## 4 Discussion  
Based on dual differential frequency photoelastic modulation, the simultaneous measurement of the two parameters of waveplate retardance and fast-axis azimuth is realized. The measurement results of the 1/4 waveplate show that the standard deviation of the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Waveplate** & **Retardance (nm)** & **Legend** & **Data Points** &
\begin{tabular}{c} **Fast-Axis** \\ **Azimuth** \\ \end{tabular} \\ \hline \multirow{3}{*}{1/4 Waveplate} & 135.0 \(\pm\) 0.5 & & 48 & 83.33 \(\pm\) 0.03 \\  & 136.5 \(\pm\) 0.5 & & 53 & 83.33 \(\pm\) 0.03 \\  & 179.28 & & 1 & 82.53 \\ \hline \multirow{3}{*}{1/2 Waveplate} & 61 \(\pm\) 0.5 & & 3 & 109.10 \(\pm\) 0.4 \\  & 265.6 \(\pm\) 0.5 & & 36 & 109.40 \(\pm\) 0.03 \\ \cline{1-1}  & 268 \(\pm\) 1 & & 63 & 109.40 \(\pm\) 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The 532 nm waveplate parameter measurements.  
Figure 7: Waveplate parameter measurement results of the 532 nm waveplate in the entire clear aperture: (**a**) 1/4 waveplate; (**b**) 1/2 waveplate.  
fast-axis azimuth is \(\sigma_{\theta}=0.02^{\circ}\), and the measurement standard deviation of the retardance is \(\sigma_{\phi}=0.03\) nm. These findings demonstrate that the proposed measurement system has good stability and repeatability. Highly sensitive waveplate parameters measurements are realized. The maximum relative deviation of the fast-axis azimuth measurement obtained by rotating the entire waveplate is 0.6%, and the maximum relative deviation of the waveplate retardance measurement is 0.06%, indicating that the test system in this study achieves high-precision waveplate parameter measurements. In addition, the system data processing is based on FPGA digital phase-locking technology, which can simultaneously eliminate measurement influences such as the fluctuation in laser light intensity. The single-point data measurement time is only 200 ms, which is suitable for fast measurements. Moreover, the presented method is compatible with the two-dimensional motorized scanning stage, which can support parameter measurements in the entire waveplate light transmission range, and the maximum area can be 150 \(\times\) 150 mm in this system. The test results of this study are compared with those in the existing literature, and are listed in Table 3.  
The proposed method achieves higher repeatability, greater precision, and faster waveplate parameter measurements than the existing methods. Moreover, the presented scheme can simultaneously measure the parameters of the entire light-passing area of the waveplate. Through the test results of the entire light-passing area, it is evident that the retardance and fast axis of the waveplate in the entire light-passing area are clearly shown, providing a comprehensive understanding of waveplate parameters. Therefore, the proposed approach serves as an effective quality inspection and calibration method for waveplates. However, the individual abnormal data points at the edges of the waveplate parameters should be eliminated. It is estimated that the laser is blocked or reflected by the edge of the rotating mirror frame, causing measurement errors. This should be eliminated when testing the quality of the waveplate.  
Moreover, it is worth noting that this study uses a He-Ne laser as the detection light source. The wavelength of the light source is 632.8 nm, and the spectral bandwidth is less than 2 pm, which can achieve the precise retardance of the waveplate at this wavelength. However, when it is applied to waveplates of other wavelengths, the spectral dispersion of the waveplate material should be considered to ensure accuracy. We will expand on and develop this topic in future work.