## 3 Results
### Experiments with Two Volumetric 3-D Objects  
Now, to confirm the feasibility of the proposed system in the practical application, two volumetric 3-D objects of 'Dice' and 'Car' were used as the test objects in the experiments. Figure 15 shows two kinds of test volumetric 3-D objects of 'Dice' and 'Car' whose sizes are 25 mm \(\times\) 25 mm \(\times\) 25 mm and 25 mm \(\times\) 21 mm \(\times\) 50 mm, respectively. Figure 14: 3-D images of ’VR’ viewed from three different viewing angles of (**a**) \(-21.0\lx@math@degree\), (**b**) \(-10.0\lx@math@degree\) and (**c**) \(-3.0\lx@math@degree\), and those of ’3D’ viewed from those of (**d**) \(3.0\lx@math@degree\), (**e**) \(10.0\lx@math@degree\) and (**f**) \(21.0\lx@math@degree\), respectively. Figure 15: Two test volumetric 3-D objects of ‘**Dice**’ and ‘**Car**’. In the experiments, the same pickup lens array was employed. Thus, the pitch and focal length of the pickup lens array were also 1.63 mm and 3.13 mm, respectively, and they were located at the distance of 50 mm from each of the 3-D objects of 'Dice' and 'Car'. Here, the 'Dice' and 'Car' objects were used for the left and right views, respectively, in the dual 3-D display. As seen in Equation (5), the viewing angle may change depending on the \(\theta_{kr}\). Thus, under the condition that the pitch and focal length of the convex mirror are given by 7.32 mm and 7.47 mm, and the CMA is located at the distance of 800 mm from the projector, the maximum \(K\) value is 38 since it is limited by half the number of lenses of 77 along the \(x\)-direction. As the \(K\) value increases, the corresponding viewing angle decreases, whereas it increases as the \(K\) value decreases, which may confirm that the \(K\) value is inversely related to the viewing angle. Figure 16 shows the synthesized DV-EIA based on the SSIM method from the captured L-EIA and R-EIA from each of the 'Dice' and 'Car', respectively, for three cases of \(K=15\), 11 and 8. Here, the DV-EIA with 1920 \(\times\) 1080 pixels is composed of 77 \(\times\) 44 EIs, where each EI has the resolution of 25 \(\times\) 25 pixels. Depending on the \(K\) values, three kinds of DV-EIAs are synthesized based on the SSIM method, which are shown in Figure 16.  
Now, these DV-EIAs can be reconstructed on the proposed display system of Figure 17.  
Figure 17 also shows the experimental results of the volumetric 3-D object images of 'Dice' and 'Car' reconstructed at the left and right viewing zones, respectively, for three cases of the \(K\) values. As seen in Figure 17, for the case of \(K=15\), the reconstructed object images of 'Dice' and 'Car' at each of the left and right viewing zones are getting truncated and disappeared just beyond the viewing angle of \(-\)19.5\({}^{\circ}\) and 19.5\({}^{\circ}\), respectively. These results show that the viewing angles of this dual-view 3-D display system have been measured to be ranged from \(-\)19.5\({}^{\circ}\) to \(-\)3.0\({}^{\circ}\) and from 3.0\({}^{\circ}\) to 19.5\({}^{\circ}\) for the left and right viewing zones, respectively. These measured left and right viewing angles of \(-\)19.5\({}^{\circ}\)  
Figure 16: Synthesized DV-EIA for the ‘Dice’ and ‘Car’ objects with different \(K\) values: (**a**) \(K=15\), (**b**) \(K=11\) and (**c**) \(K=8\). Figure 17: Reconstructed dual-view 3-D object images of ‘Dice’ and ‘Car’ at the left and right viewing zones, respectively, for three cases of the \(K\) values. and 19.5\({}^{\circ}\) have been found to be almost the same as those calculated values of \(-20^{\circ}\) and \(20^{\circ}\), where the error ratio between the calculated and measured viewing angles has been calculated to around 3.0%. Moreover, as we move from the left to the center and center to right directions, different perspectives of the object images of 'Dice' and 'Car' can be viewed, as seen in Figure 17, which confirms the volumetric 3-D reconstruction of the 'Dice' and 'Car' objects in the proposed system.