## 5 Experiment Results
### Comparison of Measurement Accuracy  
In the experiments, the three methods (EPCM, PM, and MPMD) are used to measure the planar window glass with a diameter of about 90 mm. According to the above three methods, the surface shape results of the planar window glass are obtained after removing the first three terms of Zernike polynomials, as shown in Figure 7. Figure 7a-e shows the reconstruction results obtained by the EPCM, PM with systematic errors, the PM after eliminating systematic errors, and the MPMD. The measurement result obtained by the interferometer are shown in Figure 7e, and its root-mean-square (RMS) and peak-to-valley (PV) values are 519.77 nm and 2328.59 nm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods/Coordinates** & \(\mathbf{x_{c}}\) & \(\mathbf{y_{c}}\) & \(\mathbf{z_{c}}\) \\ \hline EPCM & 344.073 & 162.974 & \(-\)17.021 \\ PM & 338.571 & 162.928 & \(-\)21.154 \\ MPMD & 339.900 & 162.334 & \(-\)17.994 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Camera coordinates are obtained in three methods (EPCM, PM and MPMD). Unit: mm. Figure 6: Experimental setup of PMD based on the entrance pupil center. The surface shape shown in Figure 7a is closest to the interferometer, and its RMS value and PV value are 558.04 nm and 2505.05 nm, respectively. Compared with the interferometer, the RMS and PV values of the surface shape in Figure 7b are 317.58 nm and 1479.31 nm, and the inaccuracy of the defocus term is directly presented. However, the surface shape of Figure 7c is obtained by eliminating the systematic error of Figure 7b, and its RMS value and PV value are 559.63 nm and 2516.01 nm, respectively. This is closer to the interferometer than that in Figure 7b. In Figure 7d, compared with interference, it can be seen that there are serious errors in both defocus and astigmatism. According to the analysis in Table 1, not only the inaccuracy of the camera coordinates but also the rotation of the screen around the \(z\)-axis has a great impact on the reconstruction results, which introduce errors in astigmatism. As a result, the reconstruction results of the planar window glass are obtained after removing the first 6 terms of Zernike polynomials, as shown in Figure 8. I It can be seen from Figure 8 that Figure 8a-c are relatively closer to Figure 8e, while the low older error in Figure 8d is not yet removed due to the initial value choice of the shape coefficient and accuracy limit of the method. In a word, for the PM with systematic errors and MPMD, error of the low-order term is generated due to inaccurate coordinates, but the EPCM still has a high measurement accuracy. To further compare their accuracy performance, an optical planar element with a diameter of about 103 mm is measured. The surface shapes are obtained after removing the first three terms of the Zernike polynomials, as shown in Figure 9. Compared with the interferometer, the errors in Figure 9a,c are mainly reflected in the astigmatism term. It can be seen from Table 1 that the error is mainly caused by the rotation of the screen around the \(z\)-axis. Both Figure 9b,d have serious errors in terms of the defocus. These are mainly caused by the inaccuracy of \(z_{c}\) and \(z_{s}\), according to Table 1. In order to remove the errors mentioned above, the surface shapes are obtained after removing the first six terms of the Zernike polynomials, as shown in Figure 10. It can be directly shown from Figure 10 that Figure 10a,c are comparable to the interferometers in shapes and magnitudes. Due to the limitation of calibration accuracy, both Figure 10b,d have significant errors compared with the interferometer. Additionally, in our previous work (see Appendix A), for the same element, the results of removing the first four terms were obtained, and the RMS and PV were 27.70 nm and 187.40 nm (\(f\)/8), respectively, which are very close to the interferometer results (24.86 nm RMS and 154.73 nm PV).