# Efficient Hogel-Based Hologram Synthesis Method for Holographic Stereogram Printing
## 3 Results
### Numerical Simulation
Thus, the hologram plane spatial sampling rate must not exceed this value if the perceived resolution is to be maximised. All hogels are encoded as phase holograms for holographic stereogram printing. The phase hologram for each hogel was calculated using the iterative Fourier transform algorithm (IFTA) after obtaining an array of parallax-related images using a phase-only spatial light modulator (SLM). Figure 7a shows the phase distribution at each iteration number of the IFTA. The holograms synthesised from light field data using the conventional and proposed method were reconstructed using an eight-level grayscale (Figure 7b-d). To evaluate visual qualities, we compared the HSs by simulating peak signal-to-noise ratios (PNSR) as shown in Figure 8. The peak signal-to-noise ratios were 11.21, 23.95, 27.21, and 31.43 dB for Figure 7b and 12.67, 24.70, 28.71, and 33.17 dB for Figure 7c,d. When recording HSs, smaller hogels afford better spatial resolution. The angular resolution of reconstructed light rays is determined by the number of hologram sampling points in each hogel. The re-arranged hogel resolution is \(50\times 50\) pixels based on a conventional pixel re-arrangement technique whereas the hogel resolution is \(200\times 200\) pixels by our method. Thus, the hologram sampling point within each hogel is four times larger than the conventional point, which is associated with retention of spatial resolution at a constant hogel size. Figure 7: Numerical reconstruction of hologram synthesis at an increasing number of iterations in iterative Fourier transform algorithm: (**a**) phase distributions, (**b**) conventional hogel re-arrangement after pixel interpolation, (**c**) views by proposed pixel-mapping algorithm for the object ”Teapot and sphere,” (**d**) views by a proposed pixel re-arrangement algorithm for the object ”Bunny and carrot.”  
The hogel size imposes a trade-off between spatial and angular resolutions. A larger hogel yields higher angular resolution, but a lower spatial resolution. We treat one hogel as the angular resolution comparison and keep the hogel size the same for both methods. The peak signal-to-noise ratio values were calculated for angular resolution of a single hogel, which was generated by the conventional and proposed pixel re-arrangement algorithms. The PSNRs were measured as 20.21 and 28.38 dB, respectively, for angular resolution of each hogel. Thus, for a given number of sampling points in the hologram plane, the proposed method increases the angular resolution of the reconstruction. In terms of the reconstructed images obtained by the conventional and proposed method, the image quality is acceptable for HS printing. Table 1 shows the comparison of computation time for both methods. The computation time was dramatically increased when fewer perspectives at higher resolution are rendered in the proposed method when compared with the conventional method. Thus, the calculation time increases for generating higher resolution hogels by the proposed hogel re-arrangement algorithm. Total computation time is divided into five parts such as rendering in Blender software, hogel generation in MATLAB software, computer-generated hologram encoding, and its numerical reconstruction via the iterative Fourier transform algorithm and printing on a holographic plate. From Table 1, it took more computation time for rendering and hogel generation due to the higher resolution perceived images. CGH generation time was faster than the conventional method. Because it is required to resize each parallax image after the pixel re-arrangement process to match the spatial light modulator size before encoding CGH in the conventional method. Whereas, the generated hogels by the proposed approach were encoded as CGH directly without pixel resize or interpolation. For checking the quality of the reconstructed image at an increasing number of iterations in the IFTA algorithm, the computation time was calculated for a single hogel.