International Symposium on Holography and Related Technologies 2015 (IWH2015)
Ginowan (Okinawa), Th2-4, (2015.12.3).

A Simulation Technique for Selection of Color Filter
Used for Full-Color High-Definition CGH
Yasuhiro Tsuchiyama1), Kyoji Matsushima1), Sumio Nakahara2), and Yuji Sakamoto3)
1)
Department of Electrical and Electronic Engineering, Kansai University
2)
Department of Mechanical Engineering, Kansai University
3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan
3)
Graduate School of Information Science and Technology, Hokkaido University
North 14, West 9, Kita-ku, Sapporo, Hokkaido 060-0814, Japan

1. Introduction
Recently, it has been possible to create computer-generated holograms (CGH) composed of several billion or
several ten billion pixels1). These high-definition CGHs make it possible to reconstruct high-quality 3D images
comparable to that by conventional optical holography. Several techniques also have been reported for fullcolor reconstruction of CGHs. For example, three images reconstructed by CGHs for RGB color are combined
into a full-color 3D image by using dichroic mirrors2). However, complex and large optical system required inthis approach has no portability and causes difficulty in adjusting alignment. As a result, it is difficult to display
full-color CGHs using the technique at museums and exhibitions. The technique of stacked CGHs has also
been proposed3). In this technique, layers of RGB CGHs printed on dichroic thin films are deposited on a single
substrate. This is excellent technique but requires a sophisticated fine processing and film formation technology.
Thus, it is difficult to apply the technique to high-definition CGHs. In this paper, we propose a technique forhigh-definition full-color CGHs by using color filters and present a simulation technique to select filter
properties appropriate for bright full-color reconstruction.
2. The principle of full-color reconstruction using a color filter
The principle of full-color reconstruction is shown in Fig.1. In this technique, the fringe pattern is spatiallydivided into RGB blocks and the fringe pattern for each block is generated by numerical interference of theobject and reference waves whose wavelength corresponds to each color. A color filter is attached to theblockwise fringe patterns so as to filter the band of illumination light. When irradiating white illumination
light, the full-color 3D image emerges by combining RGB images reconstructed by each block.
The layered structure of full-color CGHs is shown in Fig.2. The fringe pattern is formed by chromium thinfilm and a color filter is attached on it. The ‘guard gap’ indicated in Fig.2 is the gaps between blocks of thefringe pattern. This guard gap allows us to increase the tolerance for positioning errors of the color filter.
3. Simulated reconstruction of full-color CGHs using color filter
Suppose that O ( x , y ) and R ( x , y ) are
Fringe patternmonochromatic object and reference wave
Color filter
fields with a wavelength of  0 , the binary
fringe pattern is given by:
Full-color*reconstruction(1)
I ( x , y )  B  Re  O R ( x , y )  
where B {} represents binarizing operator andthus the value of I ( x , y ) is either 0 or 1. Whena light with spectrum of L (  ) illuminates theCGH, the reflected wave field immediately
after the color filter may be written as:

Glass substrate
Color filterP ( x, y;  )L ( )White light

Fig. 1 The principle of full-color
reconstruction of highdefinition CGHs using acolor filter.

Guard gap

Fringe pattern
by Cr film

Fig. 2 The layered structureof full-color highdefinition CGHs.

International Symposium on Holography and Related Technologies 2015 (IWH2015)
Ginowan (Okinawa), Th2-4, (2015.12.3).

P ( x, y;  )  I ( x , y ) r  r  t (  )  r  L (  )Crglass

2CF(2)

CF

where rC r is reflectance of chromium film, which corresponds to the pixels having the value of ‘1’ in I ( x , y ) .
The rglass is also reflectance of the glass substrate, corresponding to ‘0’-value pixels. We assume that theseare constants with respect to the wavelength. The transmittance and reflectance of the color filter are given byt C F (  ) and rC F , respectively. While the former is a function of  , the latter is assumed to be a constant. Notethat the square in t C F (  ) expresses a double transmission of the filter.
We calculated many monochromatic images from P ( x , y ;  ) using discrete spectrum of L (  ) , where theimages are of simulated reconstruction given by numerical image formation in virtual optics. Thesemonochromatic images were combined into a XYZ color image using the CIE XYZ color matching function,and finally, converted to the sRGB color image.
4. Optical and simulated full-color reconstruction of CGH
The 3D scene and parameters of the test CGH are shown in Fig. 3 and Table 1. We assessed two color filters;
Filter 1 and 2. Filter 1 is the simplified low-cost filter made by a reversal film, while Filter 2 is one of genuine
filters used for LCD panels. Here, Filter 1 is real existing but Filter 2 is only catalog data. Figure 4 shows
optical or simulated reconstruction using these filters. Measured constants rglass  7.1% , rC r  6 0 .6 % andrC F  3.5% are used in the simulation. Figure 4 (a) and (b) are optical and simulated reconstruction using Filter
1, while (c) is only simulation using Filter 2. The simulated reconstruction in (b) is definitely darker than thatin (c) and well fit with optical reconstruction in (a). In fact, the CGH using Filter 1 is too dark to exhibit it inordinary room. This problem is most likely relieved by adopting Filter 2 because of its higher transmission.
5. Conclusion
In this paper, full-color CGHs using a color filter and the simulation technique are proposed for selection ofthe color filter. The result shows that this technique makes it possible to reconstruct full-color images and thefilter used for LCD panel most likely gives better reconstruction.
This work was supported by the JSPS KAKENHI (15K00512) and the MEXT strategic research foundationat private universities (2013-2017).
Reference
1) K. Matsushima, and S. Nakahara: “Extremely High-Definition FullParallax Computer-Generated Hologram Created by the PolygonBased Method”, Appl. Opt. 48, H54-H63 (2009).
2) T. Miyaoka, K. Matsushima, S. Nakahara: “Optimization of designwavelength for unobtrusive chromatic aberration in high-definitioncolor computer holography”, SPIE Proc. 9386, 93860N(2015).
3) T. Kämpfe, E. Kley, A. Tunnermann, P. Dannberg: “Design andfabrication of stacked CGH for multicolor image generation”, Appl.
Opt. 46, 5482-5488(2007).

Table 1 Parameters used for creating
the full-color test CGH.
Number of65,536 × 65,536
pixelsPixel pitches
0.8 μm × 0.8 μm
Design630, 520, 460 nm
Wavelength
RGB stripe
100 μmwidth
Guard-gap
50 μm
width

Units : mmFig. 3 3D scene of the full-color
test CGH.

(c) Filter 2(a) Filter 1(b) Filter 1Fig. 4 (a) Optical and (b) simulated reconstruction using Filter 1. (c)Simulated reconstruction using Filter 2.