Abstract

Reconfiguration is a computational algorithm of adaptively updating computer generated holograms (CGHs) for the positional change of an observer’s viewing window with low computational load by efficiently using pre-calculated elementary CGHs. A fast reconfiguration algorithm of CGHs for three-dimensional mesh objects is proposed. Remarkable improvement is achieved in the computation speed of CGHs, which is at least 20-times faster than repetitive re-computation of CGHs. The image quality of reconfigured CGHs is analyzed.

© 2012 OSA

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References

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  1. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A13(3), 470–473 (1996).
    [CrossRef]
  2. M. A. Neifeld, “Information, resolution, and space-bandwidth product,” Opt. Lett.23(18), 1477–1479 (1998).
    [CrossRef] [PubMed]
  3. 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,” Appl. Opt.50(34), H87–H115 (2011).
    [CrossRef] [PubMed]
  4. R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (2008).
    [CrossRef]
  5. 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. SPIE6911, 69110V, 69110V-10 (2008).
    [CrossRef]
  6. 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]
  7. 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]
  8. T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express13(6), 1923–1932 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1923 .
    [CrossRef] [PubMed]
  9. E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE7690, 76900E, 76900E-13 (2010).
    [CrossRef]
  10. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express14(17), 7636–7641 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7636 .
    [CrossRef] [PubMed]
  11. 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. Express18(10), 9955–9960 (2010).
    [CrossRef] [PubMed]
  12. 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]
  13. M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging2(1), 28–34 (1993).
    [CrossRef]
  14. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express20(4), 4018–4023 (2012).
    [CrossRef] [PubMed]
  15. Y. Sando, D. Barada, and T. Yatagai, “Fast calculation of computer-generated holograms based on 3-D Fourier spectrum for omnidirectional diffraction from a 3-D voxel-based object,” Opt. Express20(19), 20962–20969 (2012).
    [CrossRef] [PubMed]
  16. 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]

2012

2011

2010

2008

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]

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

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]

2006

2005

2002

1998

1996

1993

M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging2(1), 28–34 (1993).
[CrossRef]

Ahrenberg, L.

Awazu, S.

Barada, D.

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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

Chen, N.

Choi, H.-J.

Dorsch, R. G.

Ferreira, C.

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. SPIE6911, 69110V, 69110V-10 (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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

Hahn, J.

Haussler, R.

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (2008).
[CrossRef]

Hayashi, Y.

Hong, J.

Ichihashi, Y.

Ito, T.

Kim, H.

Kim, Y.

Lee, B.

Leister, N.

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

Lohmann, A. W.

Lucente, M.

M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging2(1), 28–34 (1993).
[CrossRef]

Magnor, M.

Masuda, N.

Mendlovic, D.

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. SPIE7690, 76900E, 76900E-13 (2010).
[CrossRef]

Nakayama, H.

Neifeld, M. A.

Oikawa, M.

Okada, N.

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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

Park, J.-H.

Sando, Y.

Schwerdtner, A.

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE7690, 76900E, 76900E-13 (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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (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. SPIE7690, 76900E, 76900E-13 (2010).
[CrossRef]

Sugie, T.

Takada, N.

Takaki, Y.

Watson, J.

Weng, J.

Yatagai, T.

Yoshimura, K.

Zalevsky, Z.

Zschau, E.

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE7690, 76900E, 76900E-13 (2010).
[CrossRef]

Appl. Opt.

J. Electron. Imaging

M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging2(1), 28–34 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Proc. SPIE

R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (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. SPIE6911, 69110V, 69110V-10 (2008).
[CrossRef]

E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE7690, 76900E, 76900E-13 (2010).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Holographic 3D display with a Fourier transform optical system. The complex angular spectrum of the image light field is displayed at the holographic display panel, and the observer can see floating holographic 3D images at a specific position where the crystalline lens is matched to the VW of the holographic display.

Fig. 2
Fig. 2

Vignetting effect on holographic 3D image seen in observation simulation. (a) light field distribution at the eye pupil plane in the case of light convergence (b) observed 3D image with a focus on the far object (c) observed 3D image with a focus on the near object (d) light field distribution at the human eye pupil plane in the case that light field is vignetted by the finite human pupil (e) observed vignetted 3D image with a focus on the far object (f) observed vignetted 3D image with a focus on the near object .

Fig. 3
Fig. 3

Geometric interpretation of reconfiguration algorithm; (i) redirection of carrier wave and (ii) spatial translation of complex light field at the reference focal plane

Fig. 4
Fig. 4

Comparison of the quality of the holographic images generated by reconfiguration and recomputation. (a) and (d) are the numerically reconstructed holographic 3D images observed at two different VW positions with the left part focused. For (a) and (d), the corresponding ASCGH patterns were totally recomputed. (b) and (e) are the numerically reconstructed holographic 3D images generated by the ASCGHs obtained by the reconfiguration of the original ASCGH that is designed for the VW located on the optical axis. (c) Phase profile of reconfigured complex ASCGH in the angular spectrum domain for the first VW position and (f) that for the second VW position. The distance of the center of mass of the object from the eye lens is set to 300mm.

Fig. 5
Fig. 5

Comparison of the quality and computation time of the holographic images generated by reconfiguration and recomputation. The height of the object is 8mm and the distance of the object from the crystalline lens plane is set to 300mm. (a) and (d) are the numerically reconstructed holographic 3D images observed at two different VW positions with the left part focused. The corresponding ASCGH patterns were totally recomputed. (b) and (e) are the numerically reconstructed holographic 3D images generated by the ASCGHs obtained by the reconfiguration of the original ASCGH that is designed for the VW located on the optical axis. (c) Phase profile of reconfigured complex ASCGH in the angular spectrum domain for the first VW position and (f) that for the second VW position.

Fig. 6
Fig. 6

(a) Setup for analyzing the accuracy of reconfiguration algorithm and estimation of accuracy of the reconfiguration algorithm (b) RMSE (%) of a triangle facet on the x-y plane, and (c) RMSE(%) of triangle 45(deg.)-tilted relative to the normal vector of the x-y plane

Equations (15)

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C k ( x,y,z )=exp[ j2π / λ ( x k x v ) 2 + ( y k y v ) 2 + ( z k z v ) 2 ]exp[ j2π( α k x+ β k y+ γ k z ) ],
W k ( x,y,z )= Γ( α α k ,β β k ) A G,k ( α,β )exp[ j2π( αx+βy+γz ) ] dαdβ ,
Γ( α α k ,β β k )={ 1for ( α α k ) 2 + ( β β k ) 2 < ρ 2 0for ( α α k ) 2 + ( β β k ) 2 ρ 2 ,
A G,k (α,β) A L ( α ( α,β ) α k ( α k , β k ), β ( α,β ) β k ( α k , β k ) ), ×exp( j2π( [ α α k ] x k +[ β β k ] y k +[ γ γ k ] z k ) )
α ( α,β ) α k ( α k , β k )=[ αcos θ k cos ϕ k +βcos θ k sin ϕ k γsin θ k ], [ α k cos θ k cos ϕ k + β k cos θ k sin ϕ k γ k sin θ 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 )=[ αsin ϕ k +βcos ϕ k ][ α k sin ϕ k + β k cos ϕ k ]. =sin ϕ k ( α α k )+cos ϕ k ( β β k )
A ¯ G,k (α,β) A L ( α ( α,β ) α k ( α k +Δα, β k +Δβ ), β ( α,β ) β k ( α k +Δα, β k +Δβ ) ) ×exp( j2π( [ α α k Δα ] x k +[ β β k Δβ ] y k ) ) ×exp( j2π( [ ( 1/λ ) 2 α 2 β 2 ( 1/λ ) 2 ( α k +Δα ) 2 ( β k +Δβ ) 2 ] z k ) ).
α ( α,β ) α k ( α k +Δα, β k +Δβ ) = α ( αΔα,βΔβ ) α k ( α k , β k )+λsin θ k ( Δα[ α α k Δα ]+Δβ[ β β k Δβ ] ),
β ( α,β ) β k ( α k +Δα, β k +Δβ )=sin ϕ k ( α α k Δα )+cos ϕ k ( β β k Δβ ) = β ( αΔα,βΔβ ) β k ( α k , β k ),
α ( α,β ) α k ( α k +Δα, β k +Δβ ) α ( αΔα,βΔβ ) α k ( α k , β k ) =cos θ k cos ϕ k ( αΔα α k )+cos θ k sin ϕ k ( βΔβ β k ).
A L ( α ( α,β ) α k ( α k +Δα, β k +Δβ ), β ( α,β ) β k ( α k +Δα, β k +Δβ ) ) A L ( α ( αΔα,βΔβ ) α k ( α k , β k ), β ( αΔα,βΔβ ) β k ( α k , β k ) ).
exp( j2π( [ ( 1/λ ) 2 α 2 β 2 ( 1/λ ) 2 ( α k +Δα ) 2 ( β k +Δβ ) 2 ] z k ) ) exp( j2πλ( α k Δα+ β k Δβ ) ) ×exp( j2π( [ ( 1/λ ) 2 ( αΔα ) 2 ( βΔβ ) 2 ( 1/λ ) 2 α k 2 β k 2 ] z k ) ) ×exp( j2π( Δx( αΔα )+Δy( βΔβ ) ) ),
A ¯ G,k (α,β)=c A G,k (αΔα,βΔβ)×exp( j2π( Δx( αΔα )+Δy( βΔβ ) ) ),
Δx=[ ( x k x v )/( z v z k )( x k x v )/( z v z k ) ] z k ,
Δy=[ ( y k y v )/( z v z k )( y k y v )/( z v z k ) ] z k .

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