# Efficient Computer-Generated Holography Based on Mixed Linear Convolutional Neural Networks
## 1 Introduction  
Digital holography [1; 2; 3] can be used in the recording and playback of object waves based on interference and diffraction. The recording process, however, is always affected by many factors since the optical interference is vulnerable to its environment. Computer-generated holography (CGH) is a light field modulation technique that obtains a custom light field distribution by encoding the intensity or phase of the coherent light wave-fronts. Especially for phase-only computational holography, the image displayed can be realized without the disturbance of a zero term and a twin image. The development of spatial light modulator (SLM) technology or a meta-material membrane provides a physical carrier for the realization of this technology. The intensity and phase modulation of spatial light can be realized by loading a specific gray scale image on the intensity or phase modulation SLM, respectively. CGH is also a light field modulation method that has been garnering much interest and has been applied to holographic light traps [4; 5], neural light stimulation [6; 7], 3D display [8; 9; 10; 11; 12], planar solar concentrators [13; 14], and near-eye AR displays [15; 16]. The goal of CGH is to obtain optimal wave modulation by inversely solving a custom light field. This problem is always a nonlinear, ill-posed non-convex inverse problem, and the solved wave modulation must be a free-space solution of the wave propagation equation. At the same time, the image quality is limited by the modulation accuracy of the SLM. It is usually difficult to represent the target light field. In practice, the solution of computational holograms is always an approximation, and numerical methods are required to determine a feasible hologram to obtain the best encoded wave front. The computation of CGH often employs iterative algorithms, such as the GS algorithm [17] and its various variants [18]. To save on computation time, non-iterativemethods have been designed, such as binary Fraunhofer holography [19]. However, these non-iterative methods always result in poor image quality and low spatial resolution during reconstruction due to speckle noise, down-sampling effects, and conjugate image interference. In recent years, the rise in deep learning and neural network technology has provided new alternatives to solving these kinds of problems. Deep learning can find optimal solutions or local optimal solutions in non-convex problems, so that it has more potential to solve CGH. It has emerged in optical problems such as those in all-optical machine learning [20], holographic imaging [21; 22; 23; 24], and tomography [25; 26; 27]. Among them, the U-net deep learning structure [22] has been tried on the CGH problem and has achieved initial success. In this paper, we design an efficient computer-generated holography (ECGH) structure to improve the CGH efficiency and the image quality by introducing mixed linear convolutional neural networks (MLCNN). The network is trained by a large number of custom light fields as parameters. ECGH can achieve higher quality phase-only holographic images based on a non-iterative calculation of the input custom light field. The simulation results prove that the network structure can save on the number of parameters by 69% but can still be trained to solve the CGH problem with a higher image quality. The merits of the proposed method lie in the following three aspects. First, the mixed linear convolutional neural network structure can reduce the number of parameters used by about two-thirds so that the computing loads can be alleviated correspondingly. Second, the method can save on half the computing time when compared with a conventional U-net structure [21; 22]. Compared to the GS algorithm [17], the MLCNN method can reduce significantly more computing time. Lastly, the mixed linear convolutional neural network structure is introduced in ECGH to improve the image quality.