# HoloForkNet: Digital Hologram Reconstruction via Multibranch Neural Network
## 4 Optical Experiments
### Results of Optical Experiments  
Digital holograms of phase objects of both types were optically registered: digits and circles. The holograms had a resolution of 2048 \(\times\) 2048 pixels. The images of 1024 \(\times\) 1024 pixels were displayed on SLM1. The size of object 1 was interpolated to 1024 \(\times\) 1024 pixels. The circle radius for object 2 was 64 pixels. The size of the displayed image on SLM2 was increased so that it occupied a similar area to SLM1 during reconstruction. Registration was performed in two cases: when the distance between the modulators, and therefore the planes, was small (1 cm) and significantly larger (20 cm). Randomly distributed circles with no intersection between them were used as object 2.  
A total of 4944 holograms were registered for object 1, of which 4500 were used for training and 444 for validation. Each training hologram was matched with two corresponding original images, forming a scene. For object 2, 10,522 holograms were recorded: 9500 were used for training and 1022 for validation. The model was trained on the obtained data. Due to the four times larger size of the input image (hologram), the interleaving step in the linear direction was increased by two times. Figure 11 shows examples of ground truth (a, c, e, g) and reconstructed (b, d, f, h) images from holograms containing two object planes. The distances from the camera to the modulators were different. The left image was closer to the camera plane. The distance between the object planes of the 3D scenes was 1 cm for Figure 11b,d and 20 cm for Figure 11f,h.  
Figure 10: Schematic of the experimental setup for recording digital holograms.  
From a visual point of view, the reconstruction quality is high for both 3D scene depth options. The model works well regardless of the distances between the planes. It successfully reconstructs even on-axis, side-by-side, located objects (see the upper objects in the right plane of Figure 11c,d). There are no visible artifacts in the reconstructed images. The quality of images was evaluated by the SSIM and CC metrics. They are given in Table 3. The values are averaged for 100 test images. Object 1 is presented in Figure 11a,e and object 2 in Figure 11c,g.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multicolumn{2}{c}{**Objects 1**} & \multicolumn{2}{c}{**Objects 2**} \\  & **1 st Plane** & **2 nd Plane** & **1 st Plane** & **2 nd Plane** \\ \hline \multicolumn{5}{c}{Small distance between planes} \\ SSIM & 0.84 \(\pm\) 0.04 & 0.85 \(\pm\) 0.03 & 0.84 \(\pm\) 0.04 & 0.930 \(\pm\) 0.009 \\ CC & 0.994 \(\pm\) 0.003 & 0.994 \(\pm\) 0.003 & 0.994 \(\pm\) 0.003 & 0.99 \(\pm\) 0.01 \\ \multicolumn{5}{c}{Large distance between planes} \\ SSIM & 0.85 \(\pm\) 0.03 & 0.80 \(\pm\) 0.03 & 0.85 \(\pm\) 0.03 & 0.923 \(\pm\) 0.007 \\ CC & 0.993 \(\pm\) 0.003 & 0.989 \(\pm\) 0.006 & 0.993 \(\pm\) 0.003 & 0.992 \(\pm\) 0.002 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Metrics for evaluating the quality of images reconstructed from optically recorded holograms.  
Figure 11: Ground truth (**a**,**c**,**e**,**g**) and neural network-reconstructed (**b**,**d**,**f**,**h**) images of scenes from recorded digital holograms. The distances between the planes are 1 cm (**a**,**c**) and 20 cm (**e**,**g**).  
It can be seen that the HoloForkNet produces high-quality reconstructed images. At the same time, it provides reconstruction without parasitic diffraction orders, which is very useful for inline digital holography. The HoloForkNet method can work with media with different particle densities. The considered example of the reconstruction corresponds to a density of 1059 particles per mm\({}^{3}\).