[Citation] The 12th Laser Display and Lighting Conference 2023 (LDC2023), Yokohama, LDC10-02 (2023.4.21, Invited talk).

Computation Techniques in Tera-pixel-scale Full-parallax Computer
Holography for 3D Display
Kyoji Matsushima, Hirohito Nishi, Ryosuke Katsura, Chang-Joo Lee
Department of Electrical, Electronic and Information Engineering, Kansai University,
Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan, +81-6-6368-0933, matsu@kansai-u.ac.jp
Abstract: Tera-pixel-scale fringe images are required for creating quality CGHs that reconstruct amazing deep 3D scenes. However,
it is very difficult to calculate such large-scale fringes in full-parallax. Techniques based on numerical field propagation aresummarized for computing object fields by physical simulation and multi-viewpoint images.

1. Introduction
Full-parallax computer-generated holograms (CGH) canreconstruct the ultimate 3D images, because they haveno conflict among depth sensations and thus thecapabilities to reconstruct amazing very deep 3D scenesthat any other 3D imaging technique cannot achieve [1].
However, it is estimated that more than trillion pixels are
required to produce 3D images with the same size as 40inch HD-TVs [2]. Computation of the tera-pixel-scale(TPS) full-parallax CGHs is a challenging task incomputer holography.
2. Object field based on physical simulation
The nature of a hologram is its fringe pattern generated
by optical interference of an object field with a reference
field. In computer holography, the object field iscalculated from the 3D model like computer graphics(CG). Many researchers prefer the point-based method(point cloud) to calculate the object field. However, thepoint-based method is too time-consuming to calculate
large-scale object field in full-parallax. Therefore, thepolygon-based method, based on field propagation, isused to create sub TPS CGHs shown in Fig.1 and 2.
2.1 The polygon-based method
Figure 3 shows computation of object fields using thepolygon-based method [4,5]. Polygon fields (c) arecalculated from surface functions (b), defined for eachpolygon, using several techniques of field propagation.
34 cm
34cm

Polygon 1

P1

Polygon 2

P3 P2y(c) Polygon fieldPolygon 3x(a) Object modely(b) Surface functionx(d) Object field

Fig. 3. Computation of object waves using thepolygon-based method [5].

2.2 Numerical field propagation
Numerical field propagation is classified into threegroups shown in Fig. 4. We developed the band-limited
angular spectrum method [6] for parallel field
propagation in (a), the rotational transform [7] for nonparallel propagation in (b), and the shifted angular
spectrum method [8] for off-axis field propagation in (c).
2.3 Mask-based occlusion processing
Occlusion processing is one of the most important but
most difficult computation techniques in computer
holography. The visibility test is commonly used in thepoint-based method but is too time-consuming for largescale CGHs. In creation of the sub TPS CGHs, a maskMobilephone

18 cm

18 cm
Mobilephone

Fig. 1. Optical reconstruction of the monochrome
sub TPS CGH. The fringe image is composed of0.36 T pix.

Fig. 2. Optical reconstruction of the full-color sub
TPS CGH using RGB color filters [3]. The fringe
image is composed of 0.1 T pix.

[Citation] The 12th Laser Display and Lighting Conference 2023 (LDC2023), Yokohama, LDC10-02 (2023.4.21, Invited talk).

q

Sourcewavefield(a)Destination
wavefield

Sourcewavefield(x0, y0)

Sourcewavefield

Destination
wavefield(b)
Destination
wavefield

4. Conclusion
Computation techniques are summarized for creating
tera-pixel-scale CGHs.
Acknowledgment
This work was partially supported by Japan Society for
the Promotion of Science (JSPS) KAKENHI 22H03712.

(c)Fig. 4. Three classes of numerical field propagation
used in large-scale computer holography.

based technique called the silhouette method [9] and its
acceleration technique, named the switchback technique[10], are used for occlusion processing.
The switchback technique, which propagates object
fields back and forth many times, has the ability toprocess self-occluded objects very fast when comparing
the visibility test. However, because the mask issilhouette, i.e., orthographic projection of the polygon,
there are gaps between masks in some cases. The gaps
are sometimes perceived as cracks of the object surface
in the optical reconstruction of large-scale CGHs. Moreexact shielding technique using surface masks and adouble rotational transform is proposed to remove thecracks [11]. Optical reconstruction of a sub TPS CGH,
where the exacter technique is used for occlusion
processing, is shown in Fig. 5.
2.4 Rendering specular surface and transparent object
Not only diffusive surfaces but also specular surfaces
can be rendered in the polygon-based method [12].
Recently, we proposed a technique to reconstructtransparent objects by physical simulation of opticalrefraction phenomenon [13].
3. Object field based on multi-viewpoint image
We can calculate full-parallax object fields from multiviewpoint images (MVI). Unfortunately, image-based
techniques do not give proper depth sensation byaccommodation in general, and thus, cause sensational
conflict in deep 3D scenes. However, since the techniqueof ray-sampling plane (RSP) uses field propagation [14],the technique can be used for large-scale computer
holography. In this technique, we can use advanced CGMobilephonerendering techniques for CGHs. Therefore, we haveproposed a hybrid technique to embed an RSP-based
object field in polygon-based object fields with properocclusion processing [15].

34 cm

17 cm

Fig. 5. Optical reconstruction of the monochrome
sub TPS CGH using exacter occlusion processing.
The fringe image is composed of 0.18 T pix.

References[1]K. Matsushima, Introduction to Computer Holography,
Chapter 1 (Springer, 2020).
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full-parallax computer holography for 3D imaging,”
Frontier in Optics + Laser Science 2022, FM5E.2 (2022).
[3] Y. Tsuchiyama, K. Matsushima, “Full-color large-scaled
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[4] K. Matsushima: “Computer-generated holograms forthree-dimensional surface objects with shade andtexture,” Appl. Opt. 44, 4607-4614 (2005).
[5] K. Matsushima, S. Nakahara, “Extremely high-definition
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[6] K. Matsushima, T. Shimobaba, “Band-limited angularspectrum method for numerical simulation of free-space
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[8] K. Matsushima, “Shifted angular spectrum method foroff-axis numerical propagation,” Opt. Express 18, 1845318463 (2010).
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[11] K. Nakamoto, K. Matsushima, “Exact mask-based
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for 3D display,” SPIE Proc. 11062, 1106204 (2019).
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[13] H. Nishi, K. Matsushima, “Rendering of transparent
objects in large-scale polygon-based computerholography,” Digital Holography and 3-D Imaging 2022,
Tu1A.4 (2022).
[14] K. Wakunami, and M. Yamaguchi, “Calculation forcomputer generated hologram using ray-sampling plane”,
Opt. Express 19, 9086-9101 (2015).
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Digital Holography and 3-D Imaging 2022, Tu1A.5(2022).