## 3 The Evaluation Experiment and Analysis
### Evaluation Experiment of Calibration Method with Multiple Geometric Constraints and Result Analysis  
The experiment is shown in Figure 9a. The gauge blocks of different thicknesses were placed on the plane target at the initial position of the laser. The laser was projected onto each surface of the gauge block; the pixel positions of the strip center point, which were on the surface of the gauge block, were obtained by the detection algorithm [21]. The coordinates of the light stripe center on the surface of the standard gauge block were solved by the plane equation parameters, and the thickness of the gauge block was the spatial distance from the center to the target plane. After increasing the number of parallel constraints each time, the parameters of the light equation were optimized, and the thickness of the gauge block was recalculated using the new light plane equation after each optimization. The error between the measured thickness and the actual thickness of each gauge block was used to characterize the accuracy of the light plane calibration. In the experiment, the laser was moved nine times, and six kinds of gauge blocks with different thicknesses were selected as the measured objects. The light plane equations corresponding to the initial position after each optimization are shown in Table 4, and the measurement errors of the gauge block are shown in Table 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Corresponding Position of the Laser** & **Light Plane Equation** \\ \hline
0 & \(3.3187X_{\text{C}}-0.40810Y_{\text{C}}+1.6432Z_{\text{C}}-1000=0\) \\
1 & \(3.3173X_{\text{C}}-0.4089Y_{\text{C}}+1.6389Z_{\text{C}}-1000.0005=0\) \\
2 & \(3.3194X_{\text{C}}-0.4072Y_{\text{C}}+1.6412Z_{\text{C}}-999.993=0\) \\
3 & \(3.3169X_{\text{C}}-0.4096Y_{\text{C}}+1.6454Z_{\text{C}}-1000.0033=0\) \\
4 & \(3.3173X_{\text{C}}-0.4077Y_{\text{C}}+1.6394Z_{\text{C}}-999.996=0\) \\
5 & \(3.3167X_{\text{C}}-0.4096Y_{\text{C}}+1.6413Z_{\text{C}}-1000.0022=0\) \\
6 & \(3.3183X_{\text{C}}-0.4104Y_{\text{C}}+1.6391Z_{\text{C}}-1000.0031=0\) \\
7 & \(3.3188X_{\text{C}}-0.4087Y_{\text{C}}+1.6363Z_{\text{C}}-999.9972=0\) \\
8 & \(3.3196X_{\text{C}}-0.4076Y_{\text{C}}+1.6411Z_{\text{C}}-999.998=0\) \\
9 & \(3.3183X_{\text{C}}-0.4096Y_{\text{C}}+1.6407Z_{\text{C}}-999.9980=0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Light plane equations after each optimization. \begin{table}
\begin{tabular}{c c} \hline \hline
**Corresponding Position of the Laser** & **Light Plane Equation** \\ \hline
4 & \(3.0016X_{\text{C}}-0.4111Y_{\text{C}}+1.6638Z_{\text{C}}-1000=0\) \\
5 & \(3.0221X_{\text{C}}-0.4156Y_{\text{C}}+1.6539Z_{\text{C}}-1000=0\) \\
6 & \(3.3346X_{\text{C}}-0.4220Y_{\text{C}}+1.6316Z_{\text{C}}-1000=0\) \\
7 & \(3.1252X_{\text{C}}-0.4215Y_{\text{C}}+1.6445Z_{\text{C}}-1000=0\) \\
8 & \(3.1449X_{\text{C}}-0.4024Y_{\text{C}}+1.6326Z_{\text{C}}-1000=0 According to the measurement results in Table 5, the measurement accuracy of the gauge block was significantly promoted by the optimized light plane equation. The measurement results showed that the structured light calibration method based on multiple geometric constraints was effective in improving the calibration accuracy. In order to discuss the relationship between the number of parallel constraints and calibration accuracy, mean errors corresponding to different numbers of parallel constraints were compared, which were the averages of the thickness measurement errors of the gauge block shown in Table 5. The comparison results are shown in Figure 10. According to the comparison results, the calibration accuracy did not change much and was slightly reduced when the number of geometric constraints exceeded five. The reason for this result was that the error points involved in the calculation also increased with the increase in the number of parallel constraints. In recent research, the methods proposed in references [19; 20] are similar to the methods in this paper.