Abstract

Precalculation methods for computer-generated holograms provide fast calculation by transforming precalculated object light in accordance with the subject shape in the spatial domain. In this paper, a novel method is proposed that uses precalculated object light recorded on a spherical surface, which makes the data size half that of the conventional method. Moreover, representations of the transforms by homogeneous coordinates on the spherical surface are discussed. These representations allow common operations of transforms and solve the calculation complexity that conventional precalculation methods have. The effectiveness of the proposed method was confirmed by optical image-reconstruction experiments successfully.

© 2012 Optical Society of America

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References

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  1. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A 20, 1755–1762 (2003).
    [CrossRef]
  2. M. Lucente, “Interactive computation of hologram using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
    [CrossRef]
  3. S. Kim and E. 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]
  4. Y. Pan, X. Xu, S. Solanki, X. Liang, R. Tanjung, C. Tan, and T. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009).
    [CrossRef]
  5. S. Kim, J. Yoon, and E. 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]
  6. S. Kim and E. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008).
    [CrossRef]
  7. M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” Proc. ACM SIGGRAPH 95, 387–394 (1995).
    [CrossRef]
  8. Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. 85, 16–24 (2002).
    [CrossRef]
  9. H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48, H212–H221 (2009).
    [CrossRef]
  10. H. Sakata and Y. Sakamoto, “Pre-calculated object light-based fast calculation method for computer-generated hologram,” Proc. SPIE 7619, 76190Y (2010).
    [CrossRef]
  11. H. Sakata, K. Hosoyachi, C. Yang, and Y. Sakamoto, “Calculation method for computer-generated holograms with cylindrical basic object light by using a graphics processing unit,” Appl. Opt. 50, H306–H314 (2011).
    [CrossRef]
  12. NVIDIA Corporation, “CUDA programming guide 3.2” (2010).
  13. NVIDIA Corporation, “CUDA CUFFT Library” (2010).

2011

2010

H. Sakata and Y. Sakamoto, “Pre-calculated object light-based fast calculation method for computer-generated hologram,” Proc. SPIE 7619, 76190Y (2010).
[CrossRef]

2009

2008

2003

2002

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. 85, 16–24 (2002).
[CrossRef]

1995

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” Proc. ACM SIGGRAPH 95, 387–394 (1995).
[CrossRef]

1993

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

Chong, T.

Galyean, T. A.

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” Proc. ACM SIGGRAPH 95, 387–394 (1995).
[CrossRef]

Hosoyachi, K.

Kim, E.

Kim, S.

Liang, X.

Lucente, M.

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” Proc. ACM SIGGRAPH 95, 387–394 (1995).
[CrossRef]

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

Matsushima, K.

Nagao, T.

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. 85, 16–24 (2002).
[CrossRef]

Pan, Y.

Sakamoto, Y.

H. Sakata, K. Hosoyachi, C. Yang, and Y. Sakamoto, “Calculation method for computer-generated holograms with cylindrical basic object light by using a graphics processing unit,” Appl. Opt. 50, H306–H314 (2011).
[CrossRef]

H. Sakata and Y. Sakamoto, “Pre-calculated object light-based fast calculation method for computer-generated hologram,” Proc. SPIE 7619, 76190Y (2010).
[CrossRef]

H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48, H212–H221 (2009).
[CrossRef]

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. 85, 16–24 (2002).
[CrossRef]

Sakata, H.

Schimmel, H.

Solanki, S.

Tan, C.

Tanjung, R.

Wyrowski, F.

Xu, X.

Yang, C.

Yoon, J.

Appl. Opt.

Electron. Commun. Jpn.

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. 85, 16–24 (2002).
[CrossRef]

J. Electron. Imaging

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

J. Opt. Soc. Am. A

Opt. Express

Proc. ACM SIGGRAPH

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” Proc. ACM SIGGRAPH 95, 387–394 (1995).
[CrossRef]

Proc. SPIE

H. Sakata and Y. Sakamoto, “Pre-calculated object light-based fast calculation method for computer-generated hologram,” Proc. SPIE 7619, 76190Y (2010).
[CrossRef]

Other

NVIDIA Corporation, “CUDA programming guide 3.2” (2010).

NVIDIA Corporation, “CUDA CUFFT Library” (2010).

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Figures (17)

Fig. 1.
Fig. 1.

Polygon model.

Fig. 2.
Fig. 2.

Five types of transforms.

Fig. 3.
Fig. 3.

Overview of basic object light method.

Fig. 4.
Fig. 4.

Plane and cylindrical basic object lights.

Fig. 5.
Fig. 5.

SBOL.

Fig. 6.
Fig. 6.

Structure of Fermi GPU.

Fig. 7.
Fig. 7.

Dividing spherical basic object light.

Fig. 8.
Fig. 8.

Parallel computation on GPU.

Fig. 9.
Fig. 9.

Setup and reconstructed images of “stars”: (a) illustrated arrangement of the “stars,” (b) focused at 15 cm, and (c) focused at 20 cm.

Fig. 10.
Fig. 10.

Tilted polygons. Parameters for tilt transform were Δ ϕ = 0 ° , Δ ψ = 0 ° in (a), Δ ϕ = 45 ° , Δ ψ = 0 ° in (b), Δ ϕ = 0 ° , Δ ψ = 45 ° in (c), and Δ ϕ = 45 ° , Δ ψ = 45 ° in (d).

Fig. 11.
Fig. 11.

Results of tilt transform. Parameters for tilt transform were Δ ϕ = 0 ° , Δ ψ = 0 ° in (a), Δ ϕ = 45 ° , Δ ψ = 0 ° in (b), Δ ϕ = 0 ° , Δ ψ = 45 ° in (c), and Δ ϕ = 45 ° , Δ ψ = 45 ° in (d).

Fig. 12.
Fig. 12.

Scaled polygons. Parameters for scaling transform were R x = 0.8 , R y = 1.0 in (a), R x = 1.0 , R y = 1.0 in (b), and R x = 1.2 , R y = 1.0 in (c).

Fig. 13.
Fig. 13.

Results of scaling transform. Parameters for scaling transform were R x = 0.8 , R y = 1.0 in (a), R x = 1.0 , R y = 1.0 in (b), and R x = 1.2 , R y = 1.0 in (c).

Fig. 14.
Fig. 14.

Skewed polygons. Parameters for skew transform were S x = 0.0 in (a), S x = 0.4 in (b), and S x = 0.8 in (c).

Fig. 15.
Fig. 15.

Results of skew transform. Parameters for skew transform were S x = 0.0 in (a), S x = 0.4 in (b), and S x = 0.8 in (c).

Fig. 16.
Fig. 16.

Setup and reconstructed image of “Venus” (a) shows the setup and (b) is the reconstructed image.

Fig. 17.
Fig. 17.

Computation times of object lights with SBOL on the CPU and GPU and Fresnel diffraction on the GPU according to the number of polygons.

Tables (4)

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Table 1. Parameters of the Hologram

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Table 2. Basic Object Light

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Table 3. Computation Times of an Object Light for a Polygon with Fresnel Diffraction and SBOL on the CPU and GPU

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Table 4. Computation Times of an Object Light for a Polygon with Fresnel Diffraction and SBOL on the GPU According to the Number of Pixels on the Hologram (Units are in Microseconds)

Equations (15)

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u b s ( ϕ , ψ ) = j λ R exp ( j k R ) g ( x , y ) × exp ( j k u cos ψ sin ϕ + v sin ψ 2 cos ψ sin ϕ ) d x d y ,
u h ( ξ , η ) = j λ t ( x ^ , y ^ ) exp ( j k r ) r d x ^ d y ^ ,
r = [ ( ξ x ^ ) 2 + ( η y ^ ) 2 + R 2 ] 1 / 2 .
u h ( ξ , η ) = C exp ( j k ( l R ) ) u b s ( ϕ , ψ ) , ϕ = tan 1 y ( x 2 + z 2 ) 1 / 2 , ψ = tan 1 x z , l = ( x l 2 + y l 2 + z l 2 ) , [ x y z 1 ] = T [ ξ η R 1 ] , T = [ t 00 t 01 t 02 t 03 t 10 t 11 t 12 t 13 t 20 t 21 t 22 t 23 0 0 0 1 ] , [ x l y l z l 1 ] = L [ ξ η R 1 ] , L = [ l 00 l 01 l 02 l 03 l 10 l 11 l 12 l 13 l 20 l 21 l 22 l 23 0 0 0 1 ] .
C = C 1 C 2 C 3 C 4 C 5 C 6 , T = T 1 T 2 T 3 T 4 T 5 T 6 , L = L 1 L 2 L 3 L 4 L 5 L 6 .
C 1 = 1 , T 1 = [ cos Δ θ sin Δ θ 0 Δ x sin Δ θ cos Δ θ 0 Δ y 0 0 1 0 0 0 0 1 ] , L 1 = [ cos Δ θ sin Δ θ 0 Δ x sin Δ θ cos Δ θ 0 Δ y 0 0 1 0 0 0 0 1 ] ,
C 2 = R R + Δ z , T 2 = [ 1 0 0 0 0 1 0 0 0 0 1 Δ z 0 0 0 1 ] , L 2 = [ 1 0 0 0 0 1 0 0 0 0 1 Δ z 0 0 0 1 ] ,
C 3 = 1 , T 3 = [ 1 0 0 0 0 cos Δ ψ sin Δ ψ 0 0 sin Δ ψ cos Δ ψ 0 0 0 0 1 ] , L 3 = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] .
C 4 = 1 , T 4 = [ cos Δ ϕ 0 sin Δ ϕ 0 0 1 0 0 sin Δ ϕ 0 cos Δ ϕ 0 0 0 0 1 ] , L 4 = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ,
C 5 = R x R y , T 5 = [ R x 0 0 0 0 R y 0 0 0 0 1 0 0 0 0 1 ] , L 5 = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ,
C 6 = 1 , T 6 = [ 1 0 0 0 S x 1 0 0 0 0 1 0 0 0 0 1 ] , L 6 = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ,
2 π R 2 Δ d 2 .
π 2 R n Δ d ϕ max ,
ϕ max = tan 1 n Δ d R tan 1 n Δ d 2 R ,
π 2 R 2 Δ d 2 .

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