## 2 Experiment and Method  
A Raman-Mie Lidar (model: LR112-D400, Raymetrics S.A., Athens, Greece) and a six-rotor UAV (model: M6E, Tiantu Aviation Technology Co. Ltd., Beijing, China) equipped with light scattering particle detectors (are the main instruments of the experiment. The Raman-Mie Lidar emission wavelength is 355 nm, and the system parameters are shown in Table 1. The 355 nm elastic scattering signal, the 387 nm nitrogen Raman scattering signal, and the 408 nm water vapour Raman scattering signal are simultaneously received by the Cassegrain telescope. The Lidar only works in the vertical state and has the ability to detect Raman signals at night. The acquired Raman signal is used to calculate the overlap factor for comparison with the method proposed in this paper. An M6E six-rotor UAV produced by Beijing Tiantong Aviation Technology Co., Ltd, Beijing, China is used for vertical flight experiments. The UAV is also equipped with a PMS A003 miniature light scattering particle detector produced by Beijing Plantor Co., Ltd., Beijing, China, which draws air into the scattering chamber. The particle detector \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline
**Transmitter** & \\ Transmitted wavelength & 355 nm \\ Pulse energy & 50 mJ \\ Pulse repetition rate & 10 Hz \\ Pulse duration & 8 ns \\ Laser beam divergence & 0.2 mrad \\
**Receiver** & \\ Telescope diameter & 400 nm \\ FOV & 0.5–2 mrad \\ Detect channels & 355, 387, 408 \\ Filter bandwidth & 1 nm \\
**Data acquisition** & \\ Sample rate & 40 MHz \\ Resolution & 12 bit \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of Raman-Mie Lidar. uses a laser diode as the light source and calculates the particle mass concentration by detecting the intensity of the side scattered light of the particle. However, the instrument cannot distinguish particle size and remove the influence of particle moisture growth. However, because the measurement object is the particle scattered light signal, which is consistent with the Lidar, the measurement data of the two instruments has a physical basis for mutual conversion. The 355 nm signal received by the Lidar is represented by the Lidar equation:  
\[X(z)=CO(z)[\beta_{a}(z)+\beta_{m}(z)]\cdot\exp\biggl{\{}-2\int_{0}^{z}\big{[} \alpha_{a}(z^{\prime})+\alpha_{m}(z^{\prime})\big{]}dz^{\prime}\biggr{\}}, \tag{1}\]  
where \(X(z)\) is the range corrected signal (RCS) at height \(z\); \(C\) is the system constant; \(O(z)\) is the overlap factor of the detection channel; \(\beta_{m}(z)\) and \(\alpha_{m}(z)\) are the atmospheric molecular backscatter coefficient and extinction coefficient calculated by the atmospheric model; \(\beta_{a}(z)\) and \(\alpha_{a}(z)\) are the aerosol backscatter coefficient and extinction coefficient, respectively, according to the Fernald method [26], calculated by \(X(z)\):  
\[\beta_{a}(z)=-\beta_{m}(z)+\frac{X(z)\cdot\exp\Bigl{[}-2(S_{1}-S_{2})\int_{z_{ C}}^{z}\beta_{m}(z^{\prime})dz^{\prime}\Bigr{]}}{\frac{X(z_{c})}{\beta_{a}(z_{ C})+\beta_{m}(z_{C})}-2S_{1}\int_{z_{C}}^{z}X(z)\cdot\exp\Bigl{[}-2(S_{1}-S_{2}) \int_{z_{C}}^{z}\beta_{m}(z^{\prime\prime})dz^{\prime\prime}\Bigr{]}dz^{\prime }}, \tag{2}\]  
where \(z_{c}\) is the calibration height, which is generally taken near the tropopause; the aerosol backscatter ratio is \(R(z_{c})=1+\beta_{a}(z_{c})/\beta_{m}(z_{c})\), and for 355 nm, its value is usually assumed to be 1.001 [27]; \(S_{1}\) is the Lidar ratio of aerosols, which is obtained by inversion of Raman signals in adjacent time periods [28]; \(S_{2}\) is the Lidar ratio of atmospheric molecules, which is equal to \(8\pi/3\). The Raman method is implemented in this work for comparison.