# High-Resolution Hologram Calculation Method Based on Light Field Image Rendering
## 3 Experiment and Results  
The pixel pitch \(d_{h}\) of the hologram is 0.318 \(\upmu\)m, which is determined by our holographic printer [9; 10; 11]. This principle of the home-made holographic printer is similar to the holographic printer introduced in Reference [12], but the light source in our holographic printer is a blue LED with a center wavelength of 365 nm rather than a laser. The maximum frequency that the holographic printer can support is \(\frac{1}{2d_{h}}=1573\) line/mm. Printing holograms at the highest resolution requires extremely stability for the printing system. In practical usage, almost half of the highest resolution is used for hologram design. In the experiment, the diffraction angles of the FOV in the \(x\) and \(y\) directions are set as \(\theta_{x}\) is 48\({}^{\circ}\), and \(\theta_{y}\) is 20\({}^{\circ}\), respectively. The angle of the reference wave in the \(y\) direction and \(z\) axis is set as 22\({}^{\circ}\), assuming the wavelength is 632 nm. Therefore, the max frequency is \(\frac{\sin(\theta_{y}/2)}{\lambda}=643\) line/mm in the \(x\) direction, and the max frequency is \(\frac{\sin(\theta_{y}/2)}{\lambda}+\frac{\sin(\theta_{refy})}{\lambda}=867\) line/mm in the \(y\) direction, respectively. This is assuming that the distance between the pinhole and holographic plane is \(f=1\) mm. In this situation, the width and length of each hogel or EI is \(w=2f\tan(\frac{\theta_{y}}{2})=0.89\) mm and \(h=2f\tan(\frac{\theta_{y}}{2})=0.35\) mm. The geometric relationship of the hologram calculation using a 3D point  
Figure 1: The rendering of elemental light field images (EIs) with a pinhole array for hologram calculation. cloud model with two layers is shown in Figure 2a. The first layer has a distance of 10 mm while the second layer has a distance of 20 mm from the holographic plane H. The two-layer Chinese characters are shifted in the vertical direction to guarantee not to overlap when they are viewed from the front view for simplicity. The 3D model has a size of \(64\times 64\times 10\) mm (\(W\times H\times D\)) with 984K object points. The front view of the 3D model is shown in Figure 2b. In the rendering of the EIs, the sampling intervals for both \(x\) and \(y\) directions are set as 4 \(\upmu\)m and the resolution of each EI is \(222\times 88\) pixels. The parameters for hologram calculation are summarized in Table 1. In the proposed method, the size of the EI is the same as the size of the hogel, but the sampling intervals are different. After we get an EI from the 3D model, this EI is firstly interpolated to a new EI with the same resolution as the hogel. The interpolated EI is used for hologram calculation according to Equation (5). In the calculation, after the size of the EI is determined, the number of the EI is calculated by \(63.6/0.89=71.46\approx 71\) and \(63.6/0.35=181.71\approx 181\). The resolution \(200\text{K}\times 200\text{K}\) of the hologram is also an approximation of the physical size of \(63.6\times 63.6\) mm. The approximation is possible because missing a little bit of data on the outer edge of the hologram does not affect the 3D display. Figure 3a shows the rendered light field image, which contains all EIs rendered from the 3D model. Figure 3b is an enlarged part of the light field image. The light field image almost has a resolution of \(16\text{K}\times 16\text{K}\), which is much higher than the resolution of current commercially available display panels. The high-resolution light field image and high-resolution hologram guarantee high imaging quality and a large FOV of reconstructed 3D images.