Abstract

This paper presents a calculation method of computer-generated holograms that involves removing the hidden surface and provides realistic rendering. The method was based on the ray-tracing method that simulates rays traveling paths. Rays are cast from every elementary hologram into virtual objects and then the traveling paths of the rays are determined. Since the method is considering intersection with objects, absorption, reflection, and refraction, the method is capable of rendering realistic images. Multiple reflections and refraction are expressed by casting additional rays into the reflection direction and the transmission direction and calculating the length of the light path. To express the quality of materials, the Phong reflection model and Cook–Torrance reflection model were used. Results of optical reconstructions show that the hidden surface removal was conducted. Moreover, the texture of material appeared as well as other effects by the proposed method.

© 2012 Optical Society of America

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References

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  1. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
    [CrossRef]
  2. Y. Sakamoto, “An algorithm of hidden surface removal using shadow-propagation method for computer-generated hologram,” IEICE Trans. Inf. Syst. J85-D-2, 1832–1839 (2002), in Japanese.
  3. 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]
  4. T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63–70 (2008).
    [CrossRef]
  5. 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]
  6. H. Kang, T. Yamaguychi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44–D54 (2008).
    [CrossRef]
  7. K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19, 9086–9101 (2011).
    [CrossRef]
  8. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005).
    [CrossRef]
  9. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47, D117–D127 (2008).
    [CrossRef]
  10. K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for CGH considering smooth shading with polygon models,” Proc. SPIE 7957, 795706 (2011).
    [CrossRef]
  11. Y. Kanazawa, Y. Sakamoto, and Y. Aoki, “Calculation method of computer generation hologram considering refraction,” IEICE Trans. Inf. Syst. J88-D-2, 88–94 (2005), in Japanese.
  12. K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48, H203–H211 (2009).
    [CrossRef]
  13. A. Appel, “Some techniques for shading machine rendering of solids,” in Proceedings of AFIPS Joint Computer Conference (ACM, 1968), pp. 37–45.
  14. T. Whitted, “An improved illumination model for shaded display,” Commun. ACM 23, 343–349 (1980).
    [CrossRef]
  15. N. Hayashi, Y. Sakamoto, and Y. Honda, “Improvement of camera arrangement in computer-generated holograms synthesized from multi-view images,” Proc. SPIE 7957, 795711 (2011).
    [CrossRef]
  16. J. P. Waters, “Holographic image synthesis utilizing theoretical,” Appl. Phys. Lett. 9, 405–407 (1966).
    [CrossRef]
  17. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (2011).
    [CrossRef]
  18. R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (2011).
    [CrossRef]
  19. H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

2011

N. Hayashi, Y. Sakamoto, and Y. Honda, “Improvement of camera arrangement in computer-generated holograms synthesized from multi-view images,” Proc. SPIE 7957, 795711 (2011).
[CrossRef]

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (2011).
[CrossRef]

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (2011).
[CrossRef]

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for CGH considering smooth shading with polygon models,” Proc. SPIE 7957, 795706 (2011).
[CrossRef]

K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19, 9086–9101 (2011).
[CrossRef]

2009

2008

2005

Y. Kanazawa, Y. Sakamoto, and Y. Aoki, “Calculation method of computer generation hologram considering refraction,” IEICE Trans. Inf. Syst. J88-D-2, 88–94 (2005), in Japanese.

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005).
[CrossRef]

2002

Y. Sakamoto, “An algorithm of hidden surface removal using shadow-propagation method for computer-generated hologram,” IEICE Trans. Inf. Syst. J85-D-2, 1832–1839 (2002), in Japanese.

1980

T. Whitted, “An improved illumination model for shaded display,” Commun. ACM 23, 343–349 (1980).
[CrossRef]

1966

J. P. Waters, “Holographic image synthesis utilizing theoretical,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Aoki, Y.

Y. Kanazawa, Y. Sakamoto, and Y. Aoki, “Calculation method of computer generation hologram considering refraction,” IEICE Trans. Inf. Syst. J88-D-2, 88–94 (2005), in Japanese.

Appel, A.

A. Appel, “Some techniques for shading machine rendering of solids,” in Proceedings of AFIPS Joint Computer Conference (ACM, 1968), pp. 37–45.

Chen, R. H.-Y.

Cook, R.

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (2011).
[CrossRef]

Fujii, T.

Hahn, J.

Hayashi, N.

N. Hayashi, Y. Sakamoto, and Y. Honda, “Improvement of camera arrangement in computer-generated holograms synthesized from multi-view images,” Proc. SPIE 7957, 795711 (2011).
[CrossRef]

Honda, Y.

N. Hayashi, Y. Sakamoto, and Y. Honda, “Improvement of camera arrangement in computer-generated holograms synthesized from multi-view images,” Proc. SPIE 7957, 795711 (2011).
[CrossRef]

Ichikawa, T.

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for CGH considering smooth shading with polygon models,” Proc. SPIE 7957, 795706 (2011).
[CrossRef]

Kanazawa, Y.

Y. Kanazawa, Y. Sakamoto, and Y. Aoki, “Calculation method of computer generation hologram considering refraction,” IEICE Trans. Inf. Syst. J88-D-2, 88–94 (2005), in Japanese.

Kang, H.

Kim, H.

Kitayama, R.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Lee, B.

Matsushima, K.

Nakahara, S.

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (2011).
[CrossRef]

Sakamoto, Y.

N. Hayashi, Y. Sakamoto, and Y. Honda, “Improvement of camera arrangement in computer-generated holograms synthesized from multi-view images,” Proc. SPIE 7957, 795711 (2011).
[CrossRef]

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for CGH considering smooth shading with polygon models,” Proc. SPIE 7957, 795706 (2011).
[CrossRef]

K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48, H203–H211 (2009).
[CrossRef]

Y. Kanazawa, Y. Sakamoto, and Y. Aoki, “Calculation method of computer generation hologram considering refraction,” IEICE Trans. Inf. Syst. J88-D-2, 88–94 (2005), in Japanese.

Y. Sakamoto, “An algorithm of hidden surface removal using shadow-propagation method for computer-generated hologram,” IEICE Trans. Inf. Syst. J85-D-2, 1832–1839 (2002), in Japanese.

Torrance, K.

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (2011).
[CrossRef]

Wakunami, K.

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

J. P. Waters, “Holographic image synthesis utilizing theoretical,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Whitted, T.

T. Whitted, “An improved illumination model for shaded display,” Commun. ACM 23, 343–349 (1980).
[CrossRef]

Wilkinson, T. D.

Yamaguchi, K.

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for CGH considering smooth shading with polygon models,” Proc. SPIE 7957, 795706 (2011).
[CrossRef]

K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48, H203–H211 (2009).
[CrossRef]

Yamaguchi, M.

Yamaguchi, T.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63–70 (2008).
[CrossRef]

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Yamaguychi, T.

Yoshikawa, H.

H. Kang, T. Yamaguychi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44–D54 (2008).
[CrossRef]

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63–70 (2008).
[CrossRef]

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

ACM Trans. Graph.

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. P. Waters, “Holographic image synthesis utilizing theoretical,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Commun. ACM

T. Whitted, “An improved illumination model for shaded display,” Commun. ACM 23, 343–349 (1980).
[CrossRef]

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (2011).
[CrossRef]

IEICE Trans. Inf. Syst.

Y. Sakamoto, “An algorithm of hidden surface removal using shadow-propagation method for computer-generated hologram,” IEICE Trans. Inf. Syst. J85-D-2, 1832–1839 (2002), in Japanese.

Y. Kanazawa, Y. Sakamoto, and Y. Aoki, “Calculation method of computer generation hologram considering refraction,” IEICE Trans. Inf. Syst. J88-D-2, 88–94 (2005), in Japanese.

Opt. Express

Proc. SPIE

N. Hayashi, Y. Sakamoto, and Y. Honda, “Improvement of camera arrangement in computer-generated holograms synthesized from multi-view images,” Proc. SPIE 7957, 795711 (2011).
[CrossRef]

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for CGH considering smooth shading with polygon models,” Proc. SPIE 7957, 795706 (2011).
[CrossRef]

Other

A. Appel, “Some techniques for shading machine rendering of solids,” in Proceedings of AFIPS Joint Computer Conference (ACM, 1968), pp. 37–45.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

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Figures (19)

Fig. 1.
Fig. 1.

Flow chart of proposed method.

Fig. 2.
Fig. 2.

Ray tracing from each elementary hologram.

Fig. 3.
Fig. 3.

Intersection determination.

Fig. 4.
Fig. 4.

Light propagation from a point light source group.

Fig. 5.
Fig. 5.

Reflectance distributions.

Fig. 6.
Fig. 6.

Phong reflection model.

Fig. 7.
Fig. 7.

Cook–Torrance reflection model.

Fig. 8.
Fig. 8.

Casting a shadow ray.

Fig. 9.
Fig. 9.

Expression of multiple reflections.

Fig. 10.
Fig. 10.

Refraction of the light ray.

Fig. 11.
Fig. 11.

Attenuation of the light.

Fig. 12.
Fig. 12.

Block diagram of calculation for CGH.

Fig. 13.
Fig. 13.

Reconstructed images of a box and check.

Fig. 14.
Fig. 14.

Experimental geometry of reflection.

Fig. 15.
Fig. 15.

Reconstructed images of each distance.

Fig. 16.
Fig. 16.

Experimental geometry of refraction.

Fig. 17.
Fig. 17.

Reconstructed images of each refractive index.

Fig. 18.
Fig. 18.

Reconstructed images from different viewpoints.

Fig. 19.
Fig. 19.

Experiment of complex scene.

Tables (3)

Tables Icon

Table 1. Specifications of the GPU

Tables Icon

Table 2. Setup Parameters for Experiment

Tables Icon

Table 3. Computation Times (s)

Equations (11)

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

hm(x,y)=i=1NmAiri(x,y)·exp(j2πλri(x,y))·exp(jϕi),
ri=(xix)2+(yiy)2+zi2,
Ir=Iaρa+(N·L)kdρd+ksρs,
ρs=(R·V)αis,
ρs=FπDG(N·V).
F=12[gcg+c]2{1+[c(g+c)1c(gc)+1]2},
D=14m2cos4ξexp(tanξm)2.
rI=i=1Iti,
rt=n1·t1+n2·t2+n3·t3,
log10(I1I0)=αL,
It=Ir·10α·t2,

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