# HoloForkNet: Digital Hologram Reconstruction via Multibranch Neural Network
## 3 Numerical Experiments
### Reconstructing Object Images 2  
The second type of phase objects (circles) were placed randomly on each object plane. Holograms of 3D scenes consisting of 2-20 planes were generated. Each of the planes contained 1-16 circular objects. The neural network was trained for each number of object planes. An example of quality evaluation for each case is shown in Figure 6. There were 10 objects in each object plane. For two planes, a total of 20 objects per 3D scene are recorded, and, for example, eight planes correspond to 80 objects in a 3D scene. The training set consisted of 25,000 holograms, and the validation set consisted of 5000 holograms. Each additional object plane increases the size of the dataset and, therefore, the training time. For eight planes, the training set consisted of (25,000 + 8 \(\times\) 25,000) = 225,000 images. In the test sample, there were (5000 + 8 \(\times\) 5000) = 45,000 images. It can be seen that as the number of planes grows, the quality of reconstruction decreases. This is explained by the increasing amount of information contained in the hologram and the correspondingly increasing reconstruction complexity. For object 1 (digits), the more important metric is SSIM. These objects are grayscale, and contrast is important for \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **1 st Plane** & **2 nd Plane** \\ \hline SSIM & 0.86 \(\pm\) 0.04 & 0.85 \(\pm\) 0.04 \\ CC & 0.97 \(\pm\) 0.02 & 0.95 \(\pm\) 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation of reconstruction quality for synthesized holograms of scenes consisting of two object planes (objects—digits). Figure 6: Correlation between the reconstruction quality and the number of object planes in the hologram. There were 10 objects in each plane. them. The SSIM metric takes it into account better. For object 2 (circles), CC is more useful. Objects are binary, for them, it is important to have no artifacts in the background and the correct location. This is better handled by CC. Both metrics are given for a more complete description of all images. In Figure 6, CC decreases more rapidly than SSIM. For example, with an increasing number of objects, the neural network does not fully draw them even with correct positioning. The CC is more sensitive to such changes. The STD value also increases, suggesting that the number of artifacts in the reconstructed object images may increase. At the same time, the quality assessment metrics, even within the STD, remain above 0.8 for each set of planes. This indicates good performance from the model. An example of images reconstructed by the neural network is shown in Figure 7c,d. The 3D scene consisted of eight object planes. There were five objects in each plane. The images are arranged from left to right as they move away from the hologram plane. For comparison, Figure 7a,b show examples of the ground truth. From a visual point of view, the quality of the reconstruction is high. The vast majority of the objects are located in the correct places and have the correct characteristics. Only a small number of artifacts were introduced in the form of a false image, traces of objects from another plane, or incomplete objects. However, in this example, the artifacts are insignificant and do not influence the perception of the reconstructed images. Figure 7: Ground truth (**a,b**) and neural network-reconstructed (**c,d**) images. The hologram contained a 3D scene consisting of eight object planes. The results were compared against those generated by the Dense-U-net [58] model. This method was chosen because it is designed for 3D scene reconstruction, similar to HoloForkNet. Other methods were not used in the comparison because they require more initial data for reconstruction (for example, some standard methods involve recording four holograms for further reconstruction of information from them).