## 3 Experiments and Results  
To verify the concept of a 3D display by means of spherical wave synthesis, a prototype was set up. Figure 3 illustrates the optical components and configuration of the proposed system, which just consists of an LA and an LCD panel. For the prototype setup, all-optical components are fixed on a stage with all six degrees of freedom to adjust the relative position between the LA and the LCD precisely. Moreover, a stepper motor is employed to adjust the distance \(d\) along the \(z\)-axis fast and accurately. The depicted images can be recorded with a camera, which is mounted vertically above the LA. In preparation for the experiment, a color image and a depth image of a 3D model (dog) were rendered by using the stereo modeling software Blender, as seen from Figure 4. The depth range of the dog is set from 80 mm to 180 mm underneath the LA and the model was sliced into 11 depth planes. By using the ray-tracing based rendering approach described in Section 2.1, the patterns to be displayed by the LCD were generated for all depth planes, as shown in Figure 5. By following Equation (4), the distance \(d\) between LCD and LA was controlled during the display process using the stepper motor. We used a CCD camera to imitate the eye of the observer. The system works in full color, yet we used a monochrome camera to better inspect fine details of the object representation. Interested readers can find the full-color Video S1 of the display in the Supplementary Material. To demonstrate focusing effects, the camera is equipped with a high numerical aperture objective with F# 0.95. The 3D display scheme is based on the effect of visual persistence [23], i.e., all recorded CCD images are added/integrated up while the distance \(d\) is scanned through all 11 depth planes. To show focus blur, we have recorded multiple images with the objective being focused on different parts of the displayed dog. The results are seen in Figure 6. In the results, it can be easily recognized that the tail of the dog is behind the head, as expected from the model. In addition, when the focusing plane of the objective is set at 80 mm, the dog's head is much clearer than the tail, and the captured image at the unfocused areas exhibits a gradual blur from neck to tail, which indicates that the reconstructed image provides continuous depth information. When the focusing plane is subsequently moved from 80 mm to 180 mm, the focused area would be changed from head to neck, forefoot, body, tail, and hindfoot, where the blurred areas are also shifted correspondingly. This phenomenon strongly \begin{table}
\begin{tabular}{l c} \hline Dimensions (mm) & 58.0 \(\times\) 60.0 \\ Size of lenslet (mm) & 5.4 \(\times\) 7.0 \\ Effective focal length EFL (mm) & 41.90 \\ Radius of lenslet (mm) & 22.0 \\ Substrate & B270 \\ Wavelength range (nm) & 400... 700 \\ Thickness (mm) & 3.0 \\ \hline \end{tabular}
\end{table} 
Table 1: Specifications of the lens array. \begin{table}
\begin{tabular}{l c} \hline Dimensions (mm) & 158.2 \(\times\) 77.9 \\ Type & IPS LCD \\ Resolution (pixel) & 1920 \(\times\) 1080 \\ Pixel size (\(\mu\)m) & 63.34 \\ \hline \end{tabular}
\end{table} 
Table 2: Specifications of the LCD panel. confirms that the reconstructed images in our system contain real depth information with focus cue, similar to what is expected from a hologram. Figure 4: (**a**) Color image and (**b**) depth image of the 3D model. Figure 3: Optical components and configuration of the wave field synthesis 3D imaging system. The lens array is placed inside the holder in a vertical distance \(d\) to the LCD. The arrows indicate the movability of the six-axis stage. The depicted images can be captured by a camera placed vertically above the lens array. Figure 5: Displayed patterns of the dog for different exemplary depth planes. Figure 6: 3D model of the dog displayed with the proposed system. For any of the displayed images, we added up 11 individually captured depth images. The camera’s objective focuses on the corresponding depth plane.