# Time-Division Color Holographic Projection in Large Size Using a Digital Micromirror Device +
## 3 Results
### Simulation Results  
Figure 9 shows the reconstruction results from the simulation. The size of all reconstructed images is approximately 11.3 cm \(\times\) 6.5 cm. The methods used in Figure 9a-f correspond to methods (a)-(f) in Table 2.  
Table 3 shows the image quality evaluation using mean squared error (MSE). The MSE evaluates the average error per pixel between the original and reconstructed images. The smaller the MSE, the closer the reconstructed image is to the original image. The MSE is expressed by  
\[\text{MSE}=\frac{1}{XY}\sum_{x=1}^{X}\sum_{y=1}^{Y}\{I_{o}(x,y)-I_{R}(x,y)\}^{2} \tag{2}\]  
where we denote the original image as \(I_{o}(x,y)\), the reconstruction intensity of the reconstructed image as \(I_{R}(x,y)\), and the size of the original and reconstructed images is \(X\times Y\).  
Comparing Figure 9a,d, Figure 9d has higher contrast. However, comparing methods (a) and (d) in Table 3, there is no significant difference in MSE. This is due to the time-division reconstruction method, which creates boundaries between the divided blocks, hindering the decrease in the MSE.  
Compared to Figure 9a, applying the multi-random phase method or pixel separation methods reduces the speckle noise, improving the image quality in each reconstructed image. Subjectively, no significant difference in the quality of the reconstructed image between the multi-random phase and pixel separation methods exists. Table 3 also shows that the MSEs are reduced by applying either the multi-random phase or pixel separation methods. Quantitatively, no significant difference between the MSEs of the multi-random phase and pixel separation method exists. Figure 9e,f of the proposed methods are subjectively superior to other methods. In particular, Figure 9f has the best MSE.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Methods**} & \multicolumn{2}{c}{**Summary**} \\ \hline  & & & Used the method of in [7]. The pixel pitch of the original image is four times (30.24 \(\mu\)m) to enlarge the reconstructed image. The pixel pitch should not exceed the Nyquist frequency. \\
**Comparison** & (a) & Pixel pitch expansion + & This combines (a) above with the multi-random phase method \\
**Methods** & (b) & Multi-random phase & [10]. Six CGHs with different random phases are projected. \\  & (c) & Pixel pitch expansion + Pixel & This combines method (a) with the pixel separation method [11] \\  & (c) & separation & and projects six CGHs with different separation images. \\ \hline  & & & A method that combines time-division reconstruction method with uneven color correction. Up-samples the original image to four times its resolution (7680 \(\times\) 4320 pixels). Divide the original image horizontally and vertically into 4 \(\times\) 4 blocks. \\
**Proposed** & (e) & Time-division reconstruction + & This combines method (d) with the multi-random phase method [10]. Six CGHs with different random phases were projected onto each block. \\  & (f) & Time-division reconstruction + & This combines method (d) with the pixel separation method [11] and projects six CGHs with different separation images. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of methods.