# Dynamic Measuring Method of Laser Beam Incident Angle for Laser Doppler Vibrometer
## 1 Introduction
[16] proposed the method of relative motion to calibrate the incident angle. This method introduces a controllable flat plate that moves along a straight line under the stiff beam (used to fixing the LDVs). Nevertheless, this method is only suitable for research in the laboratory. When the LDVs are installed on the detection instrument and work with the vehicle bumps for some time, the calibrated angle may change again. Therefore, it is essential to propose a convenient and feasible high-precision measuring method for the incident angle of the LDV laser beam. Various kinds of lasers have been used in engineering practice [22], providing reference for calibration and measurement methods. These methods include methods based on camera images [23], methods based on differential mathematical models [24], methods based on three-dimensional distance [25], methods based on data processing fusion technology [26], methods based on high-precision laser probes [27], methods based on chessboards [28; 29], and methods based on large laser planar systems [30]. These researchers solved and calibrated the laser orientation using geometric constraints such as plane, sphere, and cone [27]. However, these calibration methods or measurement models are complex, and the measuring devices may require relatively large space, which is unsuitable for limited space. For example, the LDV laser beam of the Laser High-speed Deflectometer passes through the middle of the twin tires of the trailer, and the narrow space hinders these traditional measuring methods. [PERSON] et al. [31] proposed that measurement accuracy strongly depends on the measuring methods. Therefore, presenting a targeted measuring method for LDV in a specific situation is necessary. The rotating disk is essential for calibrating LDVs [32; 33]. [PERSON] et al. [32] studied the uncertainty of LDV measurement velocity by using a rotating disk processed with slits. [PERSON] and [PERSON] [33] developed a system based on a commercial optical chopper (essentially a rotating disk) for calibrating the velocity and uncertainty of LDV. [PERSON] et al. [34] adopted a rotating cylinder with a radius of 600 mm to provide a more extensive velocity range, lower velocity uncertainty, and more minor alignment errors. However, these research works focus on calibrating the accuracy of LDV itself, such as speed measurement range, measurement uncertainty, etc., while ignoring the influence of the actual working scene on the direction of the LDV laser beam. Inspired by the above work, this paper proposes a dynamic measuring method for the LDV laser beam incident angle. This method uses a rotating disk to simulate the dynamic response of the measured object. It calculates the incident angle according to the projected relationship between the LDV values and simulated speed. To verify the correctness of the measuring method, this paper obtains the actual value of the laser beam incident angle based on the traditional measuring method. The correctness of the dynamic measuring method is verified according to the comparison results of the two methods. This new dynamic measuring method can replace the angle measuring method of the original laser high-speed deflectometer, and can also be used as a metrological calibration means to verify the measurement results of the original method. The structure of the rest of this paper is organized as follows. In Section 2, the measuring principle of LDV and its application on the laser high-speed deflection instrument is briefly explained. Section 3 reproduces the traditional measuring device and method for the laser beam angle, and calculates one of the critical parameters through image recognition: the physical displacement of the laser spot. In Section 4, this paper proposes a dynamic measuring method, builds an experimental test device, and completes the dynamic angle measurement. In Section 5, this paper analyzes four primary error sources of the proposed dynamic measuring device and proposes targeted optimization measures, respectively.