Abstract

We propose a method to obtain a computer-generated hologram that renders reflectance distributions of individual mesh surfaces of three-dimensional objects. Unlike previous methods which find phase distribution inside each mesh, the proposed method performs convolution of angular spectrum of the mesh to obtain desired reflectance distribution. Manipulation in the angular spectrum domain enables its application to fully-analytic mesh based computer generated hologram, removing the necessity for resampling of the spatial frequency grid. It is also computationally inexpensive as the convolution can be performed efficiently using Fourier transform. In this paper, we present principle, error analysis, simulation, and experimental verification results of the proposed method.

© 2016 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. S.-C. Kim and E.-S. Kim, “Efficient generation of computer‐generated hologram patterns using spatially redundant data on a 3d object and the novel look‐up table method,” J. Inform. Display 10(1), 6 (2009).
    [Crossref]
  3. T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15(11), 2722–2729 (1976).
    [Crossref] [PubMed]
  4. M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
    [Crossref]
  5. Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
    [Crossref]
  6. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
    [Crossref] [PubMed]
  7. W. Lee, D. Im, J. Paek, J. Hahn, and H. Kim, “Semi-analytic texturing algorithm for polygon computer-generated holograms,” Opt. Express 22(25), 31180–31191 (2014).
    [Crossref] [PubMed]
  8. Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Improved full analytical polygon-based method using Fourier analysis of the three-dimensional affine transformation,” Appl. Opt. 53(7), 1354–1362 (2014).
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  9. 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]
  10. J.-H. Park, S.-B. Kim, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, S.-H. Kim, and S.-B. Ko, “Continuous shading and its fast update in fully analytic triangular-mesh-based computer generated hologram,” Opt. Express 23(26), 33893–33901 (2015).
    [Crossref] [PubMed]
  11. 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]
  12. T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “Calculation method of reflectance distributions for computer-generated holograms using the finite-difference time-domain method,” Appl. Opt. 50(34), H211–H219 (2011).
    [Crossref] [PubMed]
  13. K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for computer-generated holograms considering various reflectance distributions based on microfacets with various surface roughnesses,” Appl. Opt. 50(34), H195–H202 (2011).
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  14. K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48(34), H203–H211 (2009).
    [Crossref] [PubMed]

2015 (2)

2014 (2)

2011 (3)

2009 (3)

K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48(34), H203–H211 (2009).
[Crossref] [PubMed]

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[Crossref]

S.-C. Kim and E.-S. Kim, “Efficient generation of computer‐generated hologram patterns using spatially redundant data on a 3d object and the novel look‐up table method,” J. Inform. Display 10(1), 6 (2009).
[Crossref]

2008 (1)

1993 (2)

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

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
[Crossref]

1976 (1)

Barabas, J.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[Crossref]

Bove, V. M.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[Crossref]

Hahn, J.

Honda, T.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
[Crossref]

Hoshino, H.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
[Crossref]

Ichikawa, T.

Im, D.

Ji, Y.-M.

Jia, J.

Kim, E.-S.

S.-C. Kim and E.-S. Kim, “Efficient generation of computer‐generated hologram patterns using spatially redundant data on a 3d object and the novel look‐up table method,” J. Inform. Display 10(1), 6 (2009).
[Crossref]

Kim, H.

Kim, H.-J.

Kim, S.-B.

Kim, S.-C.

S.-C. Kim and E.-S. Kim, “Efficient generation of computer‐generated hologram patterns using spatially redundant data on a 3d object and the novel look‐up table method,” J. Inform. Display 10(1), 6 (2009).
[Crossref]

Kim, S.-H.

Ko, S.-B.

Lee, B.

Lee, W.

Li, B.

Li, X.

Liu, J.

Lucente, M.

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

Matsushima, K.

Nakahara, S.

Nishi, H.

Ohyama, N.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
[Crossref]

Paek, J.

Pan, Y.

Park, J.-H.

Sakamoto, Y.

Smalley, D. E.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[Crossref]

Smithwick, Q. Y. J.

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[Crossref]

Subagyo, A.

Sueoka, K.

Wang, Y.

Yamaguchi, K.

Yamaguchi, M.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
[Crossref]

Yatagai, T.

Yeom, H.-J.

Zhang, H.

Appl. Opt. (7)

J. Electron. Imaging (1)

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

J. Inform. Display (1)

S.-C. Kim and E.-S. Kim, “Efficient generation of computer‐generated hologram patterns using spatially redundant data on a 3d object and the novel look‐up table method,” J. Inform. Display 10(1), 6 (2009).
[Crossref]

Opt. Express (3)

Proc. SPIE (2)

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).
[Crossref]

Q. Y. J. Smithwick, J. Barabas, D. E. Smalley, and V. M. Bove., “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).
[Crossref]

Supplementary Material (3)

NameDescription
» Visualization 1: MP4 (105 KB)      movie clip for uniform mesh phase simulation
» Visualization 2: MP4 (878 KB)      movie clip for diffuse mesh surface simulation
» Visualization 3: MP4 (952 KB)      movie clip for ambient, diffuse, specular mesh surface simulation

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Figures (8)

Fig. 1
Fig. 1 The unit vector of the carrier wave uc with angles θx and θy.
Fig. 2
Fig. 2 Concept of the angular spectrum accumulation. (a) Desired reflectance distribution of a mesh, (b) accumulation of individual angular spectrums.
Fig. 3
Fig. 3 Concept of the proposed convolution based method. (a) Desired reflectance distribution, (b) convolution in the global spatial frequency grid.
Fig. 4
Fig. 4 [uxlT uylT]Tfxy;θxθy and [uxlT uylT]T f ˜ xy; θ x θ y on reference angular spectrum Gr(A-Tfx,y) and frequency domain difference Δf between fxy;θxθy and f ˜ xy; θ x θ y according to different inclinations (φx, φy) of a mesh with respect to the hologram plane: (φx, φy) = (a) (0°,0°), (b) (30°,0°), (c) (0°,30°), (d) (30°,30°), (e) (60°,60°), and (f) (90°,90°).
Fig. 5
Fig. 5 Simulation configuration.
Fig. 6
Fig. 6 Simulation results: Hologram reconstructions observed from different directions. (a) Uniform phase on mesh surfaces (see Visualization 1), (b) diffuse component added by the proposed method (see Visualization 2), (c) ambient, diffuse, and specular components added by the proposed method (see Visualization 3).
Fig. 7
Fig. 7 A hologram generated by the accumulation based method and convolution based method; (a) configuration of the experiment, (b) angular spectrum and optical reconstruction.
Fig. 8
Fig. 8 Angular spectrum, numerical and optical reconstruction of (a) non-diffusive case, (b) diffusive case, (c) Phong reflection case.

Tables (1)

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Table 1 Computation time

Equations (11)

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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 ]/det( A ),
f xl,yl = f xl,yl 1 λ [ u xl T u yl T ] u c ,
H( f x,y )= G( f x,y ; θ x , θ y ) I( θ x , θ y ) e jϕ( θ x , θ y ) d θ x , θ y ,
G( f x,y ; θ x , θ y )= G r ( A -T f xl,yl )exp[ j2π ( A -T f xl,yl ) T b ] det( A ) exp[ j2π f xl,yl,zl T c ] f zl / f z .
G( f x,y ; θ x , θ y )= B( f x,y ; θ x , θ y ) det( A ) exp[ j2π f xl,yl,zl T c ] f zl / f z ,
B( f x,y ; θ x , θ y )= G r ( A -T f xl,yl ) = G r ( A -T { [ R 11 R 12 R 13 R 21 R 22 R 23 ] f x,y,z 1 λ [ u xl T u yl T ] u c } ),
B( f x,y ; θ x , θ y )= G r ( A -T [ u xl T u yl T ]{ f x,y,z 1 λ u c } ) = G r ( A -T [ u xl T u yl T ][ f x 1 λ sin θ x f y 1 λ sin θ y 1 λ 2 f x 2 f y 2 1 λ 1 sin 2 θ x sin 2 θ y ] ) = G r ( A -T [ u xl T u yl T ] f xy; θ x θ y ).
B ˜ ( f x,y ; θ x , θ y )=B( f x,y [ 1 λ sin θ x 1 λ sin θ y ];0,0 ) = G r ( A -T [ u xl T u yl T ][ f x 1 λ sin θ x f y 1 λ sin θ y 1 λ 2 ( f x 1 λ sin θ x ) 2 ( f y 1 λ sin θ y ) 2 1 λ ] ) = G r ( A -T [ u xl T u yl T ] f ˜ xy; θ x θ y ).
H( f x,y ) B ˜ ( f x,y ; θ x , θ y ) det( A ) exp[ j2π f xl,yl,zl T c ] f zl f I( θ x , θ y ) e jϕ( θ x , θ y ) d θ x , θ y ={ exp[ j2π f xl,yl,zl T c ] det( A ) f zl f } B( f x,y [ 1 λ sin θ x 1 λ sin θ y ];0,0 ) I( θ x , θ y ) e jϕ( θ x , θ y ) d θ x , θ y ={ exp[ j2π f xl,yl,zl T c ] det( A ) f zl f }{ B( f x,y ;0,0 )D( f x,y ) },
D( f x,y )= I( θ x , θ y ) e jϕ( θ x , θ y ) | θ x = sin 1 λ f x , θ y = sin 1 λ f y .

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