## 3 Experiment
### Phase Modulation Amplitude Setting and System Initial Offset Calibration  
PEM is an optical electromechanical device with resonant characteristics. The phase modulation amplitude of the processed PEM is proportional to the peak-to-peak value of the driving voltage, and the phase modulation amplitude can be precisely adjusted by the driving voltage [11]. From the theoretical analysis of Equations (5)-(7), it is necessary to reasonably set the phase modulation amplitudes of the two PEMs, which makes the 0 th and 1 st order Bessel series, \(J_{0}\) and \(J_{1}\), take the maximum value, and the amplitudes of the fundamental frequency harmonic terms (\(V_{\omega_{1}}\) and \(V_{\omega_{2}}\)) and the difference frequency harmonic term (\(V_{\omega_{2}-\omega_{1}}\)) are large. Thus, the fundamental frequency and difference frequency signals are the main components of the modulated light intensity signals, and a high signal-to-noise ratio for data processing is obtained. The numerical calculations of the Bessel series that varies with the PEM phase modulation amplitude are shown in Figure 2.  
As shown in Figure 2, when the phase modulation amplitudes of the two PEMs are set near 1.435 rad, the Bessel series terms, \(J_{0}J_{1}\) and \(J_{1}J_{1}\), take the maximum value. In this study, the peak-to-peak driving voltages of the two PEMs are set to 190.5 V and 189.2 V, respectively, so that the phase modulation amplitude reaches 1.435 rad.  
First, when no sample is used, the detection light signal is modulated by the two PEMs and the modulated light intensity signals are digitally phase-locked for data processing to complete the calibration of the initial value of the system. The digital phase-locking cycle is set to 1008 cycles for the differential frequency signal, i.e., \(\omega_{2}-\omega_{1}=5.041\) kHz, and the data point is measured at an interval of 200 ms. The fundamental harmonic terms (\(V_{\omega_{1}}\) and \(V_{\omega_{2}}\)) and the difference frequency harmonic terms (\(V_{\omega_{2}-\omega_{1}}\)) are extracted and recorded, as shown in Figure 3.  
When no sample is used, the differential frequency harmonic term (\(\overline{V}_{\omega_{2}-\omega_{1}}=3.899\times 10^{8}\) a.u.) is much larger than the two fundamental harmonic terms (\(\overline{V}_{\omega_{1}}=2.077\times 10^{5}\) a.u. and \(\overline{V}_{\omega_{2}}=6.254\times 10^{5}\) a.u.), and the harmonic term ratios are small, (\(\overline{R}_{1}=0.533\times 10^{-3}\) and \(\overline{R}_{\rm{II}}=1.604\times 10^{-3}\)). In fact, when there is no sample, the two ratios should approach zero. This is mainly due to the small residual birefringence of the two PEMs. However, the two PEMs in the system are elaborately manufactured, and the harmonic term ratios do not exceed the order of \(10^{-3}\). To achieve high-precision measurement of the waveplate parameters, this study regards the above two non-zero ratios as the initial offset values of the system. In actual measurements, the obtained signal ratio must be subtracted from the initial offset value of the system to reduce or eliminate the system measurement error to the greatest extent possible.  
Figure 2: Bessel series variation in accordance with PEM phase modulation amplitude.