# AR Displays: Next-Generation Technologies to Solve the Vergence-Accommodation Conflict
## 5 Multifocal Approach by LightSpace Technologies
### Computational Aspects for Multi-Plane 3D Rendering
The simplest way of how to \"slice\" the part, that falls within the limits displayable by the multi-focal AR device, is depicted by green arrows (Figure 8a)--pixels belonging to a region of depth space between the two closest midpoints or a midpoint and extreme boundary are allocated onto a corresponding image depth plane. As this approach excludes any overlapping pixels, even in a head-mounted display situation, in practice the boundary lines can be noticeable. This can be seen in Figure 9b, where this principle is used for multi-plane image rendering. Typically, the effect is observed on slanting surfaces and objects and is perceived as a visual artefact degrading the perceived image quality. On one hand the effect would not be as noticeable, if higher physical discretization of the depth space could be obtained. On the other hand, this is easily mitigated by interplane antialiasing (depth blending). Figure 8: Schematics depicting how a 3D scene can be divided among a limited number of physical focal planes: (**a**) Without interplane antialiasing; (**b**) with interplane antialiasing. Represented is reciprocal depth space or optical space. The blue figure represents a 3D scene, purple vertical lines represent positions of physical image depth planes (focal planes), while grey dotted lines correspond to midpoint between adjacent focal planes. Blue dotted lines mark the outer boundaries for what depth space can be comfortably depicted on a multifocal display device. Colored arrows correspond to a depth region, pixels of which are mapped onto a corresponding focal plane. The approach for interplane antialiasing is depicted in Figure 8b. The general setting is similar as with example of Figure 8a--the only difference is that the depth region allocated to each physical depth plane is expanded. Even a slight overlapping by depicting single pixel information on two image depth planes (optical diffuser elements) can yield noticeable improvements. Nevertheless, quite obviously, there are no reasons to expand this depth region beyond positions of adjacent focal planes. The particular example of Figure 8b considers expansion of depth allocation region to neighboring focal planes, thus ensuring full depth antialiasing for every pixel that falls within the interplane space. Furthermore, when a pixel is output onto two focal planes, the corresponding values have to be attenuated not to exceed the native value (brightness). It has been found that a very good results are ensured by simple linear blending algorithm, where based on the pixel's position in the interplane space its intensity is divided among the adjacent focal planes [14; 15]. For example, if the pixel falls exactly in the midpoint, 50% of its intensity is shown on both nearest image focal planes, whereas if it is displaced from the midpoint, it will be depicted with higher intensity on the closer focal plane. Nevertheless, the blending algorithm which determines in what proportions the intensity is distributed among focal planes based on the location of pixels can be arbitrary; it has been found that deviations from the linear approach can provide slight benefits [18]. In practice when linear interplane antialiasing is used, the image appears to be smooth without any noticeable discontinuities. This has been shown in Figure 9c. The slight banding that can be observed in this case at the interplane boundaries is associated to a non-linear response of the physical image source. To overcome this, a calibration has to be performed and additional scaling factors introduced. For comparison, the same content has been rendered on a single focal plane that corresponds to the basic stereoscopic way of image representation (Figure 9a). It can be seen that with interplane antialiasing, identical image quality to basic stereoscopic rendering can be achieved with an important exception of supported monocular focus cues (see Figure 7).