# Computer-Generated Hologram Based on Reference Light Multiplexing for Holographic Display
## 3 Numerical Simulation and Emulation  
In order to prove the viability of proposed method, we conducted numerical simulations. The parameters used in the computation included a 1080 \(\times\) 1920 resolution for the CGH, and a pixel size of 8 \(\upmu\)m \(\times\) 8 \(\upmu\)m. The simulations were performed by a computer with MATLAB on Core i7-7700, 3.6 GHz, and 8G RAM.  
In the numerical simulations, we first used different cylindrical light waves as reference light waves and reconstructed four independent images at the same position, as shown in Figure 4. The numerical reconstructions without iterations are shown in Figure 4e-h, which demonstrates how the proposed method can reconstruct different images successfully; although, there is some crosstalk and speckle noise in the reconstructed images. RMSE and SC of reconstructed images are shown in Table 1. In numerical simulations, a total of 20 iterations is enough to guarantee that images will be reconstructed accurately; the reconstructed results with 20 iterations are presented in Figure 4i-l. The results show that the reconstructed images created after these iterations are more accurate and clearer to the naked eye. The RMSE decreases by 51.1%, 50.1%, 56.5%, and 52.1%, and SC decreases by 43.8%, 41.9%, 37.3%, and 37.8%, respectively, compared with the results of the non-iteration process. It is apparent that crosstalk and speckle noise is small in reconstructed images obtained from 20 iterations. Hence, the proposed method can increase information  
Figure 3: Flowchart of proposed method.  
capacity. It is noteworthy that the RMSE and SC increase by 60.9% and 51.4% when nine independent images are reconstructed at the same position, indicating that the quality of reconstructed images under these circumstances is not satisfactory enough.  
In order to improve information capacity further, we reconstructed different images at different positions. We chose different spherical light waves as reference light waves. Images shown in Figure 5a-d were located at 200 mm from the CGH plane, whereas the images shown in Figure 5e-h were located at 210 mm. The reconstructed results with 20 iterations are shown in Figure 5i-p. It is apparent that all images were reconstructed successfully. RMSE and SC of the reconstructed images are shown in Table 2. From these results, we can conclude that information capacity can be multiplied by the proposed method with position multiplexing.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Iteration** & **Image** & **RMSE** & **SC** \\ \hline \multirow{4}{*}{0} & pepper & 0.325 & 0.513 \\  & cameraman & 0.337 & 0.518 \\  & baboon & 0.352 & 0.536 \\  & woman & 0.303 & 0.516 \\ \hline \multirow{4}{*}{20} & pepper & 0.159 & 0.288 \\  & cameraman & 0.168 & 0.301 \\ \cline{1-1}  & baboon & 0.153 & 0.336 \\ \cline{1-1}  & woman & 0.145 & 0.321 \\ \hline \hline \end{tabular}
\end{table}
Table 1: RMSE and SC of numerical reconstructions.  
Figure 4: Numerical reconstructions; (**a**) ’pepper’, (**b**) ’cameraman’, (**c**) ’baboon’, (**d**) ’woman’ are target images, (**e**–**h**) are reconstructed images without iterations, and (**i**–**l**) are reconstructed images with 20 iterations.