Abstract

A fast calculation method for computer-generated holograms for hidden surface removal is proposed. In this method, a three-dimensional object is considered as a set of point light sources emitting light rays. To achieve the hidden surface removal, only appropriate light rays are selected according to their geometrical position, which are then converted into a Fourier spectrum of the wavefront. After the Fourier spectrum on the spherical surface is obtained, diffraction in arbitrary directions is calculated. Numerical simulation of a series of diffracted wavefronts onto arbitrary observation planes has been demonstrated to verify the effectiveness of our proposal.

© 2013 Optical Society of America

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References

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  1. J. W. Goodman, “Holography,” in Introduction to Fourier Optics, S. W. Director, ed., 2nd ed. (McGraw-Hill, 1996), pp. 295–392.
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    [CrossRef]
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    [CrossRef]
  4. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48, H54–H63 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. Y. Sakamoto, M. Takase, and Y. Aoki, “Hidden surface removal using z-buffer for computer-generated hologram,” Proc. SPIE 5005, 276–283 (2003).
    [CrossRef]
  14. R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48, 4246–4255 (2009).
    [CrossRef]
  15. T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
    [CrossRef]

2013 (1)

2012 (3)

2011 (1)

2009 (3)

2008 (2)

2005 (1)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
[CrossRef]

2003 (1)

Y. Sakamoto, M. Takase, and Y. Aoki, “Hidden surface removal using z-buffer for computer-generated hologram,” Proc. SPIE 5005, 276–283 (2003).
[CrossRef]

1993 (1)

N. Hashimoto and S. Morokawa, “Real-time electroholographic system using liquid crystal television spatial light modulators,” J. Electron. Imaging 2, 93–99 (1993).
[CrossRef]

1978 (1)

A. W. Lohmann, “Three-dimensional properties of wave-field,” Optik 51, 105–117 (1978).

Aoki, Y.

Y. Sakamoto, M. Takase, and Y. Aoki, “Hidden surface removal using z-buffer for computer-generated hologram,” Proc. SPIE 5005, 276–283 (2003).
[CrossRef]

Barada, D.

Chen, R. H.-Y.

Finke, G.

Fütterer, G.

Goodman, J. W.

J. W. Goodman, “Holography,” in Introduction to Fourier Optics, S. W. Director, ed., 2nd ed. (McGraw-Hill, 1996), pp. 295–392.

Hahn, J.

Hashimoto, N.

N. Hashimoto and S. Morokawa, “Real-time electroholographic system using liquid crystal television spatial light modulators,” J. Electron. Imaging 2, 93–99 (1993).
[CrossRef]

Häussler, R.

Hayashi, Y.

Hennelly, B.

Ichikawa, T.

Kanbayashi, Y.

Kang, H.

Kato, H.

Kim, H.

Kozacki, T.

Kujawinska, M.

Leel, B.

Leister, N.

Lim, Y.

Lohmann, A. W.

A. W. Lohmann, “Three-dimensional properties of wave-field,” Optik 51, 105–117 (1978).

Matsushima, K.

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48, H54–H63 (2009).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
[CrossRef]

Morokawa, S.

N. Hashimoto and S. Morokawa, “Real-time electroholographic system using liquid crystal television spatial light modulators,” J. Electron. Imaging 2, 93–99 (1993).
[CrossRef]

Nakahara, S.

Okada, N.

Onural, L.

Pandey, N.

Park, G.

Reichelt, S.

Sakamoto, Y.

T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
[CrossRef]

Y. Sakamoto, M. Takase, and Y. Aoki, “Hidden surface removal using z-buffer for computer-generated hologram,” Proc. SPIE 5005, 276–283 (2003).
[CrossRef]

Sando, Y.

Takaki, Y.

Takase, M.

Y. Sakamoto, M. Takase, and Y. Aoki, “Hidden surface removal using z-buffer for computer-generated hologram,” Proc. SPIE 5005, 276–283 (2003).
[CrossRef]

Usukura, N.

Wilkinson, T. D.

Yamaguchi, K.

Yaras, F.

Yatagai, T.

Appl. Opt. (6)

J. Electron. Imaging (1)

N. Hashimoto and S. Morokawa, “Real-time electroholographic system using liquid crystal television spatial light modulators,” J. Electron. Imaging 2, 93–99 (1993).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Optik (1)

A. W. Lohmann, “Three-dimensional properties of wave-field,” Optik 51, 105–117 (1978).

Proc. SPIE (2)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
[CrossRef]

Y. Sakamoto, M. Takase, and Y. Aoki, “Hidden surface removal using z-buffer for computer-generated hologram,” Proc. SPIE 5005, 276–283 (2003).
[CrossRef]

Other (1)

J. W. Goodman, “Holography,” in Introduction to Fourier Optics, S. W. Director, ed., 2nd ed. (McGraw-Hill, 1996), pp. 295–392.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of the virtual optical system for observation of a diffracted wavefront.

Fig. 2.
Fig. 2.

Spectrum on the hemispherical surface corresponding to the diffraction directions.

Fig. 3.
Fig. 3.

Coordinate system for observation of light rays emitted in the (Θ,Φ) direction.

Fig. 4.
Fig. 4.

Schematic of light rays emitted in the (θ,ϕ) direction from (a) all point light sources and (b) the most frontward point light sources, respectively.

Fig. 5.
Fig. 5.

Schematic of the virtual optical system for observation of radially diffracted wavefronts. (a) Perspective view and (b) top view.

Fig. 6.
Fig. 6.

World map that is to be spherically mapped onto the object surface.

Fig. 7.
Fig. 7.

Simulation results. (a) and (d) are for the case of ξ=90°, (b) and (e) are for the case of ξ=0°, and (c) and (f) are for the case of ξ=135°. (a)–(c) and (d)–(f) are calculated with and without the hidden surface removal process, respectively.

Fig. 8.
Fig. 8.

Total calculation time required for multiple diffraction patterns.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

F(u,v)=i4πO(u,v,1/λ2u2v2)1/λ2u2v2×exp(i2πR1/λ2u2v2),
O(u,v,1/λ2u2v2)=Op(1/λ,θ,ϕ)|0θπ,π/2ϕπ/2.
g(Θ,Φ)=o(x,y,z)exp(i2πZλ)dXdYdZ.
g(Θ,Φ)=o(x,y,z)exp[i2πλ(sinΘcosΦx+sinΘsinΦy+cosΘz)]dxdydz=o(x,y,z)×exp[i2π(Ux+Vy+Wz)]dxdydz=O(U,V,W),
U=sinΘcosΦ/λ,V=sinΘsinΦ/λ,W=cosΘ/λ.
g(Θ,Φ)=Op(1/λ,Θ,Φ).

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