# A Fast Computer-Generated Holographic Method for VR and AR Near-Eye 3D Display
## 1 Introduction  
A holographic display is a promising candidate for 3D display because the phase and amplitude of a 3D scene can be completely reconstructed. It is possible to implement computer-generated holograms (CGH) for a holographic 3D display [1, 2]. High resolution holograms such as rainbow holograms and Fresnel holograms have been proposed [3, 4]. Many dynamic holographic display solutions have also been implemented [5, 6, 7, 8, 9, 10]. Among them, notable frequency domain multiplexing methods are used for color video display through Fresnel hologram with red, green and blue lasers as illumination [7, 8]. However, such an optical system is often bulky and the image quality is poor because of the coherent illumination, which affects the practical application of the technology. A lot of efforts have been made, but the progress on the holographic 3D display still has proven difficult due to the following constraints, such as the computational difficulty for the large size of 3D point cloud data, the limited bandwidth of spatial light modulator (SLM), and the speckle noise of the reconstructed 3D images due to the use of coherent illumination sources. The narrow diffraction angle of the current SLM often dictates that the holographic 3D display is restricted to quite small 3D images and narrow viewing angles, with no sign of a significant improvement in the short run. While these difficulties exist, Virtual Reality (VR) and Augmented Reality (AR) displays have become emerging technologies. In the VR display, the human eye views the virtual image through the display device. However, in the AR display, users can view both real scenes and some virtual images simultaneously [11]. In this technique, the virtual image is displayed in front of the human eye through an optical system and AR eyepiece and ambient light from a real object can pass incident on the human eye through the AR eyepiece without distortion. The combination of holography and VR or AR display to achieve a true 3D display is quite intuitive and thus desirable, which can avoid the accommodation convergence conflict problem existing in binocular parallax-based 3D displays [12; 13]. The Fresnel hologram is often chosen to produce 3D displays with large depths of field using a coherent source such as laser as illumination. However, it is not quite suitable for holographic VR or AR display because of the large imaging distance between the reconstructed image and the Fresnel hologram. Additionally, for use of a coherent illumination source, speckle noise of holographic 3D display can also bring a negative impact on image quality. Several hologram computation methods such as point cloud-based, layer-based, and triangular mesh-based algorithms [14; 15; 16; 17; 18; 19] have been proposed for speeding up the calculation of the Fresnel hologram. To improve the calculation efficiency, holographic stereogram methods using numerous projection images have been proposed [20; 21]. The essence of those methods is to represent the information of one point in the frequency domain by the superimposition of one orthogonal projection image multiplied by the phase of the corresponding direction. Subsequently, the frequency is converted into a spatial domain for an image plane hologram calculation or using Fresnel diffraction for Fresnel hologram calculation. While those methods have merits, a huge number of projected images are required for high-resolution hologram calculation. In order to achieve an efficient and more compact holographic display system, a hologram calculation method similar to holographic stereogram and an optical display system for holographic near eye VR and AR display are proposed. Within this calculation method, a plurality of images with different angles are projected on a projection plane near the holographic plane.