International Workshop on Holography and related technologies 2011 (IWH2011), Utsunomiya, A4,pp.7-8 (2011.11.16).

High-Definition Image CGH Created by the Polygon-Based Methodand its Reconstruction by White LightHiroshi Yamashita,1) Kyoji Matsushima,1) and Sumio Nakahara2)
1) Department of Electrical and Electronic Engineering, Kansai University,
3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan
2) Department of Mechanical Engineering, Kansai University
3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan

1. Introduction
Recently, we presented polygon-based high-definition CGHs (PBHD-CGH) that reconstruct brilliant 3Dimages of occluded virtual 3D scenes [1]. These PBHD-CGHs are fabricated using a laser lithographysystem available on the market. All PBHD-CGHs created so far were Fresnel-type holograms, i.e. all objects
comprising the 3D scene were set in the position of several centimeters behind the hologram. If we would
place the objects too close or so as to overlap the hologram plane, the shade and texture of the objects could
be lost in the optical reconstruction. This is generally caused by image-type binary holograms not only in useof the laser lithography system. Binary-amplitude fringe patterns are commonly unable to reconstruct object
shading and texture-mapping, because amplitude information of the object field is removed by thebinarization if the object is too close to the hologram.
In this paper, optimized error diffusion is applied to encoding binary-amplitude image-type CGHs inorder to improve reconstruction of surface shading and texture-mapping. In this technique, a set ofcoefficients of error diffusion are iteratively optimized so that brightness of a test pattern is reproduced insimulated reconstruction. We will demonstrate some actual image-type high-definition CGHs created by theproposed technique and verify that the CGHs can be reconstructed by white light source without much
chromatic aberration.
2. Technique of optimized error diffusion
The 3D scene used to optimize diffusion coefficients is shown in Fig. 1. In the scene, a test pattern of 2D
image is placed in front of the hologram. The fringe pattern is generated by numerical interference between
the calculated object wave and reference wave, and then the binary fringe of the image CGH is produced bybinarization employing error diffusion. Reconstruction of the CGH is numerically simulated by a numericalimage formation technique based on wave-optics. Reproducibility of brightness of the test pattern isevaluated by root mean squared error (RMSE) between the defined and measured brightness of the testpattern. The diffusion coefficients are iteratively modified employing simultaneous perturbation algorithm(SPA) [2] so that the RMSE decreases. These coefficients optimized for the test pattern are applied forbinarization of the CGH fringe pattern for 3D object.
Figure 2 shows examples of simulated reconstruction of the image-type binary CGH encoded by asimple threshold in (a) and the optimized error-diffusion in (b). It is verified that brightness of the test patternis reproduced better with the optimized error-diffusion than that with the simple threshold.
3. Creation of image-type high-definition CGH
We created an image-type high-definition CGH named “i-Shion” by the error diffusion technique using thecoefficients optimized for the test pattern. The total number of pixels of the CGH is more than 4 G pixels.
The 3D scene of the CGH is shown in Fig. 3. Simulated reconstruction of the CGH encoded by a simple
threshold is shown in Fig. 4 (a) and the optimized error-diffusion in (b). Shading of the object is obviouslyInternational Workshop on Holography and related technologies 2011 (IWH2011), Utsunomiya, A4,pp.7-8 (2011.11.16).

Hologram
Test pattern

Units: mm
Fig.1 The 3D scene used foroptimization.

Units: mm
Fig.3 The 3D scene of “i-Shion”.

(a)(b)
Fig.2 Simulated reconstruction of the binary CGH of the test
pattern encoded by a simple threshold (a) and the
optimized error-diffusion (b).

(a)(b)
Fig.4 Simulated reconstruction of “i-Shion” with a simple
threshold (a) and the optimized error-diffusion (b).

improved by employing the proposed error diffusion technique.
4. Optical reconstruction and conclusion
Optical reconstruction of “i-Shion” by using a white light source is shown in Fig. 5. It is verified that the 3D
surface with shading and texture-mapping is clearly reconstructed. However, it was also shown that the shade
and texture are not completely reconstructed in every viewpoint.
References
1) K. Matsushima and S. Nakahara: “Extremely high-definition full-parallax computer-generated hologram
created by the polygon-based method”, Appl. Opt. 48, H54-63(2009).
2) Y. Maeda, H. Hirano and Y. Kanata: “A learning rule of neural networks via simultaneous perturbationand its hardware implementation”, Neural Networks 8, 251-259(1995).
(a) Left(b) Center(c) Right

Fig.5 Photographs of optical reconstruction of the image-type high-definition CGH“i-Shion” by white light. Photographs (a) – (c) are taken from different viewpoints.