# Vibration Compensation of the Frequency-Scanning-Interferometry-Based Absolute Ranging System
## 3 Experiments and Results  
### Vibration with Given Parameters  
To verify the feasibility of the proposed method and deduce the applicable range of vibration compensation, the experiments were respectively carried out in the vibration environment and natural environment. First, the target was attached to a Precise PIHera Linear Nanopositioning System (Physik Instrumente GmbH, Karlsruhe, Germany) which was serving as a vibration source; the entire measurement system and target were placed on the same optical platform, and all experiments were carried out in a constant temperature and humidity environment, as shown in Figure 2. The Continuous Wave (CW) tunable laser (Lunainc, Blacksburg, VA, USA) was used as a sweeping source, and it had a tuning range of 1515-1565 nm and the tuning speed of 1-2000 nm/s. The output of the tunable laser was divided into two parts. One passed through the reference optical path, and its beat signal was used to remove the influence of nonlinear tuning; the delay fiber length which was calibrated by the gas absorption cell [1] certified by the National Institute of Standards and Technology (NIST) was 55.05 m. Since the fiber length variation caused by temperature variation was very small, the influence of fiber length variation on measurement accuracy was negligible. The other passed through the measuring optical path, and its beat signal contained the wanted distance information. Then, the beat signals of the reference optical path and the measuring optical path were respectively detected by photodetector 1 (PD1) and photodetector 2 (PD2), of which both were Thorlabs PDA10 CS-EC detectors. After that, all the PD signals were simultaneously sampled and recorded by an oscilloscope ([PERSON], New York, NY, USA). According to Equation (8), the frequency change of the beat signal in a single scanning period was given by:  
\[\Delta f=\frac{4\
u\alpha_{0}}{c}(\frac{T_{m}}{2}-\tau)=\frac{\upsilon B}{c}(4- \frac{16R}{cT_{m}}). \tag{17}\]  
In order to make the frequency change of the beat signal in a single scanning period as small as possible, the laser scanning bandwidth had to be small, the target vibration velocity had to be low, and the scanning period had to be short. Considering that the measured spectral resolution was inversely proportional to the scanning bandwidth, the scanning bandwidth of the laser and the modulation speed were set to 1 nm (1550-1551 nm) and 100 nm/s, respectively. The experiments were carried out separately in the static and vibration environments. First, we repeated for 20 times the measurement for the stationary target, and then the target was subjected to a sinusoidal vibration with the amplitude of 10 \(\upmu\)m at the frequency of 1 Hz. For the purpose of processing convenience, the amplitude of the beat signal was normalized. The obtained distance spectrum is shown in Figure 3, where the purple line denotes the CZT of the measurement beat signal for the stationary target (the distance value was calculated to be 2.962702 m), the red and blue lines denote the CZTs of the measurement beat signals of two adjacent scanning periods when the target vibrated (the distance values were calculated to be 2.962155 and 2.963275 m, respectively), and theblackline denotes the CZT of the new signal after the vibration compensation (the distance value was calculated to be 2.962710 m). It should be noted that the ranging errors before the vibration compensation were 547 and 573 \(\upmu\)m, i.e., they were about 28 times larger than the actual vibration range of the target. After the vibration compensation, the ranging error was reduced to 8 \(\upmu\)m, and the spectral resolution was cut down by half. The distance error before and after the vibration compensation is shown in Figure 4. After 20 repeated measurements, the standard deviation was reduced from 775 to 12 \(\upmu\)m by using the proposed method.