# High Bandwidth-Utilization Digital Holographic Reconstruction Using an Untrained Neural Network
## 5 Experiment  
To verify the performance of the proposed method in a real-world system, we designed the DH experiment for the standard phase resolution target and COS-7 (ATCC CRL-1651, CV-1 in Origin Simian-7) cells. Here, we use the Digital holographic smart computational light microscope (DH-SCLM) [3] developed by SCILab and turn it to a slightly off-axis state for hologram acquisition. In the DH-SCLM, the object wave transmitting the objective lens (UPLanSAPO \(\times\)10/0.4 NA, Olympus, Japan) interferes with the reference light and is recorded by the camera (The Imaging Source DMK 23U274, 1600 \(\times\) 1200, 4.4 \(\upmu\)m). The central wavelength of the illumination is 532 nm. In our method, according to the cost function in Equation (3), a reference light intensity map needs to be captured separately to obtain the reconstructed hologram, which is a no-need-repeat system calibration process. Figure 5 shows the reconstructed results of the standard phase resolution target (QPTTM, Benchmark Technologies Corporation, United States, Ri = 1.52). When the zero-order and \(\pm\)1-order are overlapped with each other in the SFD (shown in Figure 5i), the phase results recovered by the conventional FT method are severely impaired by imaging artifacts due to the autocorrelation term, as shown in Figure 5b,f. In VHQPI, the frequency component extraction (uVID) [43] can remove the zero-order term to a certain extent. However, influenced by the physical limitations (e.g., iterative instability and parameter uncertainty), the reconstructed phase results still suffer from imaging artifacts, as shown in Figure 5c,g. The proposed method migrates the physical model to the training process's cost function to recover the artifacts-free phase results iteratively, as shown in Figure 5d,h. The  
Figure 4: The comparison of phase reconstruction results at noise levels of 0.1 and 0.2, respectively. (**a,g**) The hologram under the noise levels of 0.1 and 0.2. (**b,j**) The corresponding spectrum of (**a,g**). (**c,h**) The ground truth at different noise levels. (**d,i**) The phase results recovered by our method. (**e,f,k,l**) The phase results are reconstructed by the FT method and VHQPI method at the noise level of 0.1 and 0.2, respectively. results of the three methods show that our method and VHQPI can clearly see the fourth element in the ninth group of the phase resolution target, while the FT method can only see the second element in the ninth group. However, the VHQPI's result has much coarser background noise due to the imaging artifacts, and that of our method is much smoother and cleaner. These demonstrate that our method can improve the imaging resolution while having better artifacts-suppression capability during low-carrier frequency fringe demodulation. Notably, the captured hologram and its spectrum based on the slightly off-axis DH system are shown in Figure 5a,e,i, and their SBU can reach 53.9% after calculation. Therefore, we can naturally conclude that the proposed method can achieve high-SBU, artifacts-free QPI under the single-frame, multiplex-free acquisition system [20]. To verify the practicality of the proposed method in biological research, we conducted an experiment on COS-7 cells under a slightly off-axis DH system. Figure 6 shows the results of phase reconstruction based on the FT method and our method. The captured hologram and its spectrum under the \(\times 20/0.45\)NA objective lens are shown in Figure 6a,d. After calculation, the SBU of the system's sensor can reach 31.7% in Figure 6d. The yellow filter window in Figure 6d is calculated from the numerical aperture of the objective used in the system, which is applied to spectrum filtering for the FT method. Figure 6b shows the phase recovery result based on the FT method. We select three regions of interest (ROI, Area1, Area2, and Area3) on the specimens, and their detailed views are shown in Figure 6(e1-e3). It can be revealed that the fringe-like error caused by overlapping spectrum dramatically degrades the phase recovery quality.