# Dynamic Measuring Method of Laser Beam Incident Angle for Laser Doppler Vibrometer
## 4 Dynamic Measuring Method of Incident Angle
### Dynamic Measuring Device and Results  
The dynamic measuring device of the LDV laser beam incident angle is shown in Figure 7. The main difference from the angular static measuring device is that the coordinate paper is replaced by a rotating disk system. This rotating disk system is controlled by a bi-directional high-precision displacement platform and can move in the \(x\) and \(y\) directions. In addition, this system also includes angel fine-tuning devices for high-precision rotation around the \(x\)-axes and \(y\)-axes. Compared with the static measuring method, the newly proposed dynamic measuring method utilizes the measurement principle of LDV. The involved measuring device has a compact structure, and its three-dimensional size is less than 100 \(\times\) 100 \(\times\) 110 mm. With a more refined design, this device can achieve a smaller size. Such features ensure that the new measuring device has the advantages of being portable with the vehicle and  
Figure 6: Schematic diagram of the dynamic measuring principle of LDV laser beam incident angle, (**a**) front view; (**b**) top view. Figure 7: Dynamic measuring device. (**a**) Physical photos; (**b**) Structure diagram. measuring the LDV incident angle at any time. Most importantly, this measuring method takes less time. The main steps of the dynamic measuring method are as follows:  
Step 1. Drive the rotating disk to rotate stably at a certain velocity \(\omega\), and start the data acquisition system of the measuring device;  
Step 2. Fine-tune the focal length of the LDV to minimize the size of the laser spot. In this case, the signal quality received by LDV is the best;  
Step 3. Use a high-precision angle sensor to measure the inclination angle of the rotating disk and correct the angle to 0 through the angle fine-tuning device;  
Step 4. Adjust the position of the rotating disk along the \(x\) and \(y\) directions simultaneously, and record the average value of the LDV measurement \(V_{\rm m}\) when the laser spot is located on the radius \(r\). When the mean value of \(V_{\rm m}\) is at its maximum, the rotating disk is in the ideal position. At this time, the projection of the laser beam on the \(oxy\) plane coincides with the tangential direction of point P;  
Step 5. Tighten the constraints of the entire system to avoid introducing unexpected system errors during the experimental test;  
Step 6. Set different angular velocity \(\omega\) for the rotating disk system, and record the angular velocity \(\omega\) of the rotating disk and the measured value \(V_{\rm m}\) of LDV in real time;  
Step 7. Perform mean value processing on the measured value \(V_{\rm m}\), and calculate the angle \(\beta_{i}\) according to Equation (7);  
Step 8. Perform mean value processing on the angle \(\beta_{i}\) to obtain the dynamic measurement angle \(\beta\). During this test, the desired radius \(r\) at the laser spot P was equal to 47.5 mm. Under the control of the DC motor, the rotating disk can achieve a smooth rotation of 1000-5000 rpm, and the rotation error accuracy is less than 2 rpm. Figure 8 shows the curves of the measured value \(V_{\rm m}\) and its mean value \(\overline{V_{\rm m}}\) of LDV at different angular velocities \(\omega\). It can be seen from these curves that \(V_{\rm m}\) is not constant. This result has many reasons, which will be explained later in Section 5. In addition, from the perspective of amplitude, \(V_{\rm m}\) fluctuates randomly around its mean value, indicating that the measured value has a strong signal-to-noise ratio. Therefore, \(V_{\rm m}\) in Equation (7) can be replaced by \(\overline{V_{\rm m}}\) to calculate the incident angle \(\beta\) of the laser beam. Table 2 lists the corresponding \(\overline{V_{\rm m}}\) and \(\beta\) of seven kinds of angular velocity \(\omega\). The mean value of \(\beta\) is 1.8714\({}^{\circ}\), the standard deviation is 0.0014\({}^{\circ}\), and the coefficient of variation is 0.074%. Like the static measuring method, the measurement results of the new method also have high stability.