## 6 Discussion and Conclusions  
We compared three methods in this study. Inaccurate system calibration is one of the major error sources in PMD, which limits its practical applications. In EPCM, the camera position is no longer calibrated by [PERSON]'s technology; the entrance pupil center is accurately calculated as a point source by EPCM. The measurement accuracy is high for measuring the low order terms of the surface if the experimental misalignment can be controlled very well. In PM, the accuracy of [PERSON]'s technique is easily affected by the quality of the calibration target and the accuracy of feature point extraction. There are also too many parameters to be addressed in the optimization of the non-linear camera model, which makes it difficult to accurately obtain the projection center of the camera lens. The projection center obtained by this method is unstable, but the accuracy is high after eliminating the systematic error [10]. In MPMD, the pre-calibration result is only used as an initial value in the post-optimization, and the screen pose can be optimized with the shape estimation for a mono-PMD system. If a good pre-calibration is obtained, the MPMD method will obtain a relatively low shape error. However, the reconstruction result will be worse if the pre-calibration is performed poorly, including an initial guess far from the reality. Figure 10: Experiment results of the optical planar element (after removing the first six terms): (**a**) EPCM; (**b**) PM with systematic errors; (**c**) PM after eliminating systematic errors; (**d**) MPMD; (**e**) Interferometer. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Experiments/Methods**} & \multirow{2}{*}{**EPCM**} & \multicolumn{2}{c}{\
\begin{tabular}{c} **PM with** \\ **Systematic Errors** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **PM after** \\ **Eliminating** \\ **Systematic Errors** \\ \end{tabular} } & \multicolumn{2}{c}{**MPMD**} & \multicolumn{2}{c}{**Interferometer**} \\ \hline  & & **RMS** & **PV** & **RMS** & **PV** & **RMS** & **PV** & **RMS** & **PV** & **RMS** & **PV** \\ \hline \multirow{4}{*}{1} & Removing the first & \multirow{2}{*}{96.26} & \multirow{2}{*}{626.81} & \multirow{2}{*}{98.96} & \multirow{2}{*}{587.14} & \multirow{2}{*}{1479.31} & \multirow{2}{*}{559.63} & \multirow{2}{*}{2516.01} & \multirow{2}{*}{624.76} & \multirow{2}{*}{105.36} & \multirow{2}{*}{598.96} & \multirow{2}{*}{101.12} & \multirow{2}{*}{601.48} \\  & & & & & & & & & & & \\ \hline \multirow{2}{*}{2} & Removing the first & \multirow{2}{*}{80.22} & \multirow{2}{*}{373.95} & \multirow{2}{*}{864.53} & \multirow{2}{*}{3361.53} & \multirow{2}{*}{79.10} & \multirow{2}{*}{366.13} & \multirow{2}{*}{1592.84} & \multirow{2}{*}{6085.75} & \multirow{2}{*}{36.63} & \multirow{2}{*}{187.00} \\  & & & & & & & & & & & \\ \hline \multirow{2}{*}{1} & Removing the first & \multirow{2}{*}{13.71} & \multirow{2}{*}{80.50} & \multirow{2}{*}{29.20} & \multirow{2}{*}{174.95} & \multirow{2}{*}{13.91} & \multirow{2}{*}{85.79} & \multirow{2}{*}{44.84} & \multirow{2}{*}{274.04} & \multirow{2}{*}{13.56} & \multirow{2}{*}{73.85} \\  & & & & & & & & & & & \\ \hline \hline \end{tabular} Number 1 represents the planar window glass, and number 2 represents the optical planar element.  
\end{table} 
Table 3: Experiment results of the planar window glass and the optical planar element. Unit: nm. It is generally believed that good results of camera calibration imply a higher accuracy of the reconstructed surface shape. Hence, some methods [7; 8; 11; 15; 21] have been developed to calibrate parameters by reducing the calibration error as much as possible. This paper shows that EPCM has a higher measurement accuracy in comparison with the other two methods. Conceptualization, R.G. and D.L. ; methodology, R.G. and D.L. ; software, R.G., D.L., X.Z., R.W. and W.Z. ([PERSON]); data curation, R.G., D.L. and X.Z. ; writing--original draft preparation, R.G. ; writing--review and editing, D.L., X.Z., R.W, X.L. and W.Z.