Design & Fabrication (ODF'18), Hiroshima, 30S4-02 (2018.11.30, Invited talk).

Very Large-Scale Computer-Generated Hologram for 3D Display
Kyoji Matsushima
Department of Electrical and Electronic Engineering, Kansai University, Japan
Abstract: Computer-generated holograms for 3D imaging have much different properties from that for optical devices. Severaltechniques are introduced to reconstruct high-quality monochrome and full-color 3D images by using very large-scale computergenerated holograms.
© 2018 OSJ
Keywords: 3D image, CGH, Computer holography, full-color image, volume hologram

1. Introduction
A computer-generated hologram (CGH) is thehologram whose fringe pattern is numerically generated
by using a computer. The idea was first proposed by A.
W. Lohmann [1]. However, the proposed concept was
not of three-dimensional (3D) imaging but wavefront
conversion. There is a considerable difference between
the CGHs for a 3D display and an optical device. The
former CGH requires high diffraction efficiency andaccuracy but does not need a large space-band product(SBP). In contrast, the latter CGH requires lessefficiency and accuracy but needs a large-scale SBP.
To generate large-scale CGHs for 3D display, wehave proposed the polygon-based method, wherepolygonal surface sources of light form an object [2].
This technique makes it possible to create display
CGHs, which are composed of billions or sometimes
tens of billions of pixels [3-8]. These CGHs could
reconstruct only monochrome 3D images before.
Recently, however, full-color CGHs have also beencreated by large-scale fringe patterns. These full-color
CGHs utilize either RGB color filters [9-10] or volume
holograms [11] for reconstructing color images.
In addition, the large-scale CGHs mentioned so far
mainly reconstruct 3D images of a virtual object, whose
shape is given by CG models. However, some CGHs
reconstruct physical objects [4,10], whose large-scalewave-field is captured by synthetic aperture digitalholography [12].
These techniques based on large-scale wave-fields
and fringe patterns are summarized in this paper.
2. Difference between CGHs as optical device and
3D display
As is well known, a hologram fringe is generated byinterference between an object wave and reference
wave. The fringe intensity is given by:2

I ( x, y ) O ( x, y ) + R ( x, y ) ,=(1)where O(x, y) and R(x, y) are an object field andreference field, respectively.
In creating a CGH used for optical devices, O(x, y)
represents the target field after wavefront conversion,
such as a beam shape. The fringe pattern, whichsometimes modulates the phase of the input field, isdirectly optimized to gain high efficiency and accuracy.
In contrast, O(x, y) is not unequivocal in CGHs for3D display. It must be calculated from the numericalmodel of an object or scene, whose 3D image isreconstructed by the CGH. In addition, in the sampled
field of O(x, y), the sampling interval determines thetravelling angle of the field, and thus, gives theviewing-zone angle of the 3D image. Hence, we mustchoose a small sampling interval such as sub-microns.
As a result, a gigantic number of sample points isrequired to achieve a given large size of the 3D image.
This is the problem of SBP in computer holography.
Since a large-scale SBP leads to a large-scalecomputational effort, the problem of SBP is, in theother word, the problem of calculation of object fields.
(a)

(b)

Fig.1. Large-scale monochrome CGH “Sailing Warship-II”(a) Distant and (b) close-up pictures
Table 1. Parameters of “Sailing Warship-II”

Number of pixels
Pixel pitches [µm]Size [cm]
Design wavelength [nm]Sampling interval of object
field [µm]67.5 × 109(225,000 × 300,000)
0.8 × 0.4
18 × 12633
0.8 × 0.8

Design & Fabrication (ODF'18), Hiroshima, 30S4-02 (2018.11.30, Invited talk).
3. Monochrome CGH
Figure 1 shows a large-scale monochrome CGH
composed of 67.4 G pixels. In this CGH, a vertical
pixel pitch of 0.4 µm and fringe over-samplingtechnique are adopted to remove the zeroth orderdiffraction light and conjugate image from thereconstructed image. A very large-scale CGH over 0.1
trillion pixels has also been developed in the same vein.
4. Full-color CGH
Two methods have been proposed to realize large-scale
full-color CGHs.
4.1 Method using RGB color filters
One of techniques to achieve full-color reconstructionof large-scale CGHs is to make use of RGB color filtersthat are usually used in LCD panels and image sensors[9]. Figure 2 (a) shows the principle. A large-scale
fringe pattern is spatially divided into three regions
corresponding to RGB colors. The fringe of each regionis generated at a wavelength of the color, and RGB
color filters are attached to the corresponding fringes.
By illuminating the CGH with white light, viewers cansee a color 3D image. An example of opticalreconstruction is shown in Fig.2 (b).
Fringe pattern madeof chromium thinfilm

RGB color filters

Full-color image

While light(a)scale CGHs generated for RGB colors are transferred tothree volume CGHs with the wavelength corresponding
to the RGB color, and then, the volume CGHs arestacked to superimpose the RGB images.
5. Conclusions
Diffrences between CGHs as an optical device and 3D
display are presented. A CGH for reconstructing 3D
images inevitably has a gigantic number of SBP andpixels. Several techniques were introduced toreconstruct monochrome and full-color 3D images.
This work is partially supported by JSPS
KAKENHI 18H03349 and the Matching Planner
Program from Japan Science and Technology Agency,
JST: Grant No. VP29117941340.
6. References[1] A. W. Lohmann and D. P. Paris: Appl. Opt. 6(1967) 1739
[2] K. Matsushima: Appl. Opt. 44 (2005) 4607.
[3] K. Matsushima, S. Nakahara: Appl. Opt. 48(2009) H54[4] K. Matsushima, Y. Arima, S. Nakahara: Appl. Opt.
50 (2011) H278
[5] H. Nishi, K. Matsushima, S. Nakahara: Appl. Opt.
50 (2011) H245
[6] K. Matsushima, H. Nishi, S. Nakahara: J. Electron.
Imaging 21 (2012) 023002[7] K. Matsushima, M. Nakamura, S. Nakahara: Opt.
Express 22 (2014) 24450[8] H. Nishi, K. Matsushima: Appl. Opt. 56 (2017)
F37[9] Y. Tsuchiyama, K. Matsushima: Opt. Express 25(2017) 2016[10] K. Matsushima, N. Sonobe: Appl. Opt. 57 (2017)
A150[11] O. Kunieda, H. Nakao, K. Matsushima:
International Symposium on Display Holography
2018 (ISDH2018), Aveiro (Portugal), (2018)[12] T. Nakatsuji, K. Matsushima: Appl. Opt. 47(2008) D136
Original
CGHRContactcopy(R laser)

OriginalCGHG

Contactcopy(G laser)

Volumehologram

ROriginalCGH

BContactcopy(B laser)

Volumehologram

G

Volumehologram

B(b)Fig. 2 Full-color CGH using RGB color filters [9].
(a) Principle and (b) optical reconstruction.

4.2 Method using volume hologram
Another technique is to make contact-copies of original
monochrome CGHs as a volume hologram [11]. Figure
3 shows the principle. In this technique, three large-White lightFig 3. Principle of stacked-volume CGH