# Dual-View Integral Imaging 3D Display Based on Multiplexed Lens-Array Holographic Optical Element
## 3 Experiments and Results  
### Fabrication of the MHOE  
In the first step, the experimental setup is shown in Figure 6a. The laser's wavelength and power are 532 nm, and 400 mW, respectively. The thickness, resolution, sensitivity and average refractive index of the photopolymer material are 15 um, 12,000 line/mm, 10 mJ/cm\({}^{2}\) and 1.47, respectively. The size of the micro-lens array used to fabricate the MHOE is 150 mm \(\times\) 150 mm, in which the jth of each lens element is 1 mm and the focal length is about 3.3 mm. The laser beam is divided into two beams by a beam splitter (BS). One of the laser beams is expanded by a spatial filter (SF) and a collimating lens (CL), then the laser beam incident into the micro-lens array with the angle \(\theta_{1}\) = 50\({}^{\circ}\) forms spherical wavefront array I. Another laser beam is reflected by mirror 1 (M1) and mirror 2 (M2), and then passes through the divergent lens (DL) to form spherical wave I. The angles of spherical wave I incident into the holographic plate is controlled to be \(\theta_{2}\) = 61\({}^{\circ}\), and \(\theta_{3}\) = 81\({}^{\circ}\). The interference occurs between the spherical waves I and spherical wavefront array I, and the interference fringes are recorded on the holographic plate. In the second step, the experimental setup is shown in Figure 6b. The laser beam is divided into two beams by a BS. One of the laser beams is expanded by a SF and a CL, then the laser beam incident into the micro-lens array with the angle \(\theta_{4}\) = 50\({}^{\circ}\) forms spherical wave array II. Another laser beam passes through the DL to form spherical wave II. The angle of spherical wave II incident into the holographic material is controlled to be \(\theta_{5}\) = 61\({}^{\circ}\), and \(\theta_{6}\) = 81\({}^{\circ}\). The interference occurs between the spherical waves I and spherical wavefront array I, and the interference fringes are recorded on the holographic plate. The holographic plate is post-processed to obtain the required MHOE. The size of the MHOE is 80 mm \(\times\) 80 mm, and the diffraction efficiency and transmittance of the MHOE are greater than 85% and 80%, respectively. The exposure time is controlled by the electronic shutters. The detailed parameters of the optical devices are shown in Table 1.  
Figure 6: Setup for fabrication of the MLAHOE, (**a**) the first step, and (**b**) the second step. In this paper, the MHOE is used as a projection screen, when the incident projection beam deviates greatly from the Bragg condition, the diffracted beam cannot be reconstructed and the 3D images also cannot be reconstructed. Therefore, the angular selectivity of the MHOE needs to be measured. The maximum deviated angle of the projection beam must be measured but the diffracted beam and 3D images cannot be reconstructed. The diffraction efficiency of the MHOE can be measured by the intensity of the transmitted and diffracted beam. The measurement formula of the diffraction efficiency can be expressed as [21]:  
\[\eta=\frac{I_{D}}{I_{T}+I_{D}} \tag{5}\]  
where \(I_{D}\) and \(I_{T}\) represent the intensity of the diffracted and transmitted beam, respectively. During the measurement, the incident angle of the reference beam is controlled by a rotation table, and the intensity of the diffracted beam of the MHOE is obtained by an optical power meter. The diffraction efficiency of the left and right view zones of the MHOE is measured, as shown in Figure 7. Through observation, when the incident angle of the reference beam is at 13\({}^{\circ}\), the diffraction efficiency of the MHOE is less than 5%. When the incident angle of the reference beam is between -4.5\({}^{\circ}\) and 4.5\({}^{\circ}\), the diffraction efficiency of the MHOE is higher than 50%. As shown in Figure 7, the maximum deviated angle of the MHOE is between -5\({}^{\circ}\) and 5\({}^{\circ}\) in the left and right viewing zones.