## 3 Experiment and Results
Figure 6: Atomic force microscopy (AFM) images and grating shape details of the fabricated 2D gratings under the initial polarization status of **(a)** (s, s, s) and **(b)** modulated polarization status (s, \(-\)33.5\({}^{\circ}\), 33.5\({}^{\circ}\)). From Figures 5 and 6, it can be concluded that the grating shape and area of these two polarization status are all consistent with the preliminarily designed value. However, before it can be employed to the grating interferometry system, grating diffraction efficiency that influencing the inference signals are required to be evaluated. An experimental setup, as shown in Figure 7a, was constructed and the measurement point distribution is shown in Figure 7b. As for the real interferometry system, the incident beam was polarized to be circular and pass through the fabricated grating. After the diffraction of the grating, four first-order diffracted lights appear on the observation screen. The power of each diffracted light can be read by the power meter, which was then divided by the output power of the laser source, thus we can get the diffraction efficiency. The measurement results were summarized by Tables 1 and 2. Each diffraction efficiency is larger than 6%, and all the sum efficiency of all the first diffraction beam are larger than 50%. For the uniformity of the +1 and the \(-1\) diffraction beams along the X- and Y-directions, the initial polarization is better than the modulated polarization, this may be because the intensity was redistributed by the two QWPs. The diffraction difference between the X- and the Y-direction is mainly due to the unideal intensity uniformity within the plane wavefront. For comparison, we conducted experiments at the incident angle \(\theta\) of 60\({}^{\circ}\) and 85\({}^{\circ}\) without polarization modulation, i.e., (s, s, s), corresponding to the grating periods of 625 nm and 3586 nm, respectively. Under such polarization and incident angle, the \(\gamma_{23}\) is larger than that of \(\theta\) of 71.8\({}^{\circ}\) \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Points** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline X + 1 & 0.21 & 0.18 & 0.17 & 0.22 & 0.19 & 0.19 & 0.22 & 0.18 & 0.18 \\ X \(-\) 1 & 0.19 & 0.16 & 0.16 & 0.21 & 0.18 & 0.18 & 0.21 & 0.17 & 0.17 \\ Y + 1 & 0.13 & 0.14 & 0.12 & 0.09 & 0.13 & 0.13 & 0.07 & 0.12 & 0.13 \\ Y \(-\) 1 & 0.13 & 0.14 & 0.13 & 0.08 & 0.13 & 0.13 & 0.06 & 0.13 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Diffraction efficiency testing result of the grating fabricated without polarization. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Points** & **I** & **II** & **III** & **IV** & **V** & **VI** & **VII** & **IX** \\ \hline X + 1 & 0.06 & 0.05 & 0.06 & 0.09 & 0.06 & 0.09 & 0.14 & 0.13 & 0.12 \\ X \(-\) 1 & 0.12 & 0.08 & 0.10 & 0.17 & 0.11 & 0.14 & 0.22 & 0.19 & 0.18 \\ Y + 1 & 0.22 & 0.23 & 0.22 & 0.12 & 0.20 & 0.17 & 0.07 & 0.13 & 0.14 \\ Y \(-\) 1 & 0.18 & 0.22 & 0.19 & 0.07 & 0.17 & 0.13 & 0.01 & 0.09 Figure 8 shows the AFM images. This result reveals that the groove of 2D gratings deviated from square and was more inclined to elliptical shape, which cannot meet the interferometry application. Therefore, it is necessary for fabricating 2D grating to operate HWPs at 60\({}^{\circ}\) and 85\({}^{\circ}\), as well as other angles. The specific values of modulation need to be calculated based on the three-dimensional polarization ray-tracing calculus [20].