Abstract

A fast algorithm with low memory usage is proposed to generate the hologram for full-color 3D display based on a compressed look-up table (C-LUT). The C-LUT is described and built to reduce the memory usage and speed up the calculation of the computer-generated hologram (CGH). Numerical simulations and optical experiments are performed to confirm this method, and several other algorithms are compared. The results show that the memory usage of the C-LUT is kept low when number of depth layers of the 3D object is increased, and the time for building the C-LUT is independent of the number of depth layers of the 3D object. The algorithm based on C-LUT is an efficient method for saving memory usage and calculation time, and it is expected that it could be used for realizing real-time and full-color 3D holographic display in the future.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (5)

2010 (3)

2009 (5)

2008 (3)

2007 (1)

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[CrossRef]

2006 (1)

2000 (1)

1993 (1)

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

1992 (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Awazu, S.

Chen, B. C.

Cheung, W. K.

Chong, T. C.

Dong, J. W.

Fujii, T.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[CrossRef]

He, H. X.

Ichihashi, Y.

Ito, T.

Jia, J.

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011).
[CrossRef]

Kang, H.

Kim, E. S.

Kim, J. H.

Kim, S. C.

Leigh, J. J. S.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Li, X.

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011).
[CrossRef]

Liang, X.

Liu, J.

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011).
[CrossRef]

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009).
[CrossRef]

Liu, Y. Z.

Lucente, M.

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

Masuda, N.

Matsushima, K.

Nakayama, H.

Niwa, M.

Oikawa, M.

M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an approximate Fresnel integral,” J. Opt. 13, 075405 (2011).
[CrossRef]

Onural, L.

Pan, Y.

Poon, T. C.

Pu, Y. Y.

Shimobaba, T.

Shiraki, A.

Solanki, S.

Stein, A. D.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Sugie, T.

Takada, N.

Takai, M.

Tan, C.

Tanaka, T.

Tanjung, R. B.

Tsang, P.

Wang, H. Z.

Wang, Y.

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011).
[CrossRef]

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009).
[CrossRef]

Wang, Z.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Xie, J.

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011).
[CrossRef]

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009).
[CrossRef]

Xu, X.

Yamaguchi, T.

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

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[CrossRef]

Yaras, F.

Yoon, J. H.

Yoshikawa, A. H.

Yoshikawa, H.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[CrossRef]

Yu, Y.

Zhang, H.

Zheng, H.

Zhou, C.

Appl. Opt. (9)

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

S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008).
[CrossRef]

S. C. Kim, J. H. Yoon, and E. S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986–5995 (2008).
[CrossRef]

S. C. Kim and E. S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48, 1030–1041 (2009).
[CrossRef]

K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000).
[CrossRef]

F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic video display system using LED illumination,” Appl. Opt. 48, H48–H53 (2009).
[CrossRef]

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009).
[CrossRef]

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, 5993–5996 (2010).
[CrossRef]

S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50, 3375–3382 (2011).
[CrossRef]

Comput. Phys. (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

J. Electron. Imaging (1)

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

J. Opt. (1)

M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an approximate Fresnel integral,” J. Opt. 13, 075405 (2011).
[CrossRef]

Opt. Eng. (2)

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011).
[CrossRef]

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Supplementary Material (1)

» Media 1: MOV (1490 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Diagram of CGH for recording 3D object.

Fig. 2.
Fig. 2.

Model of 3D object: (a) set of sliced 2D image planes with different depths and (b) points falling on different sliced 2D image planes.

Fig. 3.
Fig. 3.

Diagram of the proposed method to generate the CGH using C-LUT.

Fig. 4.
Fig. 4.

Setup of full-color holographic display system.

Fig. 5.
Fig. 5.

Comparisons of the off-line calculation time for building an LUT among the LUT, the S-LUT, and the new algorithm (C-LUT).

Fig. 6.
Fig. 6.

Comparison of the in-line computational time among different algorithms.

Fig. 7.
Fig. 7.

Numerical reconstructed image: (a) original image, (b) distortion image in z j = 10 mm , (c) distortion image in z j = 20 mm , and (d) image without distortion.

Fig. 8.
Fig. 8.

Reconstructed 3D image: (a) perspective image of 3D object, (b) numerical simulation results of focusing on the teapot reconstructed in 1010 mm, (c) focusing on the cup reconstructed in 980 mm, (d) optical experimental results of focusing on the teapot reconstructed in 1010 mm, and (e) focusing on the cup reconstructed in 980 mm.

Fig. 9.
Fig. 9.

Reconstructed colorful 3D images. (a) Perspective object and (b) reconstructed image (Media 1).

Tables (5)

Tables Icon

Table 1. Pseudo Code of Off-Line Computational Program

Tables Icon

Table 2. Pseudo Code of In-Line Computational Program

Tables Icon

Table 3. Complexity, Operation, and Memory Usage Comparison Among Algorithms

Tables Icon

Table 4. CGH and Table Parameters

Tables Icon

Table 5. Memory Usage Comparition Among Algorithms

Equations (14)

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H ( x p , y q ) = j = 0 N 1 A j exp [ i ( k r j + ϕ j ) ] ,
r j = ( x p x j ) 2 + ( y q y j ) 2 + ( d z j ) 2
V s ( y q ) = j = 0 N y 1 A j V ( y q y j , z j ) ,
H N y ( x p , y q ) = V s ( y q ) × H ( x p x j , z j ) .
H FH ( x p , y q ) = j = 0 N 1 A j exp [ i k ( x p 2 + y q 2 2 ( d z j ) x p x j + y q y j d z j ) ] ,
H FH ( x p , y q ) = j = 0 N 1 A j exp [ i k x p 2 + y q 2 2 ( d z j ) ] × exp ( i k x p x j + y q y j d ) = j = 0 N 1 A j exp [ i k x p 2 + y q 2 2 ( d z j ) ] × exp ( i k x p x j d ) exp ( i k y q y j d ) ,
H FH ( x p , y q ) = j = 0 N 1 A j H ( x p , x j ) V ( y q , y j ) L ( z , z j ) .
H FH ( x p , y q ) = j z = 0 N z 1 [ j x y = 0 N x y 1 A j x y H ( x p , x j x y ) V ( y q , y j x y ) ] × L ( z , z j z ) ,
H FH ( x p , y q ) = j z = 0 N z 1 { j x = 0 N x 1 [ j y = 0 N y 1 A j y V ( y q , y j y ) ] × H ( x p , x j x ) } L ( z , z j z ) ,
ε H = φ H φ H = k ( x p x j d x p x j d z j ) = k ( z j d ( d z j ) x p x j ) ε V = φ V φ V = k ( y q y j d y q y j d z j ) = k ( z j d ( d z j ) y q y j ) } ,
δ x j = x j x j = d z j d x j x j = z j d x j δ y j = y j y j = d z j d y j y j = z j d y j } ,
Δ φ H = Δ φ V = d d z j .
H ( x p ) Δ φ H = [ exp ( i k x p x j d ) ] d d z j = exp ( i k x p x j d × d d z j ) = exp ( i k x p x j d z j ) ,
Δ φ λ = φ λ φ λ = k r k r = ( λ λ λ λ ) 2 π r δ x j = x j x j = λ λ x j x j = ( λ λ 1 ) x j δ y j = y j y j = λ λ y j y j = ( λ λ 1 ) y j δ z j = z j z j = λ λ z j z j = ( λ λ 1 ) z j } ,

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