Digital Holography & 3D Imaging 2022, Cambridge (UK), Tu1A.5 (2022.08.02)

Hybrid Technique of Polygon-Based and Ray-Sampling
Plane-Based methods in Full-Parallax High-Definition
Computer Holography
Ryosuke Katsura*, and Kyoji Matsushima
Department of Electrical and Electronic Engineering, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan.
*Corresponding author e-mail: k167063@kansai-u.ac.jp

Abstract: Reconstructing photorealistic 3D images of deep objects is still challenging for fullparallax large-scale computer-generated holograms. To address this problem, we propose a hybrid
technique based on physical simulation and multi-viewpoint images. © 2022 The Authors
1. Introduction
Several techniques have been proposed for calculating computer-generated hologram (CGH). One of the commontechniques is polygon-based method [1]. Recently, many full-parallax high-definition CGHs (FPHD-CGH),
composed of several tens billion or sometimes a hundred billion pixels, have been created using the polygon-based
method [2]. The 3D images of these FPHD-CGHs are very impressive because they reconstruct very deep 3D scene
without any conflicts of depth sensation.
In the polygon-based method, the object wave is calculated from planar surface light sources that have polygonal
shapes. Since this technique is based on physically simulation, all depth cues in human perception can be satisfied
naturally. However, advanced rendering techniques established in computer graphics (CG), such as refraction andanisotropic reflection, have not been developed in this method. On the other hand, the method based on raysampling plane (RSP) can deal with this problem [3]. In this approach, the RSP is defined near the object, and theobject ray is sampled from multi-viewpoint images (MVI) in the RSP. The sampled ray is converted into the object
wave by Fourier transform. Hence, advanced rendering techniques used in CG can be directly applied for calculating
object waves. However, this method is not suitable for deep objects, whose shape spreads in the depth direction,
because the object wave is obtained from MVI without any depth information.
In this paper, we propose a hybrid technique of the polygon-based and RSP-based methods to reconstruct deep
photorealistic 3D images by FPHD-CGHs.
2. Principle of the proposed techniqueFigure 1 shows the 3D scene used for creating a FPHD-CGH. Only the yellow toy train is calculated using the RSPbased method, while the gray parts of the model, i.e., other than the yellow part are calculated using the polygonbased method. Here, note that the gray and yellow toy trains partially hide each other. Thus, we must deal with thecomplicated mutual occlusion over two different methods.
yhologram

100RSP

105

95

xz

Units: mmFig. 1. The 3D scene of the created FPHD-CGH.

Fig. 2. Occlusion processing in a segment of the RSP.

Digital Holography & 3D Imaging 2022, Cambridge (UK), Tu1A.5 (2022.08.02)

The proposed technique consists of three steps. In the first step, the object wave behind the RSP is generated by
the polygon-based method, then it is numerically propagated to the RSP. Next, the object wave is obtained using theRSP-based method. Here, in the proposed method, the occlusion processing is performed by a procedure based onray-wavefront conversion technique [4].
Figure 2 shows the occlusion processing for one of the MVI in the RSP. Let 𝑢𝑏 [𝑚, 𝑛] denote the converted ray
information from the background wavefield calculated by the polygon-based method and 𝑢 𝑓 [𝑚, 𝑛] denotes therendering image by CG, where m and n represent sample points in the given MVI. MRSP is the binary mask whose
̅ RSP is an inverted binary mask
value is 0 in the region including the objects processed by the RSP-based method. Mof MRSP . In the proposed technique, the ray information is obtained by the following mutual masking:̅ RSP𝑢𝑜 [𝑚, 𝑛] = 𝑢𝑏 [𝑚, 𝑛]MRSP + 𝑢 𝑓 [𝑚, 𝑛]M(1)

Finally, the object wave in the front side of the RSP is calculated using the polygon-based method again. Note thatocclusion processing in the polygon-based method is performed by the switch-back technique [5].
3. Creation of FPHD-CGH
Optical reconstruction of the FPHD-CGH, created using the proposed technique, is shown in Fig. 3. The CGH is
composed of 128K × 256K pixels where 1K = 1024; the total pixel number exceeds 34 billion. The horizontal pixel
pitch is 0.8 μm, while vertical one is 0.4 μm to avoid non-diffraction and conjugate light using the fringe-oversamplingtechnique [6]. The reconstruction wavelength is 630 nm. The RSP is composed of 256 × 256 segments; each segment
has 512 × 512 pixels. Figure 3 confirms that the created FPHD-CGH reconstructs appropriate occlusion and motion
parallax in both the horizonal and vertical directions.
4. Conclusion
In this paper, we proposed a hybrid technique based on the polygon-based and RSP-based methods, and created aFPHD-CGH. It is verified by the optical reconstruction that the proposed technique seamlessly combines the 3D
images produced by two methods.
5. References[1] K. Matsushima: “Computer-generated holograms for three-dimensional surface objects with shade and texture”, Appl. Opt. 44, 4607-4614(2005).
[2] K. Matsushima, Introduction to Computer Holography, Sect. 1.3 (Springer, 2020).
[3] K. Wakunami, and M. Yamaguchi: “Calculation for computer generated hologram using ray-sampling plane”, Opt. Express 19, 9086-9101(2015).
[4] K. Wakunami, H. Yamashita, and M. Yamaguchi: “Occlusion culling for computer generated hologram based on ray-wavefront conversion”,Opt. Express 21, 21811-21822 (2013).
[5] K. Matsushima, M. Nakamura, and S. Nakahara “Silhouette method for hidden surface removal in computer holography and its acceleration
using the switch-back technique”, Opt. Express 22, 24450–24465 (2014).
[6] K. Matsushima, Introduction to Computer Holography, Sect. 8.8.3 (Springer, 2020).

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Fig. 3. Optical reconstruction of the FPHD-CGH created using the proposed technique.