# Real-Time Tunnel Deformation Monitoring Technology Based on Laser and Machine Vision
## 4 Test Results and Analysis
### Image Acquisition Module Calibration Experiment
#### 4.2.1 Horizontal Calibration Experiment  
Given the different positions of the measured points in the tunnel, the image acquisition module will often roll along the \(z\)-axis after it is installed. As a result, an angle will form between the \(x^{\prime}\)-axis of the image coordinate system and the \(x\)-axis of the world coordinate system. Given this angle, the change in the position information of the laser spot center obtained by the image acquisition module cannot directly represent the settlement and the diameter convergence of the measured point. Therefore, the horizontality of the image coordinate system needs to be calibrated.  
A simplified model for the relationship between the world coordinate system and the image coordinate system is shown in Figure 11[37]. Here, \(o\)-\(xy\) represents the world coordinate system, \(o^{\prime}\)-\(x^{\prime}y^{\prime}\) represents the image coordinate system, and \(\theta\) represents the rotation angle. The line \(l\) is a horizontal line, which is parallel to the \(ox\) axis and comes from a laser cast instrument. The laser cast instrument produced a horizontal laser line with a \(\pm 10\)\" accuracy. Supposing that the slope of the line \(l\) in the image coordinate system is \(k\), the relationship between \(\theta\) and \(k\) is as shown in Equation (10):  
\[\theta=180^{\circ}-tan^{-1}k. \tag{10}\]  
After the rotation angle \(\theta\) was obtained, the horizontal calibration of the image coordinate system could be completed by rotating the image coordinate system by an angle \(\theta\) around point \(o^{\prime}\), as the rotation center in the reverse direction. The horizontal calibration process is shown in Figure 12.  
Before the horizontal calibration, when the image acquisition module horizontally moved along the micro motion platform, as shown in Figure 9, both the \(x\)-axis and \(y\)-axis values of the laser spot  
Figure 11: Simplified coordinate model.  
Figure 12: Horizontal calibration experiment.  
center in the image coordinate system changed with the movement. After the horizontal calibration was completed, only the \(x\)-axis value changed, thereby indicating that the horizontal calibration of the image coordinate system was successful. The micro motion platform moved at an interval of 5 mm. The experimental data curves are shown in Figure 13.  
According to Figure 13, the displacement of the micro motion platform was from 0 mm to 70 mm, and the change in the \(y\)-axis value after calibration was as follows:  
\[\Delta Y=318.52\,-\,317.01=1.51\ (\text{pixel}).\]  
Therefore, within the permitted error, the \(y\)-axis values were basically unchanged, and the horizontal calibration of the image coordinate system was successful.  
In the tunnel environment, a universal arm was used to hold the laser cast instrument during the horizontal calibration, as shown in Figures 14 and 15, and the calibration method was the same. Every time before using the system, the horizontal calibration was required to be done first.  
Figure 14: Universal arm.  
Figure 13: Coordinate change before and after horizontal calibration.  
Figure 15: Tunnel environment.