## 3 Experiments and Results  
In this study, the input image resolution was 110 \(\times\) 110, and the resolution of output phase information was 1920 \(\times\) 1080. The reconstruction was calculated in two parts. In the first part, the multi-depth image, the digits \"1\", \"2\", and \"3\" were placed at the reconstruction distance 0.2 m, 0.3 m, and 0.4 m for phase-locked encryption transform. By switching the corresponding phase-locked key, the image with corresponding depth could be effectively reconstructed. Figure 8 shows the reconstruction simulation results. Figure 8 display the differences. With a phase-locked algorithm, coaxial reconstruction with distinct depth essentially reduced the interference caused by coaxial out-of-focus image information, as in Figure 8. The image assessment results are shown in Table 1.  
In the second part, the multi-angle image, the digits \"1\", \"2\", and \"3\" were placed at the reconstruction distance 0.2 m, with the encryption angles of 42\({}^{\circ}\), 45\({}^{\circ}\), and 48\({}^{\circ}\), respectively, for the phase-locked encryption transform. By switching the corresponding phase-locked keys in the reconstruction, the images with corresponding angles could be effectively reconstructed. Figure 9 shows the reconstruction simulation results. Noticeable differences can be seen in Figure 9,b; with the phase-locked algorithm, the interference of coaxial out-of-focus image information was drastically reduced in the reconstruction with the same depth but different angles, as shown in Figure 9. The image assessment results are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Picture** & **RDE** & **RMSE** & **SNR** \\ \hline \multirow{3}{*}{MGSA} & 1 & 69.22\% & 0.0262 & 3.52 dB \\ \cline{2-5}  & 2 & 76.62\% & 0.0246 & 5.16 dB \\ \cline{2-5}  & 3 & 62.17\% & 0.0286 & 3.72 dB \\ \hline \multirow{2}{*}{Phase encryption algorithm} & 1 & 82.56\% & 0.0180 & 6.75 dB \\ \cline{2-5}  & 2 & 92.99\% & 0.0122 & 11.23 dB \\ \cline{2-5}  & 3 & 91.66\% & 0.0132 & 10.41 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Assessment results of reconstruction images simulated with multi-depth phase encryption algorithm. Figure 8: Results of coaxial reconstruction with distinct depth (**a**) with phase-locked algorithm and (**b**) without phase-locked algorithm. The optical experiment was also conducted to verify the phase-locked algorithm's effectiveness further. The optical setup is depicted in Figure 10. It comprises a collimated light source, a beam splitter (BS), two spatial light modulators (SLMs), and a charge coupled device (CCD). The collimated light source has a wavelength of 532 nm. These two SLMs are pure-phase-modulated from Jasper Display Corp (JD8554), with 1920 \(\times\) 1080 pixels, 256 grey levels, and a pixel size of 6.4 \(\upmu\)m \(\times\) 6.4 \(\upmu\)m. The phase-locked key and encryption image phase are added to the two SLMs accordingly. When the collimated light propagates through the BS and SLM1, the light can be modulated by the phase-locked key loaded on SLM1. Then, the modulated light can illuminate SLM2 after the reflection of SLM1. The images with the corresponding phase-locked keys could be effectively reconstructed by switching the corresponding phase-locked keys in the reconstruction. The results of the experiments are slightly different from the simulations due to factors such as the system alignment and the tolerance of image capturing, but the results of the phase-locked algorithm optimization can be identified. Noticeable differences can be seen in Figures 11a,b and 12a,b; with the phase-locked algorithm, the interference of coaxial out-of-focus image information was reduced in the reconstruction, as shown in Figures 11a and 12a.