# A Study of Correction to the Point Cloud Distortion Based on MEMS LiDAR System
## 3 Experiment  
In order to verify the above theory, we conducted the following experiments. For reference, the specifications of the MEMS LiDAR system are summarized in Table 1 and applied the correction method to the system's 3D imaging experiment. The experimental parameters are shown in Table 2. The scanning parameters of the MEMS mirror are the following: the sampling rate is 50 kHz and each frame scans 64 lines, each line contains 256 points, so a frame contains 64 \(\times\) 256 = 32,768 points, the frame frequency is about 3 Hz, and the scanning trajectory adopts raster scanning. \begin{table}
Laser
1064 nm wavelength  
4 ns pulse width  
\end{table} 
Table 1: Specifications of the MEMS LiDAR system. Combine the two-dimensional coordinates (\(x\), \(y\)) of the MEMS scanner in a certain frame with the z-coordinates converted from time measurement, and analyze the changes in the data, and use the correction method mentioned in this article to process the data to obtain the three-dimensional imaging invert the image. We first measured a simple whiteboard plane. The experimental results are shown in Figure 5. Figure 5a is the point cloud image of the whiteboard before calibration. It can be seen that there is an obvious distortion. Figure 5b is the point cloud after applying the method of this paper to correct. In order to quantitatively illustrate the effectiveness of the method in this paper, we respectively analyze the edge contour part of the whiteboard, as shown in Figure 6. The four pictures in Figure 6 are the plane contour point clouds after the boundary contours in the x and y directions are superimposed with the coordinates in the z-direction. We define the deflection angle of the boundary point of the plane contour centerline relative to the horizontal axis as an index of the degree of distortion of the point cloud image. That is, the degree of point cloud distortion is judged by the size of \(\alpha\) and \(\beta\) the Figure 6. The specific data is shown in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Transmitter & \\ Beam diameter & 3.0 mm \\ Pulse energy & 4.8 uJ \\ Angle of divergence & 0.51 mrad \\ Transmitting system optical aperture & 32 mm \\ Receiver & \\ Receiving system optical aperture & 50 mm \\ APD photosensitive surface size & 3.0 mm \\ APD response frequency band & 250 MHz \\ Spectral response range (minimum) & 600 to 1150 nm \\ ADC sampling rate & 5 GSa/s \\ ADC bandwidth & 1 GHz \\ ADC sampling digit & 14 bit \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values used in the experiments. Figure 5: Planar point cloud image obtained by experiment: (**a**) point cloud before correction; (**b**) point cloud after correction. It can be seen from Table 3 that the distortion degree of the XZ plane profile before correction reaches 15.255\({}^{\circ}\), and after correction, it is reduced to 3.901\({}^{\circ}\). Our method reduces the distortion by 74.428%. The contour distortion of the YZ plane is also reduced by more than 70%. Therefore, our method almost reduces the point cloud distortion by 72.5%. It can be seen that our method works well. In order to prove the robustness of the method proposed in this paper, we further designed an experiment as shown in Figure 7. Using a LiDAR system to scan complex targets. The experimental results are shown in Figure 8. Figure 8a shows the imaging inversion obtained by combining the scanning coordinates (\(x,y\)) and the ranging coordinates \(z\). This is the imaging effect before calibration. Obviously, the inverted point cloud image has obvious distortion. Figure 8c shows the corrected point cloud image, and in order to show the results more clearly, the singular points in the point cloud model and the large-scale outliers of the relative point cloud data are eliminated, that is, the laser 3D scanning imaging point cloud data is directly processed for de-noising [20], the point cloud images after de-noising are shown in Figure 8b,d, respectively.