# High-Resolution Hologram Calculation Method Based on Light Field Image Rendering
## 3 Experiment and Results
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of points in the 3D model & 984K \\ Size of hologram & \(63.6\times 63.6\) mm \\ Resolution of hologram & \(200\text{K}\times 200\text{K}\) \\ Pixel pitch of hologram & \(0.318\upmu\)m \\ Resolution of hogel & \(2800\times 1108\) pixels \\ Wavelength & \(632\) nm \\ Size of EI & \(0.89\times 0.35\) mm \\ Pixel pitch of EI & \(4\upmu\)m \\ Resolution of EI & \(222\times 88\) pixels \\ Number of EIs & \(71\times 181\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for hologram calculation. Figure 2: The geometric relationship for hologram calculation: (**a**) the side view of the holographic plane H and 3D model; (**b**) the front view of the 3D model. The first layer Chinese characters are the abbreviation of “Beihang” University and the second layer Chinese characters mean “Holography”. Because of the independent property of calculations for each hogel in the proposed method, \"parfor\" in MATLAB is used for parallel acceleration. MATLAB 2015b and a laptop (i7-9750 HQ CPU, 16G RAM and 1024G SSD) were used for hologram calculations. Six CPU cores were used in the hologram calculation. The computational time was about 8 min for the calculation of this hologram, including the time used for EI rendering. The hologram was printed with our home-made holographic printer from the Institute of Information Optics, Zhejiang Normal University, in about 4.5 h.  
The overall diagram of the holographic printer is shown in Figure 4. The light from the LED is filtered and collimated to illuminate the digital micro mirror (DMD) with a resolution of \(1024\times 768\) pixels. A small portion of the calculated hologram with a resolution of \(600\times 600\) pixels is first zero padded to the same resolution as the DMD and then loaded into the DMD for display. The modulated light from the DMD is imaged on the photosensitive material through the objective lens, and this small portion of the hologram is printed. Controlled by the computer, the motion platform is moved to the next position to print the next hologram section. With this holographic printer, the maximum size (a \(200\times 200\) mm hologram with pixel pitch of 0.318 \(\upmu\)m) can be printed on a photoresist plate. The part of the calculated hologram and the printed hologram are shown in Figure 5a,b, respectively. Figure 4: The diagram of holographic printer. Figure 3: The rendered light field image: (**a**) light field image; (**b**) enlarged part of (**a**). In the reconstruction, a halogen lamp available in our lab is used as illumination source. The reconstruction of the hologram is demonstrated in Figure 6a. The white light is coupled into the fiber and a divergent light from the fiber head illuminates the hologram H with a proper incline angle in the \(y\) direction. The diffracted light propagates into the human eye for watching the reconstructed 3D image. The real image in front of the hologram plane or the virtual image behind the hologram plane can be watched by selecting a proper illumination angle. Figure 6b-d show three reconstructed images from three different viewing angles. Video S1 shows the reconstruction from different viewpoints. Figure 5: Holograms for 3D display: (**a**) part of the calculated hologram; (**b**) printed hologram. From the optical reconstruction, the parallax is smooth and the FOV is large. The brightness is a little different due to the uneven incline illumination on this large-area hologram. Figure 7 shows three images captured by our camera, focusing on part of the holographic plane with different viewing angles. The two speckles in the red and green circles on the holographic plane are used as reference positions. From the results we can know that different perspectives of light come from different positions on the holographic plane, which is the core point of our method to encode the propagation of each pixel in the EI to different angles with divergent sphere wave phase factors.