# HoloForkNet: Digital Hologram Reconstruction via Multibranch Neural Network
## 3 Numerical Experiments
### Reconstructing Object Images 2
The results of the quality assessment metrics for the five objects on each of the eight planes are shown in Table 2.  
Several factors contribute to the difference in reconstruction quality. The most important ones are the overlapping objects from different object planes and the non-uniformity of intensity over the reconstructed object area. Initially, Dense-U-net was designed to work with smaller, non-overlapping objects and the reconstructed 3D scene was not separated into individual 2D planes. The object overlapping and non-uniformity are not as impactful. Thus, it is possible to say that HoloForkNet shows better performance in cases of larger and overlapping objects spread across fewer object planes. Figure 8 shows a plot describing the quality of reconstruction for each of the eight object planes. There were five objects in each plane. It can be seen that all planes are approximately equal in quality. This is explained by the fact that all planes have the same complexity of elements: number, shape and density of objects. In experimental data, the number of objects is rarely strictly fixed. Therefore, to extend the evaluation of the method's capabilities, the model was tested with samples with different numbers of objects in planes. At the same time, within one sample, the scenes contained the same number of objects in each plane. The plot for reconstruction quality in relation to the number of objects in each plane is shown in Figure 9. Holograms of 3D scenes containing eight object planes were used. The total number of objects for the left point of the graph is 8 \(\times\) 1 = 8 and for the right one, 8 \(\times\) 16 = 128. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **HoloForkNet** & **Dense-U-net** \\ \hline SSIM & 0.972 \(\pm\) 0.004 & 0.93 \(\pm\) 0.09 \\ CC & 0.98 \(\pm\) 0.04 & 0.7 \(\pm\) 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical evaluation of reconstruction quality for computer-generated holograms of 3D scenes consisting of eight object planes (five objects in each plane). Figure 8: Correlation between the reconstruction quality and the object plane index. The hologram contained a 3D scene consisting of eight object planes. It can be seen that an increase in the number of objects in the plane leads to a decrease in the quality of reconstruction. This can be explained by the increased reconstruction complexity. In this case, the neural network model works well up to approximately 10 objects per plane. Therefore, Figure 6 shows exactly this number of objects per plane. With a further increase in the number of objects, the quality begins to fall faster. The reduction in the CC with the reduction in the complexity (for one and two objects in the plane) of the scene can be explained by the suboptimal conditions for the neural network since it was trained on the dataset with five objects in each plane. This could be enough of a deviation from the optimal conditions to cause one of the metrics to suffer slightly. Experiments were also conducted with a random number of objects in each plane. The number can be from 1 to 20 objects. Hence, the average number of objects in the plane in the large sample was 10.5. The number of planes in 3D scenes was eight. The estimated quality of neural network reconstruction was: SSIM = 0.94 \(\pm\) 0.01, CC = 0.90 \(\pm\) 0.09. This is consistent with the values obtained for the case where each plane contained 10 objects. It can be concluded that for the model, the total number of objects in the scene is more important than the number of objects in each plane. Thus, the HoloForkNet trained on computer-generated data has shown good performance. Further, the HoloForkNet architecture will be verified on experimentally recorded digital holograms in order to confirm its applicability not only to the data obtained by computer modeling but also to optically obtained holograms.