## 3 The Evaluation Experiment and Analysis
### Camera Calibration and Initial Parameter Solution  
Before calibrating the structure light, the camera's internal parameters and distortion coefficients were obtained by [PERSON]'s method [6], and the camera could no longer be moved in the experiment. In the process, nine images of checkerboard calibration plates were used as calibration images, and the checkerboard calibration plates were needed to cover the visual field of the camera. In the camera calibration, matrix \(A\) contained the camera's internal parameters, which are shown in Equation (10). In the distortion coefficients, k\({}_{1}\), k\({}_{2}\), p\({}_{1}\), and p\({}_{2}\) were the radial distortion and tangential distortion, respectively.  
\[A=\begin{bmatrix}\alpha&\gamma&u_{0}\\ 0&\beta&v_{0}\\ 0&0&1\end{bmatrix} \tag{10}\]  
The camera calibration results are shown in Table 2. The spatial positions of the calibration board in the experiment are shown in Figure 6, and the calibration board images used to calibrate the internal parameters and distortion coefficients are shown in Attached Figure 11.  
In structured light calibration, the clamp was used to ensure that the calibration plate surface and target were coplanar. The laser was fixed on the straight slide, and the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{\pi}\) & \(\mathbf{\beta}\) & \(\mathbf{\gamma}\) & \(\mathbf{u_{0}}\) & \(\mathbf{v_{0}}\) & \(\mathbf{k_{1}}\) & \(\mathbf{k_{2}}\) & \(\mathbf{p_{1}}\) & \(\mathbf{p_{2}}\) \\ \hline
6884.70 & 6885.044 & 0.835078 & 628.1419 & 470.1564 & 0.146356 & 1.580898 & 0.000322 & 0.000299 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Camera internal parameters and distortion coefficients.  
Figure 5: Schematic diagram of calibration experiment. 1. Camera, 2. support fixture, 3. plane target, 4. line-structured light plane, 5. line laser, 6. mobile platform.  
Figure 6: The position of the calibration board.  
projected light plane intersected the plane targets. The coordinates of the light stripe center were calculated, and the pixel coordinates of the center were achieved by the detection algorithm [21]. The images of the plane targets are shown in Figure 7, and the red points were the light stripe center.  
When the laser was in the initial position, six plane target images with different postures were collected, and the coordinates of the center point were obtained; the center points of the light stripe in the images are shown in Figure 8. The equation of the plane was obtained by the least square method, and the data points were all light stripe centers, which was named the basic light plane calibration model in the experiment. The equation was calculated on the basis of the basic light plane calibration model at the initial position, and the equation is shown:  
\[3.3185X_{C}-0.4073Y_{C}+1.6432Z_{C}-1000=0 \tag{11}\]  
The laser was moved along the linear guide, and the light plane equations were obtained using the basic calibration model; the plane equations at each position are shown in Table 3.  
Figure 8: Spatial distribution of the light stripe center.  
Figure 7: The image of the plane target for line structure calibration.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Corresponding Position of the Laser** & **Light Plane Equation** \\ \hline
0 & \(3.3187X_{C}-0.40810Y_{C}+1.6432Z_{C}-1000=0\) \\
1 & \(3.2571X_{C}-0.43128Y_{C}+1.65452Y_{C}-1000=0\) \\
2 & \(3.0877X_{C}-0.4158Y_{C}+1.6719Z_{C}-1000=0\) \\
3 & \(3.2051X_{C}-0.4305Y_{C}+1.6535Z_{C}-1000=0\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calibration results at ten positions.