Abstract

Fully analytic mesh-based computer generated hologram enables efficient and precise representation of three-dimensional scene. Conventional method assigns uniform amplitude inside individual mesh, resulting in reconstruction of the three-dimensional scene of flat shading. In this paper, we report an extension of the conventional method to achieve the continuous shading where the amplitude in each mesh is continuously varying. The proposed method enables the continuous shading, while maintaining fully analytic framework of the conventional method without any sacrifice in the precision. The proposed method can also be extended to enable fast update of the shading for different illumination directions and the ambient-diffuse reflection ratio based on Phong reflection model. The feasibility of the proposed method is confirmed by the numerical and optical reconstruction of the generated hologram.

© 2015 Optical Society of America

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References

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  1. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
    [Crossref]
  2. K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express 21(19), 21811–21822 (2013).
    [Crossref] [PubMed]
  3. K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
    [Crossref]
  4. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
    [Crossref] [PubMed]
  5. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
    [Crossref] [PubMed]
  6. Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
    [Crossref] [PubMed]
  7. H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
    [Crossref] [PubMed]
  8. Y. Pan, Y. Wang, J. Liu, X. Li, J. Jia, and Z. Zhang, “Analytical brightness compensation algorithm for traditional polygon-based method in computer-generated holography,” Appl. Opt. 52(18), 4391–4399 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  12. D. Im, E. Moon, Y. Park, D. Lee, J. Hahn, and H. Kim, “Phase-regularized polygon computer-generated holograms,” Opt. Lett. 39(12), 3642–3645 (2014).
    [Crossref] [PubMed]
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  14. J.-H. Park, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, and S.-H. Kim, “Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching,” Opt. Express 23(6), 8006–8013 (2015).
    [Crossref] [PubMed]
  15. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
    [Crossref]
  16. S. Oh and I. K. Jeong, “Cylindrical angular spectrum using Fourier coefficients of point light source and its application to fast hologram calculation,” Opt. Express 23(23), 29555–29564 (2015).
    [Crossref]
  17. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
    [Crossref]
  18. H. Kim and D. Im, “Representation and synthesis of computer-generated holograms,” in 15th International Meeting on Information Display (IMID 2015), paper 38–2.

2015 (3)

2014 (1)

2013 (3)

2012 (1)

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

2008 (2)

2005 (2)

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44(22), 4607–4614 (2005).
[Crossref] [PubMed]

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

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

Ahrenberg, L.

Benzie, P.

Chen, B.-C.

Cho, J.

Dong, J.-W.

Hahn, J.

He, H.-X.

Im, D.

Jeong, I. K.

Ji, Y.-M.

Jia, J.

Kim, H.

Kim, H.-J.

Kim, S.-H.

Lee, B.

Lee, D.

Li, B.

Li, X.

Liu, J.

Liu, Y.-Z.

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Magnor, M.

Matsushima, K.

Moon, E.

Nakahara, S.

Nishi, H.

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50(34), H245–H252 (2011).
[Crossref] [PubMed]

Oh, S.

Pan, Y.

Park, J.-H.

Park, Y.

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

Pu, Y.-Y.

Wakunami, K.

Wang, H.-Z.

Wang, Y.

Watson, J.

Yamaguchi, M.

Yamashita, H.

Yeom, H.-J.

Zhang, H.

Zhang, Z.

Appl. Opt. (7)

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975).
[Crossref]

J. Electron. Imaging (2)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21(2), 023002 (2012).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (1)

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

Other (1)

H. Kim and D. Im, “Representation and synthesis of computer-generated holograms,” in 15th International Meeting on Information Display (IMID 2015), paper 38–2.

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (482 KB)      Movie of optical reconstruction for illumination direction update

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Figures (6)

Fig. 1
Fig. 1 Concept of the fully analytic triangular-mesh-based CGH synthesis.

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Fig. 2
Fig. 2 Concept of the proposed continuous shading method: Reference triangle has (a) uniform amplitude in the conventional method and (b) spatially varying amplitude in the proposed method.

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Fig. 3
Fig. 3 Numerical and optical reconstruction of the hologram generated by (a) conventional flat-shading method, (b) proposed continuous shading method.

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Fig. 4
Fig. 4 Phase of the angular spectrums for fast update of the shading (a) Gdiffuse,x(fx,y), (b) Gdiffse,y(fx,y), (c) Gdiffuse,z(fx,y), (d) Gambient(fx,y).

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Fig. 5
Fig. 5 Numerical and optical reconstruction results with different ambient-diffuse coefficients: (a) ka = 1.0, kd = 0.0, (b) ka = 0.5, kd = 0.0 (c) ka = 0.0, kd = 1.0.

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Fig. 6
Fig. 6 Reconstruction results with different illumination vectors s: (a) numerical reconstruction (b) optical reconstruction (Visualization 1).

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Equations (14)

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G( f x,y )= G l ( f xl,yl )exp[ j2π f xl,yl,zl T c ] f zl / f z ,
G l ( f xl,yl )= G r ( A -T f ′ xl,yl )exp[ j2π ( A -T f ′ xl,yl ) T b ] C det( A )
f ′ xl,yl = f xl,yl − 1 λ [ u xl T u yl T ] u c ,
C=exp{ −j 2π λ ( [ u xl T u yl T ] u c ) T r v,xlyl }exp{ j2π d v,vf λ },
G entire ( f x,y )= ∑ m a m G m ( f x,y ),
a m = a o,m ( k a + k d n m ⋅s ),
g r ( x r , y r )={ ( a v,2 − a v,1 ) x r +( a v,3 − a v,2 ) y r + a v,1 , inside triangle  0,              outside triangle ,
G r ( f xr,yr )=( a v,2 − a v,1 ) D 1 +( a v,3 − a v,2 ) D 2 + a v,1 D 3 ,
D 1 = e −j2π( f rx + f ry ) j−2π( f rx + f ry ) 8 π 3 f ry ( f rx + f ry ) 2 + e −j2π f rx 2π f rx −j 8 π 3 f rx 2 f ry ,   + j( 2 f rx + f ry ) 8 π 3 f rx 2 ( f rx + f ry ) 2
D 2 = e −j2π( f rx + f ry ) j( f rx +2 f ry )−2π f ry ( f rx + f ry ) 8 π 3 f ry 2 ( f rx + f ry ) 2 + e −j2π f rx −j 8 π 3 f rx f ry 2 ,   + j 8 π 3 f rx ( f rx + f ry ) 2
D 3 = e −j2π( f rx + f ry ) −1 4 π 2 f ry ( f rx + f ry ) + e −j2π f rx 1 4 π 2 f rx f ry ,   + −1 4 π 2 f rx ( f rx + f ry )
a v,i = a v,i,o ( k a + k d n v,i ⋅s ), i=1, 2, 3,
G entire ( f x,y )= ∑ m G m ( f x,y ) .
G entire ( f x,y )= k a G ambient ( f x,y )       + k d { s x G diffuse,x ( f x,y )+ s y G diffuse,y ( f x,y )+ s z G diffuse,z ( f x,y ) },

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