# Fast 3D Content Update for Wide-Angle Holographic Near-Eye Display
## 5 Numerical Investigation of Hologram Update Algorithm  
In this section, the test results on the accuracy and calculation time of the proposed hologram update algorithm are provided. For generation of CGHs and filling of their blank region, the A-PAS method was utilized with segment size \(N_{s}=512\) and extension factor \(q=3\). These parameters are used in the experimental section in Section 6. Investigation of accuracy requires employment of the propagation tools for image reconstruction. In the case of wide FoV, for known numerical propagation algorithms an accurate recovery of the entire optical field of image space requires an enormous amount of RAM and calculation time. The approach proposed in this chapter is based on analyzing the reconstruction quality of several points that are mutually separated in space. This eliminates the need for calculating the entire image space. Only its corresponding fragments are reconstructed with the Rayleigh-Sommerfeld Off-Axis direct integration method (OADI) [41]. The accuracy test had two parts: the first checked the quality of a single hologram update for different sizes of the overlap area, while the second analyzed the algorithm's performance over hundreds of hologram update cycles. The calculation time was investigated on a PC with Intel i9-9900 and 64 GB RAM, without GPU and multithreading support. The accuracy of the proposed update method was quantified by reconstructing holograms of point sources. The investigated scene geometry is illustrated in Figure 4a, where the viewpoints marked with the eye icon also represent the hologram plane. The test object consisted of five point sources, P\({}_{n}\), distributed linearly along the diagonal of the image space. The first point is center point P\({}_{0}\)(0, 0, 2), while the last is off-axis point P\({}_{4}\)(\(-0.45B_{x3}\), \(-0.45B_{x3}\), \(z\)). All considered points are shown in Figure 4b. Their coordinates are given according to the coordinate system of the starting viewpoint position, noted as 'View A' in Figure 4a. The object plane is located 1000 mm away from the hologram plane. In the simulation, the viewpoint rotated horizontally around the center point, P\({}_{0}\). As a result, the positions of the other points were changed in relation to the hologram plane. Overlap factor \(F\) describes the hologram displacement in a single step. After 1000 cycles, the hologram reached the 'View B' position. The perspectives of the object at 'View A' and 'View B' are presented in Figure 4c. Figure 4: (**a**) Investigated geometry for viewpoint change; (**b**) starting points positions in the image space; (**c**) perspectives on point object for ‘View A’ and ‘View B’. The first experiment examined the accuracy of a single hologram update cycle for different overlap sizes. As a measure of accuracy, the amplitude ratio of points reconstructed from an updated hologram and calculated with A-PAS was used. A similar approach has been applied to assess image quality loss due to the presence of optical aberrations [42]. Reconstructions of each point were calculated for its focus plane. The hologram update method was tested for overlap sizes of factor \(F\): 0.875, 0.75, 0.625, and 0.5. The obtained results are presented in Figure 5a, where the effect of optimization of the \(f_{s}\) can be noticed. The highest image quality was obtained for point P3 and P2, while points P0 and P4 had a similar level of update error regardless of the overlap size. In total, the amplitude ratio of every point exceeded 0.97. Thus, the updated hologram was accurate in its entire volume. Figure 5b presents the direct comparison of reconstructed point P4 from a starting hologram generated with the A-PAS algorithm and the proposed update method for 1 st and 1000 th frame, with overlap \(F\) = 0.5. In the second test, the accuracy of the hologram update method was investigated for a large number of update cycles. The point distribution of the former experiment was used here as well. The test examined 1000 cycles of hologram update.