Frontier in Optics + Laser Science 2022, Rochester, USA, FM5E.2 (2022.10.17, Invitaed talk).

Challenges to Tera-pixel-scale Full-parallax
Computer Holography for 3D Imaging
Kyoji Matsushima* and Hirohito Nishi
Department of Electrical, Electronic and Information Engineering, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan*Corresponding author e-mail: matsu@kansai-u.ac.jp

Abstract: Computer holography requires a trillion pixels and a full-parallax view to reconstructquality three-dimensional images comparable to those reconstructed in traditional opticalholography. Large-scale full-parallax computer-generated holograms are presented to introduce
state-of-the-art computer holography. © 2022 The Authors
1. Introduction
Clear three-dimensional (3D) imaging in the field of holography was realized in the early 1960s by the pioneers
Yuri Denisyuk, Emmett Leith, and Juris Upatnieks. Leith and Upatnieks displayed their first laser holograms in
1964 at the annual meeting of the OSA. This can be considered the birth of 3D holographic imaging in practicebecause previous 3D holographic images were not clear owing to a lack of coherent light sources. Since then,although many techniques and materials have been invented and developed to record and reconstruct excellent 3Dholographic images, the technology has remained essentially the same. The 3D image is recorded on light-sensitive
material as a continuous fringe pattern, and the physical subject is needed to produce the 3D image; the image ofvirtual objects cannot be reconstructed unlike computer graphics. Traditional holography is not considered as amodern digital technology because the holograms cannot be stored and transmitted with digital media.
The nature of a hologram is the fringe pattern generated by interference with a reference wave. The origin of theconcept of computer-generated holograms (CGHs), where the fringe pattern is calculated by computers, goes back tothe days immediately after the realization of 3D imaging in optical holography. However, CGHs comparable tooptical holograms were not realized until recently. This is entirely due to the extremely large space-bandwidth
product (SBP) required for quality holograms. The SBP of typical optical holograms is estimated to exceed 1trillion; i.e., the fringes are considered to be a tera-pixel-scale image.
Over the past 15 years, we have developed computer holography to create quality CGHs for 3D imaging [1].
The maximum SBP has reached approximately 0.2 trillion as of August 2022 and is predicted to exceed 0.5 trillion
within a year. These large-scale CGHs reconstruct not only monochromatic images but also full-color images. The
impressive full-parallax 3D images give an amazing sensation of depth to the viewer, which has not been realized byother technologies. Some of the latest CGHs are introduced and demonstrated in this paper.
2. Necessary SBP and parallax
The viewing angle of a CGH (i.e., the angular range that the viewer can move the viewpoint) is mainly determinedby the pixel pitches x and y of the fringe image (see Sec. 8.3 in [1]). As an example, when x = y = 0.6 m, theviewing angle of the CGH is 48° in blue color (488 nm). As a result, when we create a CGH with the dimensions ofa 40-inch high-definition television (88.4 cm × 49.8 cm), the number of pixels is approximately 1.22 T pix.
It is difficult to generate a tera-scale fringe image using computers within a realistic computational time. Theeasiest way to reduce the problem is to restrict the parallax to the horizontal direction. The computational cost of ahorizontal-parallax-only CGH (HPO-CGH) is the square root of that of the full-parallax CGH. However, when weview the 3D image reconstructed by an HPO-CGH, there is inevitably conflict between the horizontal and verticalaccommodation of the eyes. The conflict loses the advantage of holographic 3D displays, i.e., the ability toreconstruct a deep 3D scene naturally.
3. Giga-scale to quasi-tera-scale CGHs
We refer to full-parallax CGHs of more than 1 billion pixels as full-parallax high-definition CGHs (FPHD-CGHs).
The first FPHD-CGH was The Venus created in 2009 [2]. The fringe of The Venus comprised 4.2 G pix and wasprinted adopting laser lithography (see Sec. 15.3 in [1]). The object field was calculated using the polygon-based
method [3]; only mutual occlusion between separate objects was processed in this CGH using the silhouette method[4]. To realize FPHD-CGHs, although we have developed several numerical techniques in the field of wave optics[5–7], the computation time of The Venus was 48 h in 2009. Nowadays the same CGH can be calculated in 20 min
and complicated self-occlusion can be properly processed using the switch-back technique [8]. CG-modeled 3D

Frontier in Optics + Laser Science 2022, Rochester, USA, FM5E.2 (2022.10.17, Invitaed talk).

objects are reconstructed with not only diffusive surfaces but also specular surfaces [9,10]. Real objects can beincorporated into a 3D scene of virtual objects [11,12]. We can reconstruct FPHD-CGHs in full-color with the twomethods [13,14]. Recently, we have developed a new technique to create flipbooks of FPHD-CGHs [15].
Figure 1 shows one of the latest monochrome FPHD-CGHs, which has dimensions of 34 cm × 17 cm. The
number of pixels is approximately 0.18 T; i.e., the CGH is of quasi-tera-pixel scale. Additionally, the latest fullcolor FPHD-CGH is shown in Fig. 2. This is a full-color version of the monochrome CGH named Brothers, which
was exhibited at the museum of the Massachusetts Institute of Technology in 2012 [16]. The fringe image comprises
0.1 T pix and RGB color filters are used for full-color reconstruction [11].
4. Conclusion
We demonstrated the latest FPHD-CGHs in monochrome and full color on a quasi-tera-pixel scale.
This work was partially supported by Japan Society for the Promotion of Science (JSPS) KAKENHI 22H03712.
5. References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]

K. Matsushima, Introduction to Computer Holography, (Springer, 2020).
K. Matsushima, S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-basedmethod,” Appl. Opt. 48, H54-H63 (2009).
K. Matsushima: “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614(2005).
A. Kondoh, K Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38, 53–61(2007)
K. Matsushima, H. Schimmel, F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular
spectrum of plane waves,” J. Opt. Soc. Am. A20, 1755-1762(2003).
K. Matsushima, T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and nearfields,” Opt. Express 17, 19662-19673 (2009).
K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18, 18453-18463 (2010).
K. Matsushima, M. Nakamura, 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).
H. Nishi, K. Matsushima, S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50,
H245-H252 (2011).
H. Nishi, K. Matsushima, “Rendering of specular curved objects in polygon-based computer holography,” Appl. Opt. 56, F37-F44 (2017).
K. Matsushima, Y. Arima, S. Nakahara, “Digitized holography: modern holography for 3D imaging of virtual and real objects,” Appl. Opt.
50, H278-H284 (2011).
K. Matsushima, N. Sonobe, “Full-color digitized holography for large-scale holographic 3D imaging of physical and nonphysical objects,”
Appl. Opt. 57, A150-A156 (2018),
Y. Tsuchiyama, K. Matsushima, “Full-color large-scaled computer-generated holograms using RGB color filters,” Opt. Express 25, 20162030 (2017).
O. Kunieda and K. Matsushima, “High-quality full-parallax full-color three-dimensional image reconstructed by stacking large-scalecomputer-generated volume holograms,” Appl. Opt. 58, G104-G111(2019).
Press release, https://www.kddi-research.jp/english/newsrelease/2022/050901.html
K. Matsushima, S. Nakahara, “Stepping closer to the perfect 3D digital image,” SPIE Newsroom, (7 Nov. 2012).

34 cm

Mobilephone

Mobilephone

18 cm

18 cm

17 cm

Left

Right

Fig.1 Optical reconstruction of the monochrome FPHD-CGH
named Sailing Warship III. The fringe image comprises
425,000 × 425,000 pixels with a pixel pitch of 0.8 μm ×0.4 μm. The illumination light source is a red laser.

Left

Right

Fig.2 Optical reconstruction of the full-color FPHDCGH named Color Brothers. The fringe image
comprises 225,000 × 450,000 pixels with a pixel
pitch of 0.8 μm × 0.4 μm. The illumination lightsource is an RGB laser.