Extended abstract of dissertation thesis
Author: Ivo Hanák,
Supervisor: Prof. Ing. Václav Skala, CSc.,

We see the world around us through a reflected light. A hologram is able to record that light and replay it. The result of a replay is indistinguishable from reality since a hologram records everything unlike photography which selects using a lens and a pinhole. This is shown on an example of computer graphics on Figure 1. When using a hologram, a view is selected by a viewer when a hologram is replayed. When using a photo, this is already done when the photo is captured. As a consequence, when viewing a hologram a viewer can see depth and s/he can focus anywhere similar to the real world. Thanks to a numerical description, we can employ holograms for presentation of a virtual scene.

Fig. 1: A simplified scene containing two light sources (shown as a red and a blue dot). (Left) When capturing a hologram, each source influences every part of the recoding plane. (Right) However, when an approach of a computer graphics is used, a viewer (a black dot) is considered and every source influences only a small location.

Computation of a hologram is much more complex process than a computing a projection of a virtual scene in computer graphics. Therefore, we are aiming acceleration of the process in this work. We are considering large holograms and by larger we mean a higher number of samples. In this case, a hologram consisted usually of 4096×4096 samples. Inspired by computer graphics, we accelerated the computation by reducing a detail. A proposed method converts a scene to coarser representation employing an unified element. A hologram of each element is generated using a method based on propagation in an angular spectrum. At the same time, visibility of an element is approximated using a modified ray-casting. Thus, the proposed method combines two different approaches which are usually used separately when a hologram is computed. We show that it is possible to combine them and that the result opens opportunities for further acceleration. An example of a replayed hologram which was calculated using the proposed method is shown in Fig. 2. In a general case, the resulting method is not the fastest but we show that a range in which our method is better includes scene which are being visualized by a computer graphics today.

Figure 2: Photos of a replayed hologram containing geometrical shapes (e.g. a cone, a cube, etc.). Photos were captured by a regular capture from a slightly different locations. Notice a tip of a cone intersects an edge of a cube (left) while from a slightly different location they are not even touching themselves (right). Similar effect cannot be achieved by a regular photography. The photos correspond to a size of 3×3 cm. The photos were captured by L. Vasa, PhD.

Besides a proposal of a new method including its acceleration, we accelerated an already existing method which is based on ray-casting. Since the method does not employ coarser representation of a scene, it cannot control a level of recorded detail. We propose a modification which allows use of a graphical processing unit (GPU) and programmable hardware to decrease the computation times significantly. An example of a photo of a replayed hologram is shown in Fig. 3.

Figure 3: A photo of a replayed hologram of a scene containing a model of a airplane. The hologram was computed using a method based on ray-cating modified for a GPU. The presented photo corresponds to a size of 3×3 cm. The photo was captured by L. Vasa, PhD.