# A Fast Computer-Generated Holographic Method for VR and AR Near-Eye 3D Display
## 3 Experiments and Result Analysis  
Our experiment utilizes the principle of off-axis amplitude hologram for achieving holographic VR and AR 3D display. Within the experiment, a liquid-crystal-on-silicon (LCoS) SLM is utilized for modulating the holograms. The parameters of the SLM are shown in Table 1. Green light LED from Osram with 1 W power, center wavelength of 528 nm, light-emitting area of 1 mm \(\times\) 1 mm, bandwidth of 28 nm is used as the illumination source. The center wavelength is used for hologram calculation. Figure 3: Diagram of the calculation of the projected image. For the center wavelength, the diffraction angle of the SLM is  
\[\theta_{d}=\sin^{-1}(\frac{\lambda}{2 pix})=1.89^{\circ} \tag{6}\]  
where _pix_ is the pixel size of the LCoS. Given that the distance between the projection plane and the holographic plane is 10 mm, it is possible to calculate the PSF. It is assumed that the plane wave perpendicular to the holographic plane is used as a reference wave, which means that the phase of the reference wave on the holographic plane is a constant value. Under this situation, the real part of the PSF in Equation (1) on the holographic plane is an amplitude type hologram. This amplitude type hologram can be regarded as new PSF, as shown in Figure 4. The resolution of the PSF is about 84 pixels \(\times\) 84 pixels, which corresponds to the viewing angle of 3.78\({}^{\circ}\) both in \(x\) and \(y\) directions from the hologram. For calculation of off-axis amplitude type hologram, only the upper half of the PSF (outlined with red rectangles) is used for the hologram calculation, as shown in Figure 4. The eight PSF sections correspond to eight PSFs of a 3D object projected onto one projection plane with eight different projection angles. Each PSF section has a resolution of 20 pixels \(\times\) 20 pixels. Each PSF section is named as _psf\({}_{i,j}\)_ according their positions. Hence in this design, the angular separation between the two adjacent projected images in the \(x\) and \(y\) directions is set as 0.9\({}^{\circ}\). Figure 5 shows the calculation of the hologram. A 3D object with size of 4.23 mm \(\times\) 7.05 mm \(\times\) 3.52 mm and a distance of 5 mm from the center of 3D object to the projection plane is used for hologram calculation. This 3D color model contains 41,022 object points. Two rows and four columns of the projected images of the 3D object are calculated according to Equation (5), and each projected image is firstly converted to grayscale image with a resolution of 600 \(\times\) 600 and then interpolated and zero padded into a projected image with resolution of 1920 \(\times\) 1080. The process of convolving the \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline SLM horizontal & 1920 \\ resolution & 1080 \\ SLM vertical resolution & 8 \(\upmu\)m \\ LED size & 1 mm \(\times\) 1 mm \\ Center wavelength of & 528 nm \\ LED & 28 nm \\ Bandwidth of LED & 28 nm \\ \hline \end{tabular}
\end{table} 
Table 1: Optical parameters in the experiment. Figure 4: The calculation of point spread functions (PSF). projected images with the corresponding PSF is shown in Figure 5. The projected image \(im_{i,j}\) convolves with the corresponding \(psf_{i,j}\). Then, the results are superimposed to obtain the hologram. The optical setup of the experiment for holographic 3D VR display is shown in Figure 6. In this setup, the divergent illumination light emitted by the green LED is collimated by the lens\({}_{1}\), and the LCoS is illuminated by the reflected light from beam splitter BS. The computer-generated hologram is loaded on the LCoS, and the illumination light is modulated. The modulated light field is filtered by the 4f optical filtering system to form a real 3D image free of zero order and high order image noise finally incident on human eye through the eyepiece lens\({}_{4}\). The lenses used for collimating, 4f optical filtering system and eyepiece are all cemented doublet achromatic lenses with focal length of 50 mm and diameter of 30 mm.