# Fine Exploration and Control of Subway Crossing Karst Area
## 2 Quantitative Exploration Method of Karst Cave Based on Three-Dimensional Laser Measurement  
### 3-D Automatic Laser Scanning Technology  
Three-dimensional automatic laser scanning technology uses laser diodes to emit laser pulses. Laser pulses propagate to the target point under testing [19]. The photosensitive secondary tube receives laser signals reflected from the surface of the object. The \"flight time\" of the laser is calculated. The distance L between the scanner and the target point under testing is calculated by the speed of light C and the \"flight time\" \(\Delta t\). A precision clock control encoder synchronously measures transverse scanning angle observation value alpha and longitudinal scanning angle observation value beta of each laser pulse. Laser scanning three-dimensional measurement uses the internal coordinate system of the instrument. The X-axis is in the transverse scanning plane, the Y-axis is perpendicular to the X-axis in the transverse scanning plane, and the Z-axis is perpendicular to the transverse scanning plane (Figure 3). The formula for calculating the coordinates of three-dimensional laser foot points can be obtained as follows:  
\[L=\frac{1}{2}c\Delta t \tag{1}\]  
\[\left\{\begin{array}{c}x\\ y\\ z\end{array}\right\}=\left\{\begin{array}{c}L\cos\beta\cos\alpha\\ L\cos\beta\sin\alpha\\ L\sin\beta\end{array}\right. \tag{2}\]  
In the formula, \(C\) is the propagation speed of the laser in the atmosphere, \(\Delta t\) is the round-trip propagation time of the laser at the distance to be measured, \(\alpha\) is the observation value of the transverse scanning angle, and \(\beta\) is the observation value of the longitudinal scanning angle.  
The automatic laser scanning system of the empty area is mainly divided into horizontal scanning mode and vertical scanning mode.  
* Horizontal scanning mode: The most commonly used scanning mode. First, the scanning head rotates vertically to the position of vertical angle \(0^{\circ}\) (the upper part of the detector is straight) and begins the first round of complete \(360^{\circ}\) horizontal scanning. After each circle of horizontal scanning, the scanning head increases the increment of steps set by the user along the vertical direction and starts the next circle of horizontal scanning until the vertical axis rotates \(180^{\circ}\) in the vertical direction. During the last horizontal scan of the scanner head, the laser emission and receiving lens of the scanner head point in front of the detector (Figure 4).
* Vertical scanning mode: Vertical scanning is suitable for scanning under some special conditions. Especially, the scanning line obtained is perpendicular to the horizontal characteristics of the scanning object so that more details that are comprehensive can be captured. As shown in the figure, in the vertical scanning process, the scanning head first rotates from vertical angle position \(0\) (the vertical direction behind the detector) to vertical angle position \(180^{\circ}\) (the laser-transmitting and -receiving lens of the scanning head points in front of the detector) along the vertical direction  
Figure 3: Schema of propagation time ranging method and internal coordinate system of laser detector. (**a**) schema of propagation time ranging method; (**b**) the internal coordinate system of laser detector.  
and completes the first vertical scanning. After each vertical scan, the scanning head increases a user-set increment along the horizontal direction and starts the next vertical scan until the horizontal axis rotates 360 degrees in the horizontal direction (Figure 5).