# Efficient Hogel-Based Hologram Synthesis Method for Holographic Stereogram Printing
## 3 Results
### Optical Experiment  
The optical setup and a photograph of the HS printer are shown in Figures 9 and 10, respectively. We applied the general operation principles of the holographic printer, which uses the X-Y translation stage described by [PERSON]. A 532-nm laser served as the light source. The object beam was spatially modulated by the hogel image displayed on phase-only spatial light modulator. This is a reflective SLM presenting 1920 \(\times\) 1080 pixels with a pixel pitch of 6.4 \(\upmu\)m. The SLM display was de-magnified by lenses L1 and L2 and allowed to interfere with the reference wave. The focal lengths of L1 and L2 were 85 and 25 mm, respectively. The beam is polarised so that all energy is directed by  
Figure 8: Peak signal-to-noise ratio (PSNR) comparison for visual quality evaluation.  
the beam splitter to the spatial light modulator display. Two apertures close to the holographic plate ensure that only the square area of the plate is exposed.  
The reference beam is delivered at 45\({}^{\circ}\) to the opposite sides of the plate through the long-focal-length lenses L3 and L4. The exposure time was optimised at 0.2 s based on the sensitivity of the Ultimate U08M silver halide holographic material used. When the signal to reference beam energy ratio was 1:1, the diffraction efficiency was relatively high. The holographic plate was installed on a motorised X-Y stage that could move both horizontally and vertically.  
We created a LabVIEW-based application for automatic HS recording in which the SLM display, the X-Y translation stage, and the electrical shutter are controlled simultaneously. Figures 11 and 12 compares the optically reconstructed images for the two synthetic 3D scenes by the conventional and proposed method under the same recording condition. In both cases, 1 \(\times\) 1 mm hogels were used to synthesise the HSs. The reconstructed images deliver full-parallax information within a field of view of \(\pm\) 30\({}^{\circ}\).  
Figure 10: Photograph of holographic stereogram printing.  
Figure 9: Optical setup for holographic stereogram printing.  
When the reconstructed image of Figure 11 was focused to different depths on the holographic plate, the printed hogels were clear but the 3D scene was blurred (Figure 13). Figure 13 also compares the spatial resolution of reconstructed HSs focused on the holographic plate to distinguish the hogel distributions re-arranged by the conventional and proposed pixel re-arrangement algorithms while maintaining a constant hogel size (\(1\times 1\) mm) in each experiment. In Figure 13a, the pixel resizing technique for conventionally re-arranged hogels increases the distance between adjacent hogels, compromising hogel uniformity, as shown in Figure 13a. A hogel, which are rearranged by the proposed pixel re-arrangement algorithm, have better spatial resolution and provides uniformity between the hogel distance, as shown in Figure 13b. Each hogel on the hologram plane acts as a directional emitter of parallax information. Thus, the hogel emits a set of beams with different intensities on the viewing zone. The viewer's both eyes intercept light rays emitted in different directions by every hogel recorded on a hologram plane.  
Figure 11: Optical reconstruction of full-parallax holographic stereogram for object “Teapot and sphere” (**a**) conventional method and (**b**) proposed method.  
Figure 12: Optical reconstruction of the second object “Bunny and carrot”: (**a**) conventional method and (**b**) proposed method.