# Progress of the Computer-Generated Holography Based on Deep Learning
## 5 Conclusions and Outlook  
In conclusion, through the analysis of CGH based on the four network structures, including U-Net, ResNet, GAN, and autoencoder, we summarized the characteristics of each form. Compared with U-Net, ResNet introduces the residual block so that the output feature map is more sensitive to the changes. It can effectively solve the gradient disappearance problem. Compared with U-Net and ResNet, GAN can be used to construct a discriminator and generator of various differentiable functions. However, it is difficult to train, as the discriminator and generator need to be well synchronized. The autoencoder  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Loss Function** & **Definition** \\ \hline Mean square error & \(MSE(X,Y)=\frac{\sum_{i=1}^{n}(X_{i}-Y_{i})^{2}}{n}\) \\ \hline Root mean square error & \(RMSE(X,Y)=\sqrt{\frac{\sum_{i=1}^{n}(X_{i}-Y_{i})^{2}}{n}}\) \\ \hline L1 loss function & \(L_{1}(X,Y)=\frac{\sum_{i=1}^{n}|X_{i}-Y_{i}|}{n}\) \\ \hline AC loss function & \(AC(X,Y)=\frac{\sum_{i=1}^{n}|X_{i}|\cdot|Y_{i}|}{\sqrt{\left|\frac{\sum_{i=1}^{ n}|X_{i}|^{2}|}{\sum_{i=1}^{n}|Y_{i}|^{2}}\right|}}\) \\ \hline Binary cross entropy loss function & \(\min_{G}\max_{D}V(D,G)=\) \\ \(E_{x\sim p_{data}(x)}(\log D(x)]+E_{x\sim p_{i}(x)}[1-D(G(z))]\) \\ \hline Negative Pearson correlation coefficient & \(L_{NPCC}(X,Y)=(-1)\times\frac{\sum_{i=1}^{n}(X_{i}-\overline{X})\big{(}Y_{i}- \overline{Y}\big{)}}{\sqrt{\sum\limits_{i=1}^{n}\big{(}X_{i}-\overline{X} \big{)}^{2}(Y_{i}-\overline{Y})^{2}}}\) \\ \hline Perceptual loss function & \(L_{percep}(X,Y)=\|P(X)-P(Y)\|_{2}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The definition of loss functions.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Deep Learning Based CGH** & **Loss Function** \\ \hline Deep–learning–generated holography [23] & MSE \\ MDHGN [29] & MSE and L1 loss function \\ Spatial variation aberration compensation [26] & MSE and L1 loss function \\ Three–dimensional generated holography [5] & RMSE \\ DeepCGH [49] & AC loss function \\ Holo–Encoder [10] & NPCC and perceptual \\ GAN-Holo [27] & Binary cross entropy loss function \\ Generative model–based CGH [25] & Binary cross entropy loss function \\ Tensor holography [50] & Data fidelity and perceptual quality measure \\ \hline \hline \end{tabular}
\end{table}
Table 3: The loss functions for deep–learning–based CGH.  
based deep CGH can automatically learn the latent encodings of CGH and make full use of the neural network advantages.  
It is suggested that advanced network architectures and smart mapping relations can be applied to obtain faster calculation and higher reconstruction quality. Moreover, more efforts are expected to accelerate the calculation in the future. Several network frameworks including physical models need to be further optimized to ensure high-fidelity optical reconstruction. Deep learning opens a new door for possible real-time CGH calculation. Along with the developments of the advanced deep networks, we believe that deep learning could be a universal solution to the CGH calculation as well as the DOE and metasurface design in the field of diffractive optics.  
Conceptualization, Y.Z. and M.Z.; investigation, Y.Z. and M.Z.; supervision, L.C.; writing--original draft preparation, Y.Z.; writing--review and editing, Y.Z., M.Z., K.L., Z.H. and L.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (NSFC), grant number 62035003, and the China Postdoctoral Science Foundation, grant number BX2021140.  
Not applicable.  
All data generated or analyzed during this study are included in this published article.  
The authors declare no conflict of interest.