## 4 Results from Numerical Simulation  
Numerical simulations are performed with parameters listed in Table 1, based on the volume hologram printer in the author's lab. Figure 6 shows numerical reconstruction simulations of 2D model (USAF-1951 resolution chart) from normal, overlapped holograms without filter and with filter. Although the simulation has been done with perfect alignment of elemental holograms, visible dark gaps between elements are observed in the normal output shown in Figure 6a. The hologram consists of 24 elemental holograms--four in horizontal and six in vertical. Since the object is assumed as the collection of self-illuminated points, such gaps might be caused sampling errors of points between elements. Figure 6b shows reconstructed image from the overlapped hologram without the digital filter with 10% overlap in both vertical and horizontal. The hologram consists of 40 elemental holograms--five in horizontal and eight in vertical. Bright strips appear in the reconstructed image because the overlapped areas are recorded twice and it makes the overlapped areas brighter. Figure 6c shows reconstructed image from the overlapped hologram with the digital filter (10% overlap in  
Figure 5: Comparisons of normal and filtered elemental hologram tiling. Horizontal axis represents \(x\) and vertical axis represents intensity of reconstructed image. Black lines show intensity of each elemental hologram and red lines show the total intensity. (**a**) Gap with normal edge; (**b**) Aligned with normal edge; (**c**) Overlap with normal edge; (**d**) Gap with filtered edge; (**e**) Aligned with filtered edge; (**f**) Overlap with filtered edge.  
both vertical and horizontal). One can find that the boundaries between elements are less visible than other results. Figure 7 shows numerical reconstruction simulations of a 3D model (skull) from normal, overlapped holograms without filter and with filter. The all holograms consist of 60 elemental holograms--six in horizontal and ten in vertical. Therefore, the printing time of all holograms will be the same. Figure 7a shows the result of normal output without overlapping. The split lines among each elemental holograms are obviously. With 10% in horizontal and 10% in vertical of overlapping, the images without filter and with filter are shown in Figure 7b,c, respectively. Bright grid appears in Figure 7b, of which the digital filter is not applied. In contrast, intensity fluctuations become smaller with the digital filter as shown in Figure 7c. From Figures 6c and 7c, it turns out that the proposed filter is effective to improve image quality of the volume hologram printer.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Laser wavelength & 532 nm \\ CGH (LCOS) pixels & 4096 \(\times\) 2160 \\ CGH (LCOS) pixel pitch & 4.0 μm \\ Distance \(d\) between CGH and virtual window & 40 mm \\ (Focal length of L3) & \\ Virtual window width \(W\) & 4.0 mm \\ Virtual window height \(H\) & 2.0 mm \\ Offset of virtual window \(M\) & 0.2 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters based on the volume hologram printer.  
Figure 6: Reconstructed images from USAF-1951 resolution chart. (**a**) Normal output without overlapping; (**b**) 10%, 10% overlapping without filter; (**c**) 10%, 10% overlapping with filter.