## 3 Experimental Results and Analysis
### Detection of Atmospheric Turbulence  
#### 3.2.1 Kolmogorov Turbulence Detection  
As mentioned above, the scintillation index \(\beta_{I}^{2}\) is received by Mie-scattering lidar when detecting atmospheric turbulence is the spherical wave scintillation index caused by the turbulence effect of the transmitting path. First, the scintillation effect and turbulence profile described by the Kolmogorov theory were detected and analyzed. The experiment was conducted from August to September 2022, and the observation lasted for approximately 20 days. Most of the time, the weather was clear and the visibility was high, and there were no obvious clouds in the detection path. Due to the strong sky background light noise received via lidar during the day, the observation was only conducted after 20:00 LST (local standard time) every night, lasting until 22:00 LST, for two hours a day. A high-speed fluorescent oscilloscope was used to collect the return signal received via lidar. Figure 5 shows the variation in return signal at a height in the range of 0-4.5 km with a single pulse and a height resolution of 37.5 m.  
The change in scintillation index in the vertical transmission path was calculated using the collected Mie-scattering lidar return signal. In the vertical direction, the turbulence intensity of the far-field signal is very weak. In the process of laser transmission, the amount of light intensity flicker caused by the turbulence of far-field signals will be relatively small. Moreover, the background sky light noise, granular noise, amplifier noise, and other noise will cause a fluctuation in light intensity changes, and the calculated scintillation index is not only caused by turbulence changes. Therefore, vertical detection by Mie-scattering lidar requires a high signal-to-noise ratio to obtain an accurate far-field signal. In this study, the Mie-scattering lidar return signal was denoised by the sliding window average method to some extent. As can be seen from Figure 5, the return signal of the Mie-scattering lidar method used in the experiment has a low signal-to-noise ratio after a height of 2500 m. Due to the lidar field of view overlap below 600 m to ensure detection accuracy, after careful consideration, the data within the 600-2000 m height range were analyzed in this study. Figure 5: Variation in Mie-scattering lidar return signal with height. Usually, the scintillation index \(\beta_{I}^{2}\) is calculated by Equation (2). In practice, the measured value is the voltage signal, and the signal voltage \(U\) is directly proportional to the incident signal light intensity \(I\), so Equation (2) can be transformed into voltage form [34]:  
\[\beta_{I}^{2}=\frac{\sigma_{U}^{2}}{\left\langle{U}\right\rangle^{2}}=\frac{ \left\langle{U^{2}}\right\rangle-\left\langle{U}\right\rangle^{2}}{\left\langle {U}\right\rangle^{2}} \tag{6}\]  
Therefore, the scintillation index is calculated by measuring the mean \(<\)\(U\)\(>\) and the variance \(\sigma_{U}^{2}\) of the signal voltage and by substituting them into Equation (6). The scintillation index of different heights was calculated by the return signal. Figure 6 shows the variation in the scintillation index with height over three different time periods, and the height resolution is 37.5 m. The red line refers to the fitted curve of the detected scintillation index. In the process of calculating the scintillation index, due to the existence of the lidar overlap area and considering that the normalization should be carried out at the place where the return signal is the strongest, according to the research and analysis of multiple groups of measured data, the normalized height was finally specified as 600 m, and the diameter of iris diaphragm of the telescope was selected as \(d_{0}\) = 0.5 mm. As can be seen from Figure 6, the scintillation index basically conforms to the trend of gradually increasing with the increase in height. In this study, the scintillation index profile was used to obtain the atmospheric refractive index constant profile \(C_{n}^{2}(h)\).