# Efficient Hogel-Based Hologram Synthesis Method for Holographic Stereogram Printing
## 3 Results  
### Numerical Simulation  
The proposed method was verified via numerical simulation. The perspectives of a virtual 3D scene were rendered using the re-centering camera model. Computer-graphic rendering process was performed on a Windows 10 64-bit PC with 8 GB of RAM, a 3.2 GHz Intel (R) i5-4570 CPU, and an NVIDIA GT 630 graphics card. Figure 5 shows the 3D scenes used in the experiment and its synthesized holograms from re-arranged hogels. Directional data for the synthetic 3D scenes were acquired at different viewing angles within a field of view of 30\({}^{\circ}\) as shown in Figure 5a,b. The distance between the object and hologram plane was 400 mm in each simulation and the depth between the two objects \"Teapot and sphere\" was 40 mm. A sub-hologram is commonly generated from many perspectives of a 3D scene, which are processed to form parallax-related images. This is defined by the \(H\) matrix as shown in Figures 3 and 4. The parallax-related images contain directional information on the hologram plane, which can be observed as a spectral representation of the hologram (thus, a collection of spatial frequency components). In full-parallax HS, all hogels are mutually independent and further encoded as phase holograms, as shown in Figure 5.  
Figure 6 shows the rendered perspective images with higher resolution in the proposed method compared with the captured perspective images at a lower resolution by the conventional method. In both cases, indexes of captured images and the resolution of a corresponding hogel is shown in numerical value and it was assumed that the hologram plane was synthesised from \(50\times 50\) hogels for both methods. Figure 6a presents 2500 perspectives (in terms of a numerical substitution of indexes \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **Rendering(s)** & **Hogel Generation(s)** & **CGH Pattern(s)** & **IFTA(s)** & **Recording(s)** & **Total Time(s)** \\ \hline Conventional method & 1375 & 120 & 857 & 32 & 3000 & 5384 \\ Proposed method & 2291 & 2759 & 756 & 46 & 3000 & 8852 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computation times. and values) captured for the conventional method and example of re-arranged hogels. Figure 6b shows fewer perspectives at higher resolution for the proposed method. For hogels with a resolution of \(200\times 200\) pixels as shown in Figure 6b, larger hogels improve the angular resolution of an HS, and the accuracy of orienting the plane waves created locally within a hogel. It is confirmed by measurement results from Equation (5). Figure 5: 3D scene and hologram synthetization from full-parallax HS: (**a**) 3D object “Teapot and sphere.” (**b**) 3D object “Bunny and carrot.”  
Figure 6: Comparison of rendered perspectives in terms of pixel disparity: (**a**) conventional method and (**b**) proposed method. The conventional pixel re-arrangement technique re-arranges hogel with \(50\times 50\) pixels, according to Equation (3), and this process makes perspective image blurring at lower resolution, as shown in Figure 6a. On the contrary, the proposed method captures 100 perspectives based on a \(10\times 10\) camera array. Each view featured \(1000\times 1000\)-pixel higher resolution, as shown in Figure 6b. In the proposed method, the size of each hogel is increased from \(50\times 50\) pixels to \(200\times 200\) pixels based on a proposed pixel re-arrangement algorithm. This process allows us to maintain the spatial resolution while benefiting from greater angular resolution from the larger hogel size compared to conventional re-arranged hogels. Figure 7 compares the numerical reconstructions of the two synthetic 3D scenes for the conventional and proposed method. The holograms were reconstructed at the distance of 400 mm for a 2 mm-diameter pupil. The holographic spatial sampling size was 129 \(\upmu\)m. The sampling requirement for the human visual system was adopted and the perceived resolution was lowered.