## 4 Experimental Validation
### Ground Simulation Facility
#### 4.1.2 Electric Charge Generated by UV LED  
Since the dominant spectral component of blue jets is distributed over the ultraviolet band, an appropriate UV LED is chosen to imitate blue jets. Based on the characteristics of the selected UV LED, designing the ground experimental facility begins with choosing operational parameters for UV LEDs, that is, the distance between UV LED and the pin-hole lens (\(D_{\text{LED}}\)) and the required radiant power for the UV LED (\(P_{\text{LED}}\)), respectively. These parameters permit the electric charge due to the UV LED to match the total electron count caused by the actual TLE as estimated in Equation (1). For this reason, the amount of electric charge output by the MaPMT due to the UV LED should be estimated first as accurate as possible. The radiant power emission of the UV LED can be obtained from the geometry relationship. The geometry of the UV LED and the detector with a pin-hole lens is illustrated in Figure 11. The circular area of the light cone at \(D_{\text{LED}}\) is calculated using the beam angle of the UV LED as in Equation (2). \[A_{\text{spot}}=\pi\left(D_{\text{LED}}\tan\frac{\theta}{2}\right)^{2}, \tag{2}\]  
where \(\theta\) is the beam angle of the UV LED. Although the UV LED delivers most of the radiant power to the front, but here it is assumed that the UV LED is regarded as a point light source and emits  
Figure 10: Detection of TLEs near the Earth’s horizon. The line of sight angle to the TLE is computed as 67.3\({}^{\circ}\) by simple trigonometry, which is within the observation range of the TLE observation system. The distance to the TLE is then denoted by \(D_{\text{limb}}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbols** & **Parameters** & **Value** & **Unit** \\ \hline Q\({}_{\text{TLE}}\) & The number of UV photons emitted from a TLE & 10\({}^{23}\) & count \\ \(\phi\) & Aperture of pin-hole lens & 0.3 & mm \\ \(h_{\text{Sat}}\) & Altitude of satellite & 575 & km \\ \(h_{\text{TLE}}\) & Altitude of TLE source & 40 & km \\ \(T\) & Duration of the TLE & 10 & ms \\ \(t_{s}\) & Sampling time & 166 & \(\mu\)s \\ \(\psi\) & Quantum efficiency of MaPMT @405 nm & 25 & \% \\ \(S\) & Radiant sensitivity of MaPMT & 80 & mA/W \\ \(G\) & Gain of MaPMT @-800 V & \(3\times 10^{5}\) & \\ \(G_{\text{min}}\) & Minimum Gain of MaPMT @-500 V & \(9\times 10^{2}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters for calculation of electric charge produced by TLE emission in space. light in three-dimensional space. Hence, the equivalent solid angle of the UV LED beam, \(\Omega_{\text{LED}}\), is determined by the ratio of the total irradiated area of a sphere at the radius of \(D_{\text{LED}}\) to the area of the light spot \(A_{\text{spot}}\). \[\Omega_{\text{LED}}=\frac{4\pi A_{\text{spot}}}{4\pi D_{\text{LED}}^{2}}. \tag{3}\]  
Note that the full solid angle is known to be \(4\pi\). The radiant intensity, defined by radiant power emitted per unit solid angle, can be utilized to eliminate the effect of power reduction over distance. Thus by ignoring the attenuation of radiant power due to the interference of the medium, the actual radiant power received at a given distance is directly computed using the solid angle of the corresponding irradiated area. The radiant intensity of the UV LED is calculated as Equation (4),  
\[I_{\text{LED}}=\frac{P_{\text{LED}}}{\Omega_{\text{LED}}}, \tag{4}\]  
where \(P_{\text{LED}}\) is the radiant power emitted by the UV LED. The actual radiant power received by the MaPMT is due to the light passing through the pin-hole lens.