## 3 Design Concept and Methodologies
This quantity is named extended SBP(eSBP), which is defined in Equation (1):  
\[eSBP=SBP*frame\ rate\ (\text{or \refresh\ rate})=(pixel\ resolution)*(frame\ rate) \tag{1}\]  
Figure 3: Basic challenge of the system design. Figure 2: (a) Conceptual drawing of the design goal. (b) Schematics of system specifications. Some of typical SLM devices are compared in terms of SBP and eSBP in Table 3. From the table, we see that although the SBP of DMD is smaller than LCD or LCoS, the eSBP value is much larger. We utilize the large eSBP value of a DMD device to spatially distribute fast refreshing hologram images by temporal multiplexing, thus achieving very wide viewing angle. The following details the basic methods that we applied to the display system design for the required specifications. 1. Image size is first enlarged by simple optical magnification using _4-f_ optics, which results in enlarged virtual SLM (from 1.27 cm to 7.62 cm). The price of this image enlargement is reduced diffraction angle of the virtual enlarged SLM (from 2\({}^{\circ}\) to 0.3\({}^{\circ}\)). 2. We make a viewing window at viewing distance of 900 mm by adding a field lens in the position of virtual SLM plane, forming the size of 4.7 mm \(\times\) 4.7 mm rectangular viewing window. 3. Seamless horizontal viewing zone is made by circularly tiling the viewing windows of the appropriate number of viewpoint-dependent hologram images. In our system, the viewing zone has a circumferential length of ~4000 mm, which can be covered by tiling more than 851 viewing windows. In actual implementation, 1024 viewing windows are tiled with some overlap between adjacent ones. This is achieved by temporal multiplexing with mechanical scanning optics. Steps (1)-(3) are shown in Figure 4.  
4. The viewpoint-dependent hologram images are designed to be seen at the center of the tabletop display, so that coalition of them makes a volumetric 3-dimentional image floating in the air. This is achieved by two stages of optics. In the first stage, the light path of the hologram image is  
Figure 4: Schematic diagram of the design (1), (2), and (3) denotes the corresponding step in the text. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**SLM Type**} & **Pixel** & **Pixel** & **Regally (Total** & **Refresh** & **eSBP** & **eSBP** & **eSBP** & **System** \\  & **Pitch (\(\mu\)m)** & **Resolution** & **Pixels)** & **Date/bit** & **(Total** & **Ratio** & **Ratio** & **System** \\  & & & & & & & & \\ \hline LCD & \(156\times 52\) & \(2560\times 2048\) & 5,242,880 & 60/8 & 2,516,582,400 & 0.63 & SeeReal \\ \hline LCoS & \(4.8\times 4.8\) & \(3840\times 2160\) & 8,294,400 & 60/8 & 3,981,312,000 & \(1\) & NICT \\ \hline DMD & \(\begin{array}{c}13.68\times\\ 13.68\end{array}\) & \(1024\times 768\) & 786,432 & 32,000/1 & 25,165,824,000 & 6.32 & ETRI \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of SBP and eSBP for different SLM devices. guided by a combination of flat mirrors into 45-degree slanted direction and in a way to overlap at the axial area of the system. In the second stage, these virtual SLM planes are transported to the top center area of the tabletop display (final hologram image plane in the air above the tabletop of the display) by image transportation function of double parabolic mirrors from one focal area to another. This is shown in Figure 5.  
Based on this principal design method, we have successfully implemented the first monocolor version of tabletop holographic display systems, which has been reported in the previous publication [22]. In the first prototype system, four DMDs are spatially tiled to make a \(2\times 2\) multivision style SLM module for enhanced resolution (from 768 \(\times\) 768 to 1,536 \(\times\) 1536) and size (1.27 to 2.54 cm). This still small size of SLM is enlarged by a cascade of two 4\(f\) optics, with the magnification factor of 1.67 and 1.65 each, overall resulting in 2.76 times of magnification effect.