## 4 Experiments and Results  
### Analysis of Speckle Suppression  
The improved system based on the research results in Section 3 is shown in Figure 10, where the green box represents the thermal control function and a vibration motor was installed behind the optical antenna. Experiments on a short path (10 cm), where the absorption of CO\({}_{2}\) was negligible, were carried out in the laboratory in order to investigate the predictions of the speckle statistical theory under controlled conditions. The lidar output beam illuminated a white painted wall, similar to a Lambertian scatter, and the illumination of many scattering centers resulted in complex Gaussian fluctuation statistics [9]. First, the wavelengths of the on and off seed lasers were adjusted to the \(\lambda_{on}\) and \(\lambda_{off\_1}\) values in Table 1, with a wavelength separation of 16 GHz. The motor was kept stationary, and we calculated the correlation coefficient and standard deviation with different smoothing times. Then, we changed the motor speed and repeated the above steps. The results, as shown in Figure 11, were in accordance with the theoretical analysis. A shorter smoothing time could achieve the target accuracy of the normalized ratio with an increase in the motor speed. The fluctuation of the normalized ratio decreased greatly with the increasing motor speed, as shown in Figure 12. Table 2 shows the correlation coefficient of the normalized intensities between on and off wavelengths, as well the mean and standard deviation of the normalized ratio with different motor speeds. The correlation coefficient increased with the acceleration of the motor speed. However, the mean value of the normalized ratio was different when the motor is rotating and stationary, due to the bias caused by motor rotation. Figure 10: The improved system configuration. The green box represents the thermal control function, and a vibration motor is installed behind the telescope. \(\langle I_{R}\rangle\) indicates the average of the normalized ratio, and \(\Delta I_{R}\) is the standard deviation of the normalized ratio. Next, we verified the influence of the wavelength difference between the on and off wavelengths on the correlation coefficient and the fluctuation of the normalized intensity ratio. The motor speed was kept at 600 rpm, the correlation coefficient and normalized intensity ratio were recorded when the on and off wavelengths were adjusted to \(\lambda_{on}\) and \(\lambda_{off\_1}\) (\(\Delta v=16\) GHz), and \(\lambda_{off\_1}\) and \(\lambda_{off\_2}\) (\(\Delta v=36.4\) GHz), respectively. The results are shown in Figure 13. When the wavelength difference between the on and off wavelengths was small, a large correlation coefficient and a smaller fluctuation of the normalized intensity ratio were obtained. These experimental results are consistent with the theoretical analysis. Finally, we chose the motor speed of 600 rpm, and selected \(\lambda_{on}\) and \(\lambda_{off\_1}\), with smaller wavelength difference, instead of \(\lambda_{off\_1}\) and \(\lambda_{off\_2}\) as the ON and OFF laser wavelengths. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Motor Speed**} & \multirow{2}{*}{**Correlation**} & \multirow{2}{*}{
\begin{tabular}{c} **1s-Smoothed** \\ **Correlation** \\ \end{tabular} } & \multicolumn{2}{c}{**Normalized Ratio \(I_{R}\)**} & \multicolumn{2}{c}{**1s-Smoothed \(I_{R}\)**} \\ \cline{3-7}  & & & \(\langle I_{R}\rangle\) & \(\Delta I_{R}\) & \(\langle I_{R}\rangle\) & \(\Delta I_{R}\) \\ \hline Stationary & 0.9214 & 0.9361 & 0.9980 & 0.0013 & 0.9980 & 0.00086 \\
60 rpm & 0.9847 & 0.9963 & 0.9971 & 0.00074 & 0.9971 & 0.00031 \\
200 rpm & 0.9937 & 0.9982 & 0.9969 & 0.00073 & 0.9969 & 0.00023 \\
600 rpm & 0.9971 & 0.9997 & 0.9971 & 0.00071 & 0.9971 & 0.00014 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients of the normalized intensities between the on and off wavelengths with different motor speeds.