# Design and Analysis of High-Accuracy Telecentric Surface Reconstruction System Based on Line Laser
## 6 Discussion  
It is indicated from Table 2 that the deviation of the measured value and the designed value is within 1 \(\upmu\)m for each step. However, the error for the step plane is too large to accept. The step master is measured repeatedly, but the result remains stable in the repeatability tests even when the direction of measurement changes. When the effect of random error is excluded, the off-surface error for every point is calculated and the corresponding result is shown in Figure 11. There is an obvious scratch for the plane fit on each step, which is in red and nearly characterized by a linear distribution. The result might be caused by the fact that the step master is used and maintained improperly. From the measured result, it is shown that the obstacle is about 10 to 20 \(\upmu\)m in height; it is a linear inclusion and there is an effect in the vertical direction which obeys an approximately Gaussian distribution. This incident would be a proper instance of the proposed system for a defect-detecting application. Moreover, several surface reconstruction methods are listed in Table 3 for comparison. The methods listed contain the main measurement approaches based on triangulation, and the lenses employed are telecentric lenses. It is indicated that the accuracy of the active method (structure light and line laser scanning) is better than passive techniques (stereo vision). The employment of binocular telecentric cameras leads to the better performance in structure light. The proposed method performs as well as [PERSON]'s method in accuracy, but the measured region is much larger. Figure 12: Measured results for some other samples. From left to right, every result presents the practicality picture, measured result in depth map (unit: mm), mesh result of surface reconstruction and partial detail for mesh result of the sample. When we come back to the three main challenges mentioned in introduction, the first challenge, the occlusion due to the principle of triangulation, cannot be completely solved with a single camera while the other two challenges are solved with the proposed methods for system calibration, telecentric intersection and laser stripe extraction. In the proposed system, the unsolved problem is made to be acceptable for the demand with the system design, but it still exists (Figure 13). There is a narrow gap at the position where the depth changes significantly in surface reconstruction, and the width of the gap mainly depends on the intersection angle designed and the jump change of the depth. The speed of the motor stage is set to 0.2 mm/s, so it would take 100 s to measure the region of 20 mm Length. The frame frequency of camera is 40 fps, which means the interval width between the point clouds is 0.005 mm. The measurement speed can be adjusted with the variation of the motor speed. Actually, the measurement speed only affects the density of the point cloud in the plane of \(L\times W\). The accuracy in depth remains stable as long as it is captured. Moreover, the speed can be improved with a better camera and displacement platform, and the application of the displacement platform for the proposed method can expand the measurement region continuously. According to the experimental results, the system designed holds the deviation of less than 1.0 \(\upmu\)m for the region of \(20\times 40\times 1\) mm\({}^{3}(L\times W\times H)\) meanwhile the uncertainty is less than 1.0 \(\upmu\)m in 68% level of confidence. The measurement region is limited by the travel range of the 1D displacement platform under the line laser (20 mm) and the size of the telecentric lens (40 mm). The 1 mm presented indicates the practical variation interval for the measured object, which is utilized in the uncertainty calculation. The measurement ability of depth depends on the depth of field of the telecentric lens employed, which is 6.8 mm.