## 3 Experimental Results and Analysis  
### Light Intensity Distribution  
Random fluctuations in the atmospheric refractive index lead to random fluctuations in laser beam intensity. As a specific random process, light intensity fluctuation can be quantitatively described by the probability density distribution of light intensity, and the probability density distribution is also the most basic method to describe the statistical characteristics of light intensity fluctuation. The working principle of Mie-scattering lidar is to obtain the scintillation index of the beam by analyzing the intensity fluctuation in the received return signal and then obtain the atmospheric turbulence intensity information by inversion. Therefore, it is of great significance to study the statistical characteristics of the light intensity fluctuation in the return signal to detect atmospheric turbulence using Mie-scattering lidar and to improve the working performance of the lidar. A large number of theoretical and experimental studies have shown that, under weak turbulence fluctuation conditions, the probability density distribution of signal light intensity fluctuations meets the log-normal distribution; that is, the logarithmic intensity follows the normal distribution [33]. In order to verify whether the Mie-scattering lidar method adopted in this study meets this conclusion, a statistical analysis of the light intensity fluctuations in the return signal received via Mie-scattering lidar in the vertical detection direction was carried out, and the actual probability distribution of light intensity was fitted. The built Mie-scattering lidar is used to measure turbulence in the vertical direction. For the vertical detection path, the atmospheric turbulence intensity varies with height, so obtaining the probability density distribution of the back-wave light intensity signal can provide a theoretical basis for the inversion of the atmospheric refractive index structure constant. The wavelength of the laser source is 532 nm, and the emission frequency is 10 Hz. As the probability density distribution of light intensity is a statistical feature of light intensity fluctuation, a large sample size is required. In this paper, 10,000 sample points composed of 10,000 pulses were analyzed as a group. By taking the 1.5 km transmission path as an example, the probability distribution characteristics of the light intensity received via Mie-scattering lidar were analyzed. First, the data collected in the experiment were normalized to make the average logarithmic light intensity (after normalization) 0, that is, \(<\)_ln1\(>\)_ = 0. The signal collected by Mie-scattering lidar is the electrical signal after photoelectric conversion, which has a linear relationship with the light intensity signal. Therefore, the optical signal can be replaced by the electrical signal characteristics, and the statistical characteristics of the optical signal can be obtained by analyzing the electrical signal. The specific normalization method is as follows: after taking the logarithm, calculate the average value of the original light intensity data; then, subtract the minimum value from the maximum value of the log light intensity, and finally, subtract the average value from the log light intensity and divide by the difference between the maximum value and the minimum value to obtain the normalized log light intensity with a mean value of 0. Here, the data from three days were actually tested and analyzed respectively. Figure 3 shows the normalized logarithmic light intensity fluctuation in the Mie-scattering lidar return signal obtained. As can be seen from Figure 3, the logarithmic light intensity signal fluctuates around the mean value with different intensities. According to Equation (2), the scintillation index of the three groups of data can be obtained as 0.000021, 0.000017, and 0.000019, respectively.