## 3 Experiment
### Waveplate Parameter Measurement Experiment  
The measurement accuracy and repeatability of the proposed scheme are determined. First, we select a 1/4 waveplate sample at the wavelength of 632.8 nm for the experiment. During the experiment, the temperature of the laboratory is set at 23 \({}^{\circ}\)C, and the temperature fluctuation does not exceed 0.1 \({}^{\circ}\)C during the entire experiment. The 1/4 waveplate is a compound zero-order waveplate (GCL-060402), produced by Beijing Daheng New Era Technology Co., Ltd. The accuracy of the waveplate retardance is \(\lambda/300\). The size of the waveplate is 1 inch. It is installed on a rotatable mirror frame with an angular rotation accuracy of 5\({}^{\prime}\). The effective clear aperture is 22 mm after the optical kit holding. The waveplate is placed in the middle of the scanning stage. The detection laser light passes through the center of the waveplate, and the azimuth angle of the fast axis of the waveplate is adjusted to 22.5\({}^{\circ}\). The harmonic terms obtained by digital phase-locking are shown in Figure 4.  
In Figure 4a, the differential frequency harmonic terms are almost zero, and the values of the two fundamental frequency harmonic terms are very close. The harmonic terms (\(V_{\omega_{1}}\), \(V_{\omega_{2}}\), and \(V_{\omega_{2}-\omega_{1}}\)) and Bessel series are substituted into Equations (7) and (8). Accordingly, the two parameters of the waveplate retardance and fast-axis azimuth can be further solved, as shown in Figure 4b. The test record lasts for approximately 1 min, with approximately 200 test data points. The measurement results show that the average fast-axis azimuth of the waveplate is \(\overline{\theta}=22.49^{\circ}\), the standard deviation is \(\sigma_{\theta}=0.02^{\circ}\), and the average retardance of the waveplate is \(\overline{\Phi}=158.43\) nm, and the standard deviation is \(\sigma_{\Phi}=0.03\) nm, indicating that the measurement system in this study has good stability and repeatability. Parameter measurements are also performed at different azimuth angles. The fast-axis azimuth of the waveplate is adjusted from 0\({}^{\circ}\) to 180\({}^{\circ}\) at intervals of 20\({}^{\circ}\), and the results are recorded in Figure 5.  
Figure 3: Digital phase-lock result of modulation signals: (**a**) amplitude of harmonic terms; (**b**) ratio of harmonic terms.  
In Figure 5a, the fast-axis azimuth angle measurements and actual values are in good agreement. When the fast-axis azimuth is rotated at 100\({}^{\circ}\), the measured value is  
Figure 4: The 1/4 waveplate parameter experimental results: (**a**) harmonic terms; (**b**) waveplate parameter measurement values.  
Figure 5: The 1/4 waveplate parameter experimental results under different angles: (**a**) fast-axis azimuth; (**b**) retardance at different fast-axis azimuths.  
100.6\({}^{\circ}\), and there is a maximum relative deviation, i.e., \(\frac{\Delta_{\Phi}}{\theta}=\frac{100.6-100}{100}\times 100\%=0.6\%\). In Figure 5b, the deviation between the retardance measurement and actual value is notably small. When the fast-axis azimuth is rotated at the position of 60\({}^{\circ}\), the measured value of the waveplate retardance is 158.33 nm, there is a maximum deviation of \(\Delta_{\Phi}=\left|\Phi-\overline{\Phi}\right|=\left|158.33-158.43\right|=0.1\) nm, and the corresponding maximum relative deviation is \(\frac{\Delta_{\Phi}}{\Phi}=\frac{0.1}{158.43}\times 100\%=0.06\%\). The results show that the system realizes the measurement of the waveplate parameters with high precision.