# A Traceable High-Accuracy Velocity Measurement by Electro-Optic Dual-Comb Interferometry
## 4 Results and Discussion  
Before moving the target, beat notes between the signal source and the local oscillator were measured by a spectrum analyzer (ROHDE&SCHWARZ FSH8, 3 kHz RBW). Then, the waveform obtained by the oscilloscope was Fourier transformed to obtain the new comb due to beat. As shown in Figure 2, we can see that the Fourier transform can basically reproduce the beat frequency spectrum. Additionally, the center frequency of the beat notes is 10 MHz, which is the driving frequency of the AOM. The frequency interval of the comb teeth is 1 MHz, which is the frequency difference between the driving frequencies of the two RF drivers. Actually, the frequency of RF driver1 is 10 GHz and the frequency of RF driver2 is 10.001 GHz. This means that \(f_{rnp.sig}=10\) GHz and \(f_{rnp.loc}=10.001\) GHz. Figure 1: Experimental system for the dual optical comb laser Doppler velocimeter (LDV). Legend: RF1, RF driver1; RF2, RF driver2; EOM, electro-optic modulator; AOM, acousto-optic modulator; EDFA, Er-doped fiber amplifier; PD, photodetector. Figure 2: Beat notes between the signal source and the local oscillator. The blue line is measured by a spectrum analyzer with the left vertical axis; the red line is the result of Fourier transforming the waveform obtained by the oscilloscope with the right vertical axis. To show the feasibility of the electro-optic dual-comb Doppler velocimeter, Figure 3 shows the difference between Fourier transforming the waveforms when the target is stationary and when it is moving. In Figure 3a, the black comb expresses the measured spectrum when the target is stationary and the red comb is that when the target is moving away from the collimator. It can be seen that every comb has a reduced offset due to the Doppler effect. As the target's velocity is much lower than that of light, the Doppler shift generated at 10 GHz repetition frequency is too small to be seen in the spectrum. In order to show that the repetition frequency has changed, we translate the red comb and move its center frequency to 110 MHz in Figure 3b. Hence, the changes of frequency interval can be seen on the high-order comb teeth due to the cumulative effect. It is thus proved that the Doppler effect causes a change in the repetition frequency, which can be used to calculate the velocity of a moving target. To show the directional discriminability, Figure 3c shows the frequency spectrum when the target is stationary, as well as leaving from and approaching the collimator with \(v\) = -100 mm/s and \(v\) = +100 mm/s. As can be seen, for the same teeth of the combs, the green line is on the left and red line is on the right. This proves that approaching leads to an increase in the repetition frequency and leaving leads to a reduction in the repetition frequency. When processing the data, we selected the two teeth at 110 MHz and 126 MHz to calculate the change in repetition frequency. This means taking the average of 16 repetition frequency data and increasing the resolution by 16 times. The greater the distance between the two teeth involved in the calculation, the higher the resolution. However, we saw only 16 sidebands in the spectrum analyzer, the other sidebands were suppressed due to their weak intensity. Hence, we selected those two teeth to make the calculation. We have conducted experiments to set the moving target at \(v\) from 100 to 300 mm/s with an interval of 50 mm/s and in the directions toward and away from the collimator. Figure 4 shows the results of velocity measurement. As shown in Figure 4, the velocity of the target is accurately measured by the dual optical comb LDV with a maximum deviation of 0.44 mm/s. Due to the minimum speed of the electric rail being 100 mm/s, we were not able to measure at a lower speed. Figure 3: Beat notes when the target is moving and stationary. The black line is the spectrum when the target is stationary; the red line is the spectrum when the target is moving away from the collimator.