normalized}}\) and \(\mathit{E}_{\mathit{displayes}}\)[0.5], thus validating the hypothesis expressed in (9). Table 1 summarizes the parameters of the linear fittings between \(\mathit{INT}_{\mathit{normalized}}\) and \(\mathit{E}_{\mathit{displayes}}\)[0.5], where high values of the coefficient of determination \(R^{2}\) can be seen, thus indicating a high correlation between \(\mathit{INT}_{\mathit{normalized}}\) and \(\mathit{E}_{\mathit{displayes}}\)[0.5]. Therefore, it can be concluded that the electric energy dissipated by the discharges is proportional to the intensity of the digital images. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Parameters** & **100 kPa** & **80 kPa** & **60 kPa** & **40 kPa** & **20 kPa** & **10 kPa** \\ \hline \multirow{3}{*}{**ac supply**} & \(\mathit{INT}_{o}\) & \(-0.3372\) & \(-0.3504\) & \(-0.8642\) & \(0.1207\) & \(2.3452\) & \(7.3545\) \\  & \(k\) & 556.52 & 833.43 & 1070.4 & 1156.4 & 1378.8 & 1511.3 \\ \cline{1-1}  & \(R^{2}\) & 0.9936 & 0.9919 & 0.9982 & 0.9896 & 0.9909 & 0.9640 \\ \hline \end{tabular}
\end{table}