## 3 Results  
To calculate the effective center wavelength of the OFC heterodyne interferometer, a square wave signal generated from a signal generator controlled the displacements of the PZT. The frequency of the square wave signal is 10 Hz, with a peak-to-peak value of 0.4 V. The sensitivity of PZT to light path variations was about 6.4 \(\upmu\)m/V, and the positions of M\({}_{3}\) were monitored precisely by the commercial interferometer.  
Figure 3a shows the phase change of OFC heterodyne interferometer and the commercial interferometers while tuning the displacements of PZT.  
The effective center wavelength at this position is calculated by:  
\[\lambda_{c}=\frac{2\pi n\Delta D}{\Delta\varphi}, \tag{13}\]  
where \(n\) is the refractive index of air. Since the displacement was larger than the wavelength, it was necessary to unwrap the phase when calculating the effective center wavelength. Environmental parameters were recorded throughout the experiment in order to calculate the air refractive index for both commercial interferometer and OFC heterodyne interferometer.  
To evaluate the stability of the effective center wavelength while the relative position of two overlapped pulses change, the bias voltage of the square wave was altered to shift the equilibrium position of PZT. The bias voltage was changed by six steps at 1 V interval (corresponding to 6.4 \(\upmu\)m).  
At each position, the effective center wavelength was measured 10 times. The average value and standard deviation are presented in Figure 4. The simulation results are also provided for comparison.  
When the pulse delay changed from \(-80\) fs to \(80\) fs, the effective center wavelength changed approximately \(1.02\) nm according to the simulation results. This is because the product of the electric amplitude of two beams was not symmetric, and the function of phase \(\varphi_{\text{beat}}\) change over the relative time delay was not a linear function. The biggest relative difference between the simulation and experiment was approximate to \(0.06\%\), which was predominantly caused by the random error of the commercial interferometer and the phase drifting caused by the AOM. The optical frequency comb had an especially wide spectrum; its coherence length was very short. When calculating the effective center wavelength for heterodyne interferometry, the displacement was only about \(2.5\)  
Figure 4: Effective center wavelength \(\lambda_{\text{c}}\) with different pulse delay. The data was measured by scanning the mirror M\({}_{3}\) through modulating the voltage of PZT. Black line: results of simulation; red line: results of experiments. Error bars represents \(+/-\)\(\sigma\) (standard deviation) for 10 measurements.  
Figure 3: (**a**) \(\varphi_{\text{beat}}\) change with time measured by lock-in amplifier; (**b**) displacement change with time measured by commercial interferometer.  
of commercial interferometer was only about 15 nm for the short displacement measurement, which was the main error source in the evaluation results shown in Figure 4. Note that the two beams in this experiment come out of the same optical fiber, thus, the initial phase \(\beta_{m}\) of two beams was equal. However, if the beams would have come from different optical fiber, the initial phase \(\beta_{m}\) of the two beams would be different because of the chirp of optical fiber. This case requires further investigation for calculating the effective center wavelength.