## 2 Principle of Detection
### Detection Method  
According to the RTS theory described above, the spatial correlation scale \(l_{I}\) of the light intensity fluctuation is calculated. According to the formula \(l_{I}=\sqrt{\lambda L}\), the spatial correlation scale increases with the increase in detection distance and incident wavelength. Here, the wavelength of the incident laser is determined to be 532 nm. When the maximum detection distance is 3 km, the maximum spatial correlation scale, \(l_{1}\), is approximately 39.9 mm. The telescope aperture \(D=\) 254 mm obviously meets the requirements of a large aperture receiving system \(D\gg\sqrt{\lambda L}\). According to the calculations, the aerosol spot scale \(l_{a}=\) 5.236 \(\upmu\)m. When the detection distance \(L=\) 1-3 km, the turbulence-related scale \(l_{t}\) is in the range of 0.058-0.033 mm. If we want to satisfy the condition \(l_{a}\ll d_{0}\ll l_{t}\), then \(d_{0}<\)0.03 mm. Where \(d_{0}\) is the diameter of the iris diaphragm. The size of the iris diaphragm is too small and difficult to implement in manufacturing. Increasing the focal length \(F\) and shortening the detection distance \(L\) can increase the iris diaphragm diameter. However, the long focal length and small iris diaphragm design will directly lead to a smaller field of view, a received weakened return signal, an increased blind area and transition area, and an increase in difficulty when aligning the optical axis and machining the aperture. Therefore, it is necessary to find a balance point in line with or close to the principle. When the condition \(l_{a}\ll d_{0}\ll l_{t}\) cannot be strictly satisfied, ensure that \(d_{0}\) is close to \(l_{t}\). Here, after considering the operability of the experiment and the actual conditions of the laboratory equipment, the diameter \(d_{0}\geq\) 0.5 mm is selected for the iris diaphragm. In this study, light intensity fluctuation is used to detect atmospheric turbulence. The fluctuation in light intensity on the receiving plane is called scintillation, which is the most important effect of turbulent atmospheric transmission. The scintillation index is used to describe the intensity of light intensity fluctuations, namely the normalized variance of light intensity fluctuations:  
\[\beta_{I}^{2}=\frac{\left<I^{2}\right>-\left<I\right>^{2}}{\left<I\right>^{2}} \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**System Name** & **Technical Parameters** \\ \hline
**Laser Emission System** & Pulsed solid-state laser (Nd:YAG) \\ Type of laser & \\ Operating wavelength/nm & 532 \\ Repetition rate/Hz & 10 \\ Single-pulse energy/mJ & 150 \\ Width of pulse/ns & 10 \\ Laser divergence angle/mrad & \(\leq\)0.5 \\ Stability of energy & \(\leq\)3\% \\ \hline
**Receiving Optical System** & \\ Type of telescope & Schmidt-Cassegrain \\ Aperture/mm & 254 \\ Focal length/mm & 2500 \\ Diameter of iris diaphragm/mm & 0–12 \\ Coupling fiber length/m & 1.5 \\ Optical fiber diameter/\(\upmu\)m & 800 \\ Numerical aperture N.A. & 0.22 \\ Filter/nm & 532 \(\pm\) 0.2 \\ \hline
**Signal Acquisition System** & \\ Photomultiplier tube model & R9880U \\ Diameter of photosensitive surface/mm & 8 \\ Model of oscilloscope & DPO410B \\ Bandwidth/GHz & 1 \\ Frequency of sampling/M/s & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of atmospheric turbulence detection Mie-scattering lidar. where \(I\) is the received light intensity, and \(\langle\cdot\rangle\) represents the ensemble average. Under a weak fluctuation condition \(\beta_{I}^{2}<1\), the relationship between the scintillation index and logarithmic amplitude fluctuation variance \(\sigma_{\chi}^{2}\) is as follows:  
\[\beta_{I}^{2}=\sigma_{InI}^{2}=\exp\left(4\sigma_{\chi}^{2}\right)-1\approx 4 \sigma_{\chi}^{2} \tag{3}\]  
Since the weak fluctuation condition is always satisfied in the actual detection process of Mie-scattering lidar, the emitted Gaussian beam can be approximately regarded as a spherical wave, and most propagation problems meet the conditions of the turbulent inertia region [2].