# High-Precision Depth Map Estimation from Missing Viewpoints for 360-Degree Digital Holography
## 4 Experiment Results and Discussion
### Qualitative Results of the Image Quality  
2.1 Comparison of the Proposed Model (HDD) with the Ground Truth Using Holographic 3D Images Reconstructed from CGH  
Figure 4 shows the comparison between 3D images to be constructed from CGH using estimated and ground truth depth maps, respectively. The 3D holographic images were reconstructed by two different methods--numerical and optical reconstruction. The CGH image of each viewpoint is calculated by the Fast Fourier Transform (FFT) algorithm [29; 30] using RGB images and depth maps. During the FFT computational process, either a pair of an RGB image and its corresponding ground truth or estimated depth map is used as input per viewpoint. The function of CGH _H(x,y)_ synthesized from the the FFT-based algorithm contains complex numbers in general and can be written as  
\[H(x,y)=|H(x,y)|e^{i\Phi(x,y)} \tag{1}\]  
where \(|H(x,y)|\) is the amplitude of _H(x,y)_ and \(\Phi(x,y)\) is its phase, respectively. After the CGHs of 1024 views were prepared for each solid object, an additional process of encoding called [PERSON]'s scheme [29] was adapted so that they could be represented on an amplitude-modulating spatial light modulator (SLM), that is, a reflective LCoS (liquid crystal on silicon)-SLM that we used in the study. [PERSON]'s method decomposes a complex-value field into four real and non-negative coefficients, \(L_{m}(x,y)\) where \(m\) is the natural number of \(1\leq m\leq 4\); the decomposition of the hologram function by [PERSON]'s encoding can be expressed by  
\[H(x,y)=L_{1}(x,y)e^{i0}+L_{2}(x,y)e^{i\pi/2}+L_{3}(x,y)e^{i\pi}+L_{4}(x,y)e^{i3 \pi/2} \tag{2}\]  
where at least two among four coefficients \(L_{m}(x,y)\) are equal to zero. The SLM that is used for optical reconstructions can display an 8-bit grayscale with a resolution of 3840 \(\times\) 2160 pixels, an active diagonal length of 0.62\", and a pixel pitch of 3.6 \(\upmu\)m. A fiber-coupled, combined beam from RGB laser sources (wavelengths: 633 nm, 532 nm, and 488 nm of the MatchBox Laser Series) passed through an expanding/collimating optical device to supply coherent, uniform illumination on the active area of the SLM. A field lens (focal length: \(f\) = 50 cm) was positioned just after the LCoS-SLM, and an experimental observation of the optically reconstructed images was performed using a DSLR camera (Canon EOD 5D Mark III), whose lens was located within an observation window that was generated near the focus of the field lens [30] (see Figure 5). The results of the camera-captured optical reconstructions and numerical reconstructions from the synthesized CGHs are shown in Figure 4. To prove the depth difference in a real 3D space between two objects based on the prepared 360-degree holographic content, we demonstrated the accommodation effect with  
Figure 4: Results of numerical and optical reconstruction from CGHs using estimated depth maps as well as ground truth for the torus. A focused object is indicated by an arrow mark. (Results for entire viewpoints are shown in Videos S1 and S2. Results of numerical and optical reconstruction with other objects can be seen in Figure S2). optically realized holographic 3D scenes. Each photograph in the optical reconstruction's column of Figure 4 presents the experimental demonstration to simultaneously indicate the clear object and the blurred object in each picture when the camera lens is set either on the rear object's focal plane or on the front object's focal plane, as shown from each photograph in the optical reconstruction column of Figure 4.  
When the holographic 3D images based on the depth map estimated from the proposed deep learning model are observed, there is a weak blurring in comparison with images based on the ground truth depth map, as shown in Figure 4. This is because the difference between depth values of the two objects on the basis of estimation has a minute deviation from that between the depth values of the two objects on the basis of a reference (ground truth).