## 3 Results
### Experiments with Two Volumetric 3-D Objects
For the case of \(K=11\), left and right viewing angles are measured to range from \(-22.0^{\circ}\) to \(-3.0^{\circ}\) and from \(3.0^{\circ}\) to \(22.0^{\circ}\), respectively, as seen in Figure 17, where those values are calculated to be \(-22.2^{\circ}\) and \(22.2^{\circ}\), respectively, using Equation (5). Thus, the error ratio between the calculated and measured viewing angles has been calculated to be around 3.6%. Here, it must be noted that the left and right viewing angles increased by \(3^{\circ}\) as the \(K\) value decreased to 11 from 15. For the case of \(K=8\), left and viewing angles are calculated to be \(-23.5^{\circ}\) and \(23.5^{\circ}\), respectively. In addition, those values have been measured to range from -23.0\({}^{\circ}\) to -3.0\({}^{\circ}\) and from \(3.0^{\circ}\) to \(23.0^{\circ}\), respectively. Thus, these measured left and right viewing angles of \(-23.0^{\circ}\) and \(23.0^{\circ}\) look almost the same as those of the calculated values of \(-23.5^{\circ}\) and \(23.5^{\circ}\). Thus, for the case of \(K=8\), the error ratio between the calculated and measured viewing angles has been calculated to around 2.1%. As seen in Figure 17, there are three kinds of viewing zones, such as active, inactive and overlapped regions. Here, the active zones marked with red color represent the DV zones, where we are able to watch the displayed 3-D objects. On the other hand, in other zones including the inactive and overlapped regions, a 3-D object cannot be properly viewed. These experimental results confirm that two different volumetric 3-D object images with their changing perspectives can be successfully reconstructed in both of the left and right viewing zones just like in the case of the previous experiments, and each of the left and right viewing angles can be changed depending on the \(K\) value. Figure 18 visually shows that two observers sitting at each of the left and right viewing directions are separately watching the two different 3-D object images of 'Dice' and 'Car' reconstructed from the proposed system, where the projector is located at the distance of 800 mm from the CMA, and two observers are seated at the distance of 1200 mm from the CMA. As seen in Figure 18, each of the left and right viewers can see only the 'Dice' or 'Car' object images reconstructed at their viewing zones, which means that two different 3-D object images can be separately viewed by two observers who are distinctly sitting in their left and right viewing zones. Experimental results on two test 3-D object images of 'Dice' and 'Car' with the proposed system have been taken as video files and attached in Figure 18 as a video clip. In the video clip, volumetric 3-D object images of the 'Dice' and 'Car' with their changing perspectives, which are viewed from \(-23.0^{\circ}\) to \(-3.0^{\circ}\) and from \(3.0^{\circ}\) to \(23.0^{\circ}\), respectively, have been recorded for the case of \(K=11\). Here, the video frame rate and total recording time are set to be 24 fps (frames per second) and 34 s, respectively. Figure 18: Photos of two observers watching two different 3-D object images of ‘Dice’ and ‘Car’ at the left and right viewing zones with the optical setup of the proposed system. In the video files, each of the left and right 3-D images of the 'Dice' and 'Car' has been recorded for 17 s, respectively. As seen in the experimental results of Figures 17 and 18, the resolution and visibility of the reconstructed 3-D images still look somewhat degraded since the fill factor of the elemental convex mirror is low [33]. Thus, using elemental mirrors with much-enhanced fill factors can enhance the resolution and visibility of those 3-D images.