# Dual-View Integral Imaging 3D Display Based on Multiplexed Lens-Array Holographic Optical Element
## 3 Experiments and Results
### Experiments for Displaying Images on the Proposed Dual-View 3D Display  
The projector is used in the experiment for displaying images. According to the incident angle requirement of the MHOE, projector I is placed on the left, and projection beam I is incident into the MHOE with a pair of angles \(\theta_{2}=61^{\circ}\) and \(\theta_{3}=81^{\circ}\). Projector II is placed on the right, and projection beam II is incident onto the MHOE with a pair of angles \(\theta_{5}=81^{\circ}\) and \(\theta_{6}=61^{\circ}\). Therefore, projection beams I and II are symmetrical to each other. Figure 9 shows the experiment setup for the dual-view 3D display. In order to satisfy the incident angle about the MHOE, the two projectors are placed vertically, and the projection lens is positioned inside. The distance between the projection lenses of the projectors and the MHOE is 31 cm. Projectors I and II are 20 cm apart from each other in the horizontal direction. The projection lenses of projectors I and II are both 21 cm away from the optical table. The height of the MHOE is 19.5 cm from the optical table. The distance between the MHOE and the car model is 3 cm. The projectors are used to project the EIAs onto the MHOE. The projection beams of the projectors that meet the Bragg-match are directly projected onto the MHOE. The MHOE is used as a screen of the dual-view 3D display. Projector I projects EIA I as projection beam I, with a pair of angles \(\theta_{2}=61^{\circ}\) and \(\theta_{3}=81^{\circ}\) onto the MHOE. Then, 3D image I is reconstructed in the left viewing zone. Projector II projects EIA II as projection beam II, with a pair of angles \(\theta_{5}=61^{\circ}\) and \(\theta_{6}=81^{\circ}\) onto the MHOE. Then, 3D image II is reconstructed in the right viewing zone. In this paper, the path of the elemental lens in the micro-lens array is 1 mm and the focal length is 3.3 mm. According to Equations (3) and (4), the viewing angles of the left and right viewing zone are \(\Omega_{1}=10.2^{\circ}\) and \(\Omega_{2}=10.2^{\circ}\), respectively. According to the parameters of the micro-lens array, the viewing angle of the conventional integral imaging is about \(12^{\circ}\). Therefore, the viewing angles in the dual viewing zones are almost the same as the conventional one. Figure 8: Reconstruction of the wavefronts of the lens array (**a**) in the left viewing zone, and (**b**) in the right viewing zone. Figure 7: Diffraction efficiency of the left and right viewing zone. EIAs I and II are shown in Figure 10a,b, respectively. Each EIA consists of \(70\times 70\) image elements. EIA I is generated by a computer and consists of the characters \"3\" and \"D\", in which \"3\" is located at \(-15\) mm, and \"D\" is located at \(+15\) mm. EIA II is also generated by a computer and consists of the characters \"A\" and \"B\", in which \"A\" is located at \(-15\) mm, and \"B\" is located at \(+15\) mm. 3D image I reconstructed in the left view zone taken from the left, right, top and bottom directions are shown in Figure 11. We can see the horizontal parallax of the \"3D\" images from the left and right directions, and the vertical parallax of the \"3D\" images from the top and bottom directions. Reconstructed 3D image I has obvious horizontal and vertical parallaxes. Visualizations 1 and 2 clearly show the horizontal and vertical parallaxes between the \"3\", \"D\" and the real object. The resolution of reconstructed 3D image I is almost the same as the conventional integral imaging 3D display, and 3D image I in the left view zone has high brightness and definition. The resolution of 3D image I is the same as the number of the image element \(70\times 70\) in EIA I. Figure 12 shows 3D image II reconstructed in the right view zone taken from the left, right, top and bottom directions. We can see the horizontal parallax of the \"AB\" images from the left and right directions, and the vertical parallax of the \"AB\" images from the top and bottom directions.