## 3 Results
### Detection Performance of the Interferometer  
According to the interferometer input-output relationship in Equation (12), the experimental interferometer system shown in Figure 3 was applied to perform a micro-vibration measurement experiment. A reflector was attached to a piezoelectric ceramic vibrator, with the driving frequency set to 1 MHz. The differential output signal of PD3 and PD2 (\(P_{32}\)) was amplified by a preamplifier with a frequency range of 20 KHz to 2 MHz and was then acquired by a digital oscilloscope (DPO 3012, Tekronix). Before detection, the same three steps as those used in Section 3.2. were followed. Here, the value recorded in Step 2 was 0.09 V. The peak-to-peak value of the sinusoidal excitation signal from the function generator was adjusted to 0.2 V, with a DC bias voltage of 0.2 V. The excitation signal is shown in Figure 7a. The output signal from the interferometer is shown in Figure 7c. Figure 7b,d show the spectra of the excitation signal and output signal, respectively.  
It can be seen from Figure 7 that the experimental interferometer system used in this paper, with the self-designed probe and proposed feedback control scheme, has a good follow-up effect on the piezoelectric ceramic excitation signal. According to the spectra of the excitation signal and output signal, the two signals have the same main frequency of 1 MHz with different intensities. In addition, compared with the excitation signal spectrum, the output interferometer signal spectrum has tiny harmonic frequencies with 1 MHz components. But the origin of these harmonics is unclear at the moment. Moreover, we successfully detected micro-vibrations with frequencies ranging from 600 kHz to 2.3 MHz by adjusting the frequency of the function generator. Higher frequency signals cannot be detected here because the frequencies are out of the frequency range of the piezoelectric ceramic vibrator and the preamplifier. If a higher frequency measurement should be implemented, a higher frequency piezoelectric ceramic vibrator would be needed to generate high frequency micro-vibrations. In addition, a preamplifier with a higher bandwidth would be needed.  
Figure 6: The result of the phase fading compensation via the feedback control scheme when the initial phase difference is located at (**a**) \([-\pi/2,\pi/2)\) and (**b**) \([\pi/2,3\pi/2)\).  
It is known that the output interferometer signal is related to the displacement of vibrations from Equation (12). The relationship is linear when the powers of the two lights from the reference arm and sensing arm are constant. However, the power of the light from the sensing arm (\(I_{2}\)) may vary slightly if the self-designed probe is moved for detection in a point-by-point scanning mode. In addition, the slight vibration caused by the external environment may give rise to the variance of \(I_{2}\). If we can obtain the value of \(I_{2}\) when the output signal is recorded, the output signal can be normalized by dividing it by \(\sqrt{I_{2}}\). In our experiment, the value of \(I_{2}\) was changed by adjusting the angle of the reflector under the condition that the amplitude and frequency of the excitation signal were constant. Three sets of measured and calculated results are shown in Table 1. It can be seen that the output signal decreases significantly as \(I_{2}\) is reduced and that the maximum deviation from the mean is 35%. By contrast, the normalized result stays stable, with a maximum deviation from the mean of 1.9%. Therefore, the normalized result can partly eliminate the effect caused by the variance of the light power from the self-designed probe.