# Vibration Compensation of the Frequency-Scanning-Interferometry-Based Absolute Ranging System
## 4 Analysis and Discussion  
In this paper, the vibration compensation is studied from two aspects, vibration velocity and vibration frequency. In the experiments, the frequency modulation term and the Doppler shift term were first introduced into the beat signal due to the tiny movement of the target, as explained in Section 2, and they were proportional to the target vibration velocity. In Figure 3, it can be seen that the distance spectrum deviated greatly compared with that of the stationary target due to the Doppler effect. In addition, the distance spectra of two adjacent scanning periods moved in opposite directions because of the opposite scanning directions. However, the influence of the frequency modulation term is not obvious in Figure 3 because of a low target vibration velocity and a short scanning period. With the acceleration of the target vibration velocity, the offset of the distance spectrum became larger, and the distance spectrum broadened, resulting in a decrease in vibration compensation, as shown in Figure 5. Consequently, it can be concluded that the target vibration velocity should be as small as possible and satisfy \(f_{d}<<\alpha_{0}\tau\). In our experiments, the laser scanning speed was 100 nm/s, the distance value was 2.9627 m, and the center wavelength of the output laser was 1550 nm. In the calculation, \(\alpha_{0}\tau=100f_{d}\) was used, and the vibration velocity was calculated to be 1.9 mm/s.  
Figure 8: Distance error before and after the vibration compensation in a natural environment.  
Figure 7: The target mirror and collimating lens placed on different platforms.  
According to the presented results, it is obvious that the effect of vibration compensation was also related to the target vibration frequency. Figure 6 shows that the measurement standard deviation and measurement error began to increase significantly when the target vibration frequency was higher than 6 Hz. This phenomenon can be explained by two reasons. Firstly, the target velocity direction could change in a single scanning period with the change in the vibration frequency, which was inconsistent with our previous assumptions, resulting in a decrease in the measurement accuracy. Secondly, the target vibration velocity was also increasing, resulting in the broadening of the distance spectrum and the increase in the measurement error. Therefore, when the laser scanning frequency was 100 Hz, the effect of vibration compensation was better for the target with a lower vibration velocity and at the vibration frequency lower than 6 Hz.  
Furthermore, we found that when the target and measurement system were placed on different platforms, the vibration became the main factor affecting the measurement result due to the inconsistent vibration frequencies of the two platforms (the influence of dispersion was very small because the distance to be measured and the scanning bandwidth were both small). After the vibration compensation, the standard deviation was reduced from 289 to 11 \(\upmu\)m, which proved the feasibility of the proposed method in the practical application.