# Fast 3D Content Update for Wide-Angle Holographic Near-Eye Display
## 6 Numerical and Optical Reconstruction of Updated CGH  
In this section, object reconstructions from CGHs calculated with hologram update method are carried out. Our research is based on the geometry of wide-angle near-eye holographic displays. Thus, parameters for optical and numerical experiments were selected for fulfilling continuous viewpoint change in a wide-angle viewing configuration. Moreover, in both experiments the same viewpoint elliptical trajectory around the 3D scene was investigated. During the full turn, the hologram displacement in a single step, given in overlap factor \(F\), varies from 0.4 to 0.6. The test object was a 3D point cloud representing a statue of [PERSON], consisting of about 4 million points and a point density of 5.5 points/mm\({}^{2}\). The object's lateral dimensions and location were selected to cover 35\({}^{\circ}\) of FoV. Experimental verification of the hologram update method is realized in the near-eye holographic display presented in Figure 8. A helium-neon red laser (\(\lambda=632.8\) nm) was employed as the illumination source. The beam passed through a half-wave plate HWP, which matched the polarization state of the illumination and the liquid crystals on SLM. Next, plane wave illumination was formed with an assembly composed of microscopic objective (MO), pinhole (PH), and collimating lens Lc (\(Fc=300\) mm). Mirror M and beam-splitting cube BS redirected the beam to the 4K SLM (HoloEye Gaea 2.0, pixel pitch 3.74 \(\upmu\)m). SLM was addressed with the phase CGH with added spatial carrier frequency, which separated zero from information order. As depicted in Figure 8, the SLM was tilted, and information  
Figure 7: Comparison of computation time of CGH made with A-PAS and update algorithm. The partial times for filling the blank region and updating the overlap region are marked with green for BR filling and orange for OR updating, respectively. order propagated along the optical axis. Next, the 4F imaging system, composed of lenses L1 and L2, demagnified the pixel pitch of the SLM. In our implementation, magnification was equal to 0.165. As a result, pixel size at the viewing window VW plane was 0.62 \(\mu\)m, which enabled an \(FoV\approx 61^{\circ}\). However, in the experimental setup, the viewing angle was limited by the diameter of lens L2, which allowed an \(FoV\approx 36^{\circ}\). Hence, the point cloud was matched to the dimensions 414 mm width, 504 mm height, and 222 mm depth in order to fit into the FoV of the optical system. For the optical experiment, CGHs corresponding to the continuous change of the viewpoint around the object were calculated with the proposed hologram update method, and the generated information was loaded in the SLM as described previously. However, as the viewpoint moved, the hidden areas of the statue changed. Thus, occlusion culling of those unseen regions was necessary for proper depth perception. The unwanted regions were removed using the occlusion culling based-PAS algorithm from [23]. As described in Section 3, occlusion culling using based-A-PAS can remove unwanted back points when selecting proper \(N_{s}\) and \(q\). The choice of PAS parameters depends on the point cloud density. In our case, the 3D point cloud of Neptune had a density of 5.5 points per millimeter square. With this density and the selected geometry of the holographic display, the angular spacing of the Neptune cloud was obtained as around 0.035\({}^{\circ}\). This criterion defines the maximum size of the extended segment as 1573 pixels [23]. Thus, for the CGH calculations of this work, \(N_{s}=512\) and \(q=3\) were used. The selected parameters allowed for fast calculations, high accuracy, and robust occlusion culling of unwanted areas. The holographic scene simulated eye movement on the horizontal plane around the object along an elliptical trajectory. The motion was counterclockwise, with the eye always facing toward the object. The minor ellipse axis had 1600 mm, while the major had 2400 mm.