# Progress of the Computer-Generated Holography Based on Deep Learning
## 2 The Principle of CGH  
Compared with traditional optical holography, CGH has obvious advantages, such as the ability to reconstruct virtual scenes and dynamic sceneries [18]. The CGH algorithms based on physical simulation can be divided into the point-based method, the ray-based method, the polygon-based method, and the layer-based method. The hologram synthesis from different primitives is shown in Figure 1.  
The point-based CGH method is based on the Huygens-Fresnel principle [32]. The model of a three-dimensional scene is sampled into the three-dimensional point array with \(N\) points. Then, every point is regarded as a point light source that emits spherical waves. The complex amplitude distribution of each point on the hologram plane is added up to get the final complex amplitude hologram. The optical field in the hologram plane from one single point can be described by  
\[H_{0}(x,y)=U_{0}\ exp\bigg{(}-j\frac{2\pi}{\lambda}\sqrt{\left(x-x_{0}\right)^{ 2}+\left(y-y_{0}\right)^{2}+z_{0}^{2}}\bigg{)} \tag{1}\]  
where \(\lambda\) is the wavelength; \(U_{0}\) stands for the complex amplitude of the object point; and \(x_{0}\), \(y_{0}\), and \(z_{0}\) represent the spatial coordinates of the point. The long calculation time is an obvious shortcoming of this method. In the ray-based method, the object is prepared based on the spatial-angular distribution of the target light rays. The hologram plane is divided into several sections of equal size, and the section-wise processing is conducted. The corresponding light field is Fourier-transformed after it is multiplied by the random phase distribution. Then, the optical information propagated to the hologram plane is synthesized numerically to obtain the final hologram. In the polygon-based method, the object is processed as the polygon mesh form. The optical field of each triangular facet is  
Figure 1: Hologram synthesis from different primitives: (**a**) point–based CGH method; (**b**) ray–based CGH method; (**c**) layer–based CGH method; and (**d**) polygon–based CGH method.  
calculated and accumulated in the hologram plane. The calculation of the triangular facet is performed by finding the relationship between the angular spectrum in the hologram plane and the triangular facet. The layer-based method divides the object scene into \(N\) layers and calculates the propagation of each layer. Compared with the point-based method, this method can effectively reduce the calculation amount and improve the image quality [33; 34; 35].  
However, physical simulation has a huge drawback: it is difficult to deal with occlusion in 3D scenes. To address this issue, the holographic stereogram is introduced. In this method, the hologram space is segmented into multiple hologram primitives. The parallax of different primitives is analyzed from different angles by synthesis. However, the depth information is partially missing [36; 37; 38]. With regard to the encoding part, the complex amplitude distribution on the hologram plane is converted into an amplitude-only or phase-only hologram. Some common encoding methods include the bipolar amplitude encoding method, phase encoding method, and binary encoding method. After encoding, the hologram can be uploaded to the SLM and illuminated with a coherent light to reconstruct the object. For the point-based, ray-based, layer-based, and polygon-based methods, it is still a big challenge to realize real-time computing. The tradeoff between the computation time and reconstruction quality limits the practical application of CGH. Therefore, the deep learning methods are introduced into the hologram generation process because of their good performance in both accuracy and calculation speed.