The research of terahertz in-line digital holographic reconstruction mainly focuses on reducing the influence of the twin-image. However, these methods generally require the acquisition of multiple holograms or multiple iterations, which are easy to introduce noise interference and fall into local optimal solutions. Deep learning, with the rapid development, has been widely used in the field of imaging. In terms of visible light two-dimensional (2D) digital holographic reconstruction, a fully trained end-to-end neural network can directly obtain the corresponding reconstructed image through the input hologram. Continuous terahertz holograms have more obvious diffraction effects than visible light holograms in general, and the number of detector pixels and target pixels are both less. There is an obvious difference between the hologram and the reconstructed image. It is difficult for neural networks to directly match the features in the terahertz hologram accurately. At present, the work of applying deep learning to 2D terahertz in-line digital holography is mainly for image processing. Therefore, it is necessary to study how to make better use of deep learning in continuous terahertz digital holography.
In this study, two deep learning methods for amplitude reconstruction of 2D continuous terahertz in-line digital holography are studied, and compared with the traditional angular spectrum method (ASM) and the amplitude constrained phase retrieval algorithm with apodization (APRA). The first is the end-to-end U-net network reconstruction method (H-UnetM), that is, the network input images are holograms. The second is the angular spectrum method with U-net network reconstruction method (AS-UnetM). The reconstructed images of targets with different lateral resolutions are obtained by different reconstruction methods using a terahertz double-exposure digital holographic imaging system with a wavelength of 118.83 μm, a detector pixel size of 0.1 mm and a pixel number of 124×124.
Simulation results show that the results obtained using AS-UnetM are the best of the 4 methods for 0.3?0.5 mm resolution targets with recording distances of 15?20 mm. H-UnetM is better than ASM but not as good as APRA, and AS-UnetM generally outperforms both traditional methods (Figs. 4 and 5). Finally, real experiments are used to verify the simulation results. H-UnetM is able to reconstruct a part of the object, but some background noise is also highlighted. Reconstruction results near the target are the best using AS-UnetM (Fig. 7). In addition, the experimental results also show that AS-UnetM can reduce the influence of noise caused by the multi-frame stacking to obtain the hologram in the real experiment (Fig. 8). For more complex targets, H-UnetM cannot be used for reconstruction, while the reconstruction effect of AS-UnetM is better (Fig. 9).
This paper studies how to improve the applicability of deep learning in amplitude reconstruction of continuous terahertz in-line digital holography based on U-net neural network. Simulation results show that H-UnetM is better than ASM but not as good as APRA. AS-UnetM overcomes the difficulty of neural network to directly match the hologram features accurately to a certain extent, and its reconstruction quality is improved overall compared with the two traditional methods. In simulation at a recording distance of 20 mm, the peak signal-to-noise ratio (PSNR) of AS-UnetM reconstruction results is at least 7.9 dB higher than those of ASM results; most of its results outperform APRA, especially with a 4.3 dB improvement in the case of a “G” target with a resolution of 0.5 mm. In addition, it is verified that the quality of reconstructed images of AS-UnetM is less affected by distance than H-UnetM.
The overall trend of the PSNR value calculated by the real experiment is consistent with the simulation results. The PSNR of the entire image reconstructed by AS-UnetM at 20 mm is 64.02 dB, which shows the improvement of 5.5 dB and 0.1 dB, compared with the results of ASM and APRA, respectively. The PSNR of the area near the target is 67.21 dB, which is 0.8 dB higher than the result of APRA. In addition, the experimental results also show that AS-UnetM can reduce the influence of noise caused by the multi-frame stacking to obtain the hologram in the real experiment to a certain extent. When the number of holograms collected reaches about 4 frame, the amplitude of the area near the target can be effectively reconstructed by AS-UnetM method, which improves the imaging efficiency.
AS-UnetM can be directly used for image reconstruction of terahertz digital holographic imaging system similar to this paper. In addition, it has reference value for digital holographic reconstruction with obvious diffraction effect at other wavelengths. At present, the structure of the targets in the training set is relatively simple, and the scenes are all ideal. In the future, measures such as improving the training set and adjusting the network structure are expected to realize the reconstruction of more complex target scenes. And it is necessary to perform the resolution plate experiment to fully evaluate the imaging effect. In order to take full advantage of holographic imaging that can directly realize three-dimensional (3D) imaging, it is also necessary to carry out further research on the applicability of AS-UnetM in 3D reconstruction.
