# Efficient Computer-Generated Holography Based on Mixed Linear Convolutional Neural Networks
## 3 Network Structure for ECGH  
Based on Equations (1) and (2), a deep learning parameter training logic can be constructed based on the following steps:  
1. First, the input target light field is calculated using the neural network model to obtain the corresponding phase value. 2. Second, the phase value is calculated to simulate the optical experimental results. 3. Third, the target light field is compared with the simulation results using a loss function. 4. Finally, the gradient of the loss value is calculated and backpropagated to update the network parameters. This is shown in Figure 2, where \(A_{in}\) represents the target field and \(NN\) is the neural network. Based on the superiority of this structural design, the label image is the input image, and additional label images do not need to be prepared. Although the U-net [28] network has shown excellent performance on many problems [29, 30, 31, 32, 33], the holograms obtained in the computational holography problem have defects that decrease the quality of the reconstruction image. Traditional convolutional neural networks rely on convolutional filters and non-linear activation functions, which means there is an assumption that the processed data are linearly separable. However, problems such as image encoding, holographic encryption, and frequency analysis are difficult to describe with linearly separable functions, and simple convolution and deconvolution are always limited to a certain area to improve the operational efficiency. The U-net cannot utilize and rewrite global information, which means that the optical image processing is very weak. The interconnected structure of the perceptron is a more efficient functional approximator that obtains more abstract feature information output [34]. A more intuitive description can be shown in Figure 3. Figure 3a gives a simplified image depicting the operations convolution and de-convolution. Figure 3c shows a series of black and white straight stripes, and the numerical distribution of the stripes is shown in Figure 3e. Figure 3d provides the result of the fast Fourier transform as shown in Figure 3c, which  
Figure 2: Network training logic. is a group of mirror-symmetrical points on the central axis in the frequency domain. It is difficult to obtain the independent points in the frequency domain in Figure 3d if only the spatial stripes are calculated by sampling and data blocks. This drawback can be solved by in-lining the fully connected layer, as in the structure shown in Figure 3b, which realizes the transfer and utilization of data across blocks. The structure of MLCNN is shown in Figure 4. The convolution kernel is a \(1\times 1\) convolution operation, which is used to deepen the network. \"DownSample\" is a down-sampling structure, and \"UpSample\" is an up-sampling structure, which is described later. \"Linear\" is a linear layer structure. \"Sigmoid\" is used as an activation function to constrain the output between 0 and 1. The dotted line is a bridge structure, forming a residual network to accelerate training and to reduce gradient disappearance and gradient explosion. In order to down-sample the network information, the \"DownSample\" structure shown in Figure 5a is used to replace the convolution and pooling operations in the traditional neural network. Input data consist of images with sizes of 2N \(\ast\) 2N, and then, the data are tiled into a one-dimensional vector with a size of \(1\ast 4\)N\({}^{2}\) after \(1\times 1\) convolution, batch normalization, and ReLu activation function. The vector is then down-sampled by the single-layer perceptron structure to obtain a one-dimensional vector of \(1\ast\) N\({}^{2}\), and the final recombination size is N \(\ast\) N. To replace the de-convolution operation in the U-net, the \"UpSample\" structure shown in Figure 5b is used to up-sample the information. The input image size N \(\ast\) N is processed by the \"UpSample\" structure to obtain an up-sampled image of a size 2N \(\ast\) 2N. It is mirror-symmetrical to the \"DownSample\" structure.