## 3 Experimental Results and Analysis
### Detection of Atmospheric Turbulence
#### 3.2.1 Kolmogorov Turbulence Detection
The influence of internal and external scales of atmospheric turbulence was not considered, and the power spectrum of atmospheric turbulence is the Kolmogorov spectrum. Therefore, on the vertical detection path, the scintillation index was calculated by Equation (5), and the Gaussian beam emitted by lidar is regarded, approximately, as a spherical wave. Figure 6: Variation in scintillation index with height. (**a**) Variation in scintillation index with height at 20:30 on 4 September 2022. (**b**) Variation in scintillation index with height at 20:30 on 5 September 2022. (**c**) Variation in scintillation index with height at 20:30 on 6 September 2022. In this study, the Newton iteration method is used to invert the \(C_{n}^{2}\) profile. The specific operation is as follows: first, \(C_{n}^{2}\) is divided into n segments in the whole height range of 0-L, and the corresponding interval of each segment is \(\Delta h\). Second, with the idea of stratification, assuming that \(C_{n}^{2}\) in the height of each segment is the same constant, \(C_{n}^{2}\) can be extracted from Equation (5) when calculating the turbulence intensity in each segment, and then \(C_{n}^{2}\) in the 0-\(\Delta h\) interval can be obtained, namely \(C_{n1}^{2}\). Third, when combined with \(C_{n1}^{2}\) and using the iterative algorithm, we can calculate \(C_{n}^{2}\) in the height range of \(\Delta h\sim\)2\(\Delta h\), that is, \(C_{n2}^{2}\). In this way, the \(C_{n}^{2}\) profile of the entire detection path can be obtained. Figure 7 shows the Kolmogorov turbulence \(C_{n}^{2}\) profiles at three different times obtained using the stratified iterative inversion algorithm combined with the scintillation index, as shown in Figure 6.  
As can be seen from Figure 7, the Kolmogorov turbulence intensity \(C_{n}^{2}\) profile obtained from inversion presents fluctuation changes with an increase in altitude, and the intensity of the upper air turbulence is small, belonging to weak turbulence [35]. Within the detection range, a turbulent layer with relatively weak turbulence intensity appears at a height of 600-800 m. Subsequently, the turbulence intensity increases with the increase in height and gradually becomes stable, which is more consistent with the general change law of turbulence intensity with height. Then, we change the iris diaphragm diameter \(d_{0}\) to detect again. Here, three iris diaphragm sizes are selected for comparison: the iris diaphragm diameters \(d_{0}\) are 1.0 mm, 0.8 mm, and 0.5 mm, respectively. The variation in the corresponding scintillation index and Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles are shown in Figures 8 and 9, respectively. Figure 7: Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles. (**a**) Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles at 20:30 on 4 September 2022. (**b**) Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles at 20:30 on 5 September 2022. (**c**) Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles at 20:30 on 6 September 2022. Figure 8: Scintillation index with height for different iris diaphragm diameters. (**a**) Variation of scintillation index with height when iris diaphragm diameter is 1.0 mm. (**b**) Variation of scintillation index with height when iris diaphragm diameter is 0.8 mm. (**c**) Variation of scintillation index with height when iris diaphragm diameter is 0.5 mm. Figure 9: Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles with different iris diaphragm diameters. (**a**) Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles when iris diaphragm diameter is 1.0 mm. (**b**) Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles when iris diaphragm diameter is 0.8 mm. (**c**) Kolmogorov turbulence intensity \(C_{n}^{2}\) profiles when iris diaphragm diameter is 0.5 mm. As can be seen from Figure 8, the smaller the iris diaphragm diameter \(d_{0}\), the greater the resulting scintillation index.