# A Layered Method Based on Depth of Focus for Rapid Generation of Computer-Generated Holograms
## 1 Introduction  
Holographic display technology is widely considered to be the most promising three-dimensional (3D) display technology since it can completely reconstruct the light field of a three-dimensional scene [1; 2; 3; 4; 5; 6; 7; 8]. A computer-generated hologram (CGH) simulates the physical interference process of holography for numerically represented 3D objects [9; 10; 11; 12], and it plays an important role in holographic display technology because these objects can be conveniently generated by computers and can be used to reconstruct virtual objects. According to the sampling method used for the numerical representation of 3D objects, the methods for generating CGH can be divided into point-based methods, polygon-based methods, and layer-based methods. The point source method is the most widely used because of its simple and intuitive principle. However, to ensure image quality, the number of discrete points in three-dimensional objects is usually millions of orders of magnitude, which leads to too long of a computation time for generating holograms. To solve this problem, many algorithms have been proposed to simplify the process and reduce calculation time [13; 14; 15; 16; 17; 18; 19; 20; 21]. However, the large number of samples is still an important factor slowing down the calculation speed. The polygon-based method treats three-dimensional objects as a collection of polygons [22; 23], which can reduce the number of samples by two to three orders of magnitude compared to the point source method. Due to this method of discretizing objects into polygons, rendering information such as lighting, shadows, and textures in computer graphics can be utilized to enhance the rendering of the scene [24]. For many years, scholars have been dedicated to the research of polygon-based methods, proposing many advanced and efficient methods [25; 26; 27; 28; 29; 30; 31]. The layer-based method performs layer sampling on 3D objects [32; 33; 34; 35], and compared to point source and panel methods, it has the least number of samples. When the number of layers is fixed, the computational complexityof layer-based methods is not affected by the scene's complexity, while point-based and polygon-based methods do not have this advantage. Layer-based methods consume less memory and compute faster, thus having great potential in real-time holographic 3D displays. At present, these methods have achieved good results in computational efficiency and imaging quality after years of development and iteration. For example, a convolutional symmetric compressed look-up table (CSC-LUT) [36] method proposed by [PERSON] et al. can achieve real-time (>24 fps) color holographic display corresponding to three perspectives of a 3D scene. The WRP-like method [37] proposed by [PERSON] et al. can compute holograms with tens of thousands of triangles in seconds, even with a CPU. [PERSON] et al. proposed a dual-channel parallel neural network (DCPNet) [38] that can generate 2 k phase holograms with high fidelity in 36 ms. In this paper, a new approach is proposed based on the study of focal depth. This method utilizes the property wherein the diffraction of a point source in the focal depth range can be approximated as its projection. The triangles on the object are layered at intervals of the focal depth, and their projections on the layers are considered their diffractions onto the layers. After layering and projecting all the triangles on the object, the object is approximated as a set of planar light sources with focal depth spacing, which are parallel to the holographic plane. Therefore, the diffracted field of an object in the hologram plane is approximated as a superposition of the diffracted fields of these parallel planes. The diffracted field is calculated using angular spectrum theory, and this calculation is accelerated by the fast Fourier transform (FFT). The proposed method projects the tilted triangles onto the layers without considering the diffraction calculation of the tilted triangles, so the calculation speed is greatly improved.