Abstract

A texturing method for the semi-analytic polygon computer-generated hologram synthesis algorithm is studied. Through this, the full-potential and development direction of the semi-analytic polygon computer-generated holograms are discussed and compared to that of the conventional numerical algorithm of polygon computer-generated hologram generation based on the fast Fourier transform and bilinear interpolation. The theoretical hurdle of the semi-analytic texturing algorithm is manifested and an approach to resolve this problen. A key mathematical approximation in the angular spectrum computer-generated hologram computation, as well as the trade-offs between texturing effects and computational efficiencies are analyzed through numerical simulation. In this fundamental study, theoretical potential of the semi-analytic polygon computer-generated hologram algorithm is revealed and the ultimate goal of research into the algorithm clarified.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  26. 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]
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2014 (1)

2013 (3)

2012 (2)

2011 (2)

2010 (5)

2008 (6)

2006 (1)

2005 (1)

2002 (1)

1998 (1)

1993 (1)

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

Ahrenberg, L.

Awazu, S.

Benzie, P.

Buschbeck, S.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

Chen, B.-C.

Chen, N.

Cho, J.

Choi, H.-J.

Dong, J.-W.

Flon, S.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

Füutterer, G.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

Hahn, J.

Hanák, I.

Häussler, R.

R. Häussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

Hayashi, Y.

He, H.-X.

Hong, J.

Ichihashi, Y.

Ichikawa, T.

T. Ichikawa and Y. Sakamoto, “A rendering method of background reflections on a specular surface for CGH,” J. Phys. Conf. Ser. 415, 012044 (2013).
[Crossref]

T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52(1), A201–A209 (2013).
[Crossref] [PubMed]

Im, D.

Ito, T.

Janda, M.

Jia, J.

Kim, H.

Kim, Y.

Kurihara, T.

Lee, B.

Lee, D.

Leister, N.

R. Häussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

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.

Masuda, N.

Matsushima, K.

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]

K. Matsushima, “Wave-field rendering in computational holography,” 9th IEEE/ACIS International Conference on Computer and Information Science, 846–851 (2010).

Min, S.-W.

Mishina, T.

Missbach, R.

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE 7690, 76900E (2010).
[Crossref]

Moon, E.

Nakahara, S.

Nakayama, H.

Neifeld, M. A.

Nishi, H.

Okano, F.

Okui, M.

Olaya, J.-C.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

Onural, L.

Pan, Y.

Park, J.-H.

Park, Y.

Pu, Y.-Y.

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(1), A201–A209 (2013).
[Crossref] [PubMed]

T. Ichikawa and Y. Sakamoto, “A rendering method of background reflections on a specular surface for CGH,” J. Phys. Conf. Ser. 415, 012044 (2013).
[Crossref]

Schwerdtner, A.

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE 7690, 76900E (2010).
[Crossref]

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

R. Häussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

Shimobaba, T.

Shiraki, A.

Stolle, H.

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE 7690, 76900E (2010).
[Crossref]

Sugie, T.

Takada, N.

Takaki, Y.

Wang, H.-Z.

Wang, Y.

Watson, J.

Yamaguchi, K.

Yoshimura, K.

Zschau, E.

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE 7690, 76900E (2010).
[Crossref]

Appl. Opt. (9)

Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. 47(19), D6–D11 (2008).
[Crossref] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008).
[Crossref] [PubMed]

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]

H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49(31), 5993–5996 (2010).
[Crossref]

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011).
[Crossref] [PubMed]

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]

T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52(1), A201–A209 (2013).
[Crossref] [PubMed]

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]

T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41(8), 1489–1499 (2002).
[Crossref] [PubMed]

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. Opt. Soc. Am. A (1)

J. Phys. Conf. Ser. (1)

T. Ichikawa and Y. Sakamoto, “A rendering method of background reflections on a specular surface for CGH,” J. Phys. Conf. Ser. 415, 012044 (2013).
[Crossref]

Opt. Express (7)

Y.-Z. Liu, J.-W. Dong, Y.-Y. Pu, B.-C. Chen, H.-X. He, and H.-Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18(4), 3345–3351 (2010).
[Crossref] [PubMed]

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on AMD HD5000 series GPU and OpenCL,” Opt. Express 18(10), 9955–9960 (2010).
[Crossref] [PubMed]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
[Crossref] [PubMed]

T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20(4), 3529–3540 (2012).
[Crossref] [PubMed]

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express 13(6), 1923–1932 (2005).
[Crossref] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14(17), 7636–7641 (2006).
[Crossref] [PubMed]

J. Cho, J. Hahn, and H. Kim, “Fast reconfiguration algorithm of computer generated holograms for adaptive view direction change in holographic three-dimensional display,” Opt. Express 20(27), 28282–28291 (2012).
[Crossref] [PubMed]

Opt. Lett. (2)

Proc. SPIE (3)

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE 7690, 76900E (2010).
[Crossref]

R. Häussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M (2008).
[Crossref]

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[Crossref]

Other (4)

http://www.israel21c.org/health/revolutionary-hologram-guided-heart-surgery-is-a-heartbeat-away/

K. Matsushima, “Wave-field rendering in computational holography,” 9th IEEE/ACIS International Conference on Computer and Information Science, 846–851 (2010).

H.-G. Lim, N.-Y. Jo, and J.-H. Park, “Hologram synthesis with fast texture update of triangular meshes,” Digital Holography and 3D Imaging Technical Digest, DW2A.8 (2013).
[Crossref]

K. Matsushima, S. Nakahara, Y. Arima, H. Nishi, H. Yamashita, Y. Yoshizaki, and K. Ogawa, “Computer holography: 3D digital art based on high-definition CGH,” 9th International Symposium on Display Holography (ISDH2012), 012053 (2013).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Observation of 3D target objects (a) without texture and (b) with texture patterns. (c) The relationship between the local coordinate system of the kth triangular facet and the global coordinate system.

Fig. 2
Fig. 2

FFT-based texturing process: (a) texturing of a triangular facet in the local coordinate system by direct multiplication of a texture pattern with a triangular facet function and (b) the local-to-global coordinate transformation of the holographic light field of the textured triangular facet.

Fig. 3
Fig. 3

Comparison of the computation times and reconstructed images of (a) I LG ( Δ L ) , (b) I LG ( Λ L ) , and (c) Δ G . The matrix size of ASCGH is set to 801 × 801. The computation times are recorded as 14.45, 14.45, and 0.15 seconds respectively.

Fig. 4
Fig. 4

Semi-analytic texturing process: (a) texturing of a triangular facet in the global coordinate system by direct multiplication of a texture pattern to a triangular facet function. (b) The equivalent convolution process of the angular spectrums of the texture and the triangular facet in the global coordinate system. Here the bilinear interpolation process is eliminated.

Fig. 5
Fig. 5

Reconstructed CGH images with texture patterns with the size of the angular spectrum matrix T ˜ G of (a) 61 × 61, (b) 81 × 81, (c) 101 × 101, (d) 121 × 121, (e) 141 × 141, (f) 161 × 161, (g) 181 × 181, (h) 201 × 201, and (i) 801 × 801.

Fig. 6
Fig. 6

(a) A comparison of computation times of the conventional FFT-based CGH method and the semi-analytic CGH method. (b) Numerically observed holographic images of 3D objects without a texture pattern and with texture patterns synthesized using the semi-analytic method. The texture pattern sizes shown are 1 × 1 (non-texture), 101 × 101, 141 × 141 and 201 × 201. The partial computational times of the key algorithmic steps of (c) the FFT-based method and (d) the semi-analytic method.

Equations (20)

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

W k ( x,y,z )= A G,k ( α,β )exp[ j2π( αx+βy+γz ) ]dαdβ .
( x y z )=( cos θ k cos ϕ k cos θ k sin ϕ k sin θ k sin ϕ k cos ϕ k 0 sin θ k cos ϕ k sin θ k sin ϕ k cos θ k )( x x k y y k z z k ).
W k ( x , y , z )= A L,k ( α α k , β β k )exp[ j2π( α x + β y + γ z ) ]d α d β ,
A G,k ( α,β )= η 0 e j2π( [ α α k ] x k +[ β β k ] y k +[ γ γ k ] z k ) A L,k ( α ( α,β ) α k ( α k , β k ), β ( α,β ) β k ( α k , β k ) )| J |,
α ( α,β ) α k ( α k , β k )=( α α k )cos θ k cos ϕ k +( β β k )cos θ k sin ϕ k ( γ γ k )sin θ k ,
β ( α,β ) β ( α k , β k )=sin ϕ k ( α α k )+cos ϕ k ( β β k ).
T( x , y )= m=M M n=N N T ˜ m,n exp( j2π( α m x + β n y ) ) .
W ¯ k,text ( x , y )= W k ( x , y ,0 )T( x , y ).
W ¯ k,text ( x , y ,0 )= W k ( x , y ,0 )T( x , y ) = [ m=M M n=N N T ˜ m,n A L,k ( α α m α k , β β n β k ) ]exp[ j2π( α x + β y ) ]d α d β = A ¯ L,k ( α , β )exp[ j2π( α x + β y ) ]d α d β ,
A ¯ L,k ( α , β )= m=M M n=N N T ˜ m,n A L,k ( α α m α k , β β n β k ) ,
A ¯ G,k ( α,β )= η 0 e j2π( [ α α k ] x k +[ β β k ] y k +[ γ γ k ] z k ) ×| J | m=M M n=N N T ˜ m,n A L,k ( α ( α,β ) α m α k ( α k , β k ), β ( α,β ) β n β k ( α k , β k ) ) .
W ¯ k ( x,y,z )= A ¯ G,k ( α,β )exp[ j2π( αx+βy+γz ) ]dαdβ .
α ( α p , β q ) α m α k ( α k , β k ) =( α p α m α k )cos θ k cos ϕ k +( β q β n β k )cos θ k sin ϕ k ( γ p,q γ m,n γ k )sin θ k ,
β ( α p , β q ) β n β k ( α k , β k )=( α p + α m + α k )sin ϕ k +( β q β n β k )cos ϕ k =( α p+m + α k )sin ϕ k +( β qn β k )cos ϕ k = α p+m sin ϕ k + β qn cos ϕ k β k ( α k , β k ),
Γ( α pm , β qn ) ( 1/λ ) 2 α p 2 β q 2 ( 1/λ ) 2 α m 2 β n 2 ,
α ( α p , β q ) α m α k ( α k , β k ) ( α pm α k )cos θ k cos ϕ k +( β qn β k )cos θ k sin ϕ k ( Γ( α pm , β qn ) γ k )sin θ k = α pm cos θ k cos ϕ k + β qn cos θ k sin ϕ k Γ( α pm , β qn )sin θ k α k ( α k , β k ).
A ¯ G,k ( α p , β q )= η 0 e j2π( [ α p α k ] x k +[ β q β k ] y k +[ γ p,q γ k ] z k ) | J | m=M M n=N N T ˜ m,n A ˜ G,k ( α pm , β qn ) ,
A ˜ G,k ( α pm , β qn ) = A L,k ( α pm cos θ k cos ϕ k + β qn cos θ k sin ϕ k Γ( α pm , β qn )sin θ k α k ( α k , β k ) , α pm sin ϕ k + β qn cos ϕ k β k ( α k , β k ) ).
( α m , β n )=( α m cos θ k cos ϕ k + β n cos θ k sin ϕ k γ m,n sin θ k , α m sin ϕ k + β n cos ϕ k ),
A ¯ G,k ( α p , β q )= η 0 e j2π( [ α p α k ] x k +[ β q β k ] y k +[ γ p,q γ k ] z k ) | J |( T ˜ A ˜ G,k ).

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