## 4 Experiment
### Experimental Data Processing  
An arbitrary target movement is generated by programming of the motorized translator. Specifically, the target maintains its initial position at about 214,777.80 m in 5.1 s. In the following, the target moves away from the range finder at a speed of 0.34 mm/s in 2.3 s. After a 1.2-s pause, the target moves towards the same direction at a speed of 0.75 mm/s in 2.37 s. Then, the target moves towards the opposite direction at a speed of 0.5 mm/s for 0.47 s. The target remains stationary at the last 0.615 s, thus completing the movement. The detailed movements of the target are listed in Table 2. The measured target movement trajectory by the absolute range finder is shown in the black lines of Figure 5. The update rate of the absolute distance measurement is 200 Hz. Note that the ASOPS-based absolute range finder used here has an inherent measurement update rate of 2 kHz determined by the offset repetition rate. However, we intentionally lower the update rate to 200 Hz by taking only one datum out of every 10 successive measurements considering the limited storage depth of the digitizer (PXIe-5122), which only allows storage of 1-s data at a 2-kHz update rate. The basic SSA filter is used to process the experimental data, and the procedure is identical to that in the simulation. The result after the basic SSA filter with a 0.25-s window length is shown in red lines in Figure 5a. The choice of a 0.25-s window length is on the basis that the motion behavior is similar to the simulation in the above section. The enlarged view of the transits are shown in Figure 5b-f. It can be seen that the basic SSA filter effectively improves the measurement signal-to-noise ratio and retrieved the trajectory of the moving target. In comparison, we also process data by moving averaging with a 64-pts sliding box, shown as green dots in Figure 5. Despite the same level of curve smoothness, the retrieved trace by moving average apparently deviates from the real trajectory, particularly at non-uniform motion stages. It is worth mentioning that the basic SSA filter is able to extract the noise sources while filtering a distance signal. Figure 6 illustrates the noise sequence separated by the basic SSA filter and the corresponding power spectral density (PSD). The PSD indicates that the Gaussian white noise process dominates during ASOPS-based absolute laser ranging. The noise STD is 16.75 m RMS. In addition, the PSD of the measured distance signal and reconstructed signal by the basic SSA filter are shown in Figure 7a, showing that the noises in the distance signal are well filtered out, while the spectral characteristics of the target movement at baseband are well preserved. Figure 4: Absolute ranging system based on a pair of free running femtosecond lasers. LD (laser diode); ISO (isolator); WDM (wavelength division multiplexing); ISO/WDM/Tap (integrated ISO, WDM and tap with 20% transmittance); CNT (carbon nanotube); Er (Er fiber); Col (collimator); HWP (half wave plate); QWP (quarter wave plate); PPKTP (periodically-poled potassium titanyl phosphate); APD (avalanche photo diode); LPF (low pass filter); ADC (analog-to-digital converter). Allan deviation analysis is utilized to evaluate the effect of the basic SSA filter on the improvement of measurement uncertainty. To this end, we calculated the Allan deviation of a section of measured distance signal (from 0 to 1.25 s in Figure 5a when the target is stationary) after basic SSA filtering, and the result is shown in the red curve in Figure 7b. The minimum absolute measurement uncertainty after basic SSA filtering is 110 nm, obtained at the fundamental 200-Hz update rate (5-ms observation time). In comparison, the Allan deviation of the same section of measured distance signal without basic SSA filtering in shown as the black curve in Figure 7b. At the fundamental 200-Hz update rate (5-ms observation time), the measurement uncertainty is 18 \(\upmu\)m, which is 163-times higher than the number obtained after basic SSA filtering.