Abstract

It takes an enormous amount of time to calculate a computer-generated hologram (CGH). A fast calculation method for a CGH using precalculated object light has been proposed in which the light waves of an arbitrary object are calculated using transform calculations of the precalculated object light. However, this method requires a huge amount of memory. This paper proposes the use of a method that uses a cylindrical basic object light to reduce the memory requirement. Furthermore, it is accelerated by using a graphics processing unit (GPU). Experimental results show that the calculation speed on a GPU is about 65 times faster than that on a CPU.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  6. H. Sakata and Y. Sakamoto, “Fast computation method for Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48, H212–H221 (2009).
    [CrossRef] [PubMed]
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  11. http://www.nvidia.com/.
  12. http://developer.nvidia.com/category/zone/cuda-zone.

2010 (1)

2009 (4)

2008 (1)

2006 (1)

2003 (1)

2002 (1)

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. Part 2 85, 16–24 (2002).
[CrossRef]

Ahrenberg, L.

Benzie, P.

Chen, R. H.-Y.

Chong, T.-C.

Ichihashi, Y.

Ito, T.

Kim, E.

Kim, S.

Kitayama, R.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Liang, X.

Magnor, M.

Masuda, N.

Matsushima, K.

Nagao, T.

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. Part 2 85, 16–24 (2002).
[CrossRef]

Pan, Y.

Sakamoto, Y.

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

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. Part 2 85, 16–24 (2002).
[CrossRef]

Sakata, H.

Schimmel, H.

Shimobaba, T.

Shiraki, A.

Solanki, S.

Sugie, T.

Takada, N.

Tan, C.

Tanaka, T.

Tanjung, R. B. A.

Waston, J.

Wilkinson, T. D.

Wyrowski, F.

Xu, X.

Yamaguchi, T.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Yoshikawa, H.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Appl. Opt. (4)

Electron. Commun. Jpn. Part 2 (1)

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn. Part 2 85, 16–24 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (3)

Other (3)

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

http://www.nvidia.com/.

http://developer.nvidia.com/category/zone/cuda-zone.

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Figures (11)

Fig. 1
Fig. 1

Fresnel–Kirchhoff diffraction theory.

Fig. 2
Fig. 2

Plane basic object light.

Fig. 3
Fig. 3

Transform of triangle by 3D affine transformation.

Fig. 4
Fig. 4

Cylindrical basic object light.

Fig. 5
Fig. 5

GPU structure.

Fig. 6
Fig. 6

Data flow on GPU board.

Fig. 7
Fig. 7

Division of cylindrical basic object light.

Fig. 8
Fig. 8

Setup.

Fig. 9
Fig. 9

Reconstructed images.

Fig. 10
Fig. 10

Images of combined transform.

Fig. 11
Fig. 11

Time increase against number of polygons.

Tables (2)

Tables Icon

Table 1 Parameter Settings for Experiments

Tables Icon

Table 2 Computation Times for Evaluated Methods

Equations (25)

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u h ( x h , y h , z 0 ) = j λ t ( x ^ , y ^ , 0 ) exp ( j k r ) r d x ^ d y ^ ,
r = [ ( x h x ^ ) 2 + ( y h x ^ ) 2 + z 0 2 ] 1 / 2 ,
u h ( x h , y h , z 0 ) = j λ z 0 exp ( j k z 0 ) t ( x ^ , y ^ , 0 ) × exp { j k z 0 [ ( x h x ^ ) 2 + ( y h y ^ ) 2 ] } d x ^ d y ^ .
u h i = T i [ u b ] ,
u h   all = i = 1 P u h i .
I = | u h   all + R | 2 .
u b c ( α , y b ) = j λ z 0 cos α exp { j k ( z 0 cos α + R 2 sin α 2 + y b 2 2 z 0 cos α ) } × g ( x ^ , y ^ , 0 ) exp ( j k u z 0 sin α + v y b z 0 cos α ) d x ^ d y ^ ,
α = tan 1 ( x h z 0 ) ,
u h ( x h , y h , z 0 ) = j λ z 0 exp ( j k z 0 ) g ( x ^ , y ^ , 0 ) × exp { j k z 0 [ ( x h x ^ ) 2 + ( y h y ^ ) 2 ] } d x ^ d y ^ = C exp ( j k L ) u b c ( α , y h cos α ) ,
u h ( x h , y h , z 0 ) = j λ z 0 exp ( j k z 0 ) g ( x ^ , y ^ , 0 ) × exp { j k z 0 [ ( x h x ^ ) 2 + ( y h y ^ ) 2 ] } d x ^ d y ^ = C 1 exp ( j k L 1 ) u b c ( α , y h cos α ) ,
C 1 = 1 , α = tan 1 ( x h z 0 ) , x h = x h cos θ + y h sin θ Δ x , y h = y h cos θ + x h sin θ Δ y , L 1 = ( x h 2 + y h 2 + z 0 2 ) 1 / 2 [ ( z 0 sin α ) 2 + ( y h cos α ) 2 + ( z 0 cos α ) 2 ] 1 / 2 .
u h ( x h , y h , z 0 + Δ z ) = j λ ( z 0 + Δ z ) exp ( j k ( z 0 + Δ z ) ) g ( x ^ , y ^ , 0 ) × exp { j k z 0 + Δ z [ ( x h x ^ ) 2 + ( y h y ^ ) 2 ] } d x ^ d y ^ = C 2 exp ( j k L 2 ) u b c ( α , y h z 0 cos α z 0 + Δ z ) ,
C 2 = z 0 z 0 + Δ z , α = tan 1 ( x h z 0 + Δ z ) , L 2 = [ x h 2 + y h 2 + ( z 0 + Δ z ) 2 ] 1 / 2 [ ( z 0 sin α ) 2 + ( y h z 0 cos α z 0 + Δ z ) 2 + ( z 0 cos α ) 2 ] 1 / 2 .
u h ( x h , y h , z 0 ) = C 3 exp ( j k L 3 ) u b c ( α ϕ , y h cos ( α ϕ ) ) ,
C 3 = 1 , α = tan 1 ( x h z 0 ) , L 3 = ( x h 2 + y h 2 + z 0 2 ) 1 / 2 [ ( z 0 sin α ) 2 + ( y h cos α ) 2 + ( z 0 cos α ) 2 ] 1 / 2 .
g scale ( x ^ , y ^ , 0 ) = g ( x ^ R x , y ^ R y , 0 ) .
u h ( x h , y h , z 0 ) = j λ z 0 exp ( j k z 0 ) g scale ( x ^ , y ^ , 0 ) exp { j k z 0 [ ( x h x ^ ) 2 + ( y h y ^ ) 2 ] } d x ^ d y ^ = C 4 exp ( j k L 4 ) u b c ( α , y h cos α ) ,
C 4 = R x R y , α = tan 1 ( x h z 0 ) , x h = R x x h , y h = R y y h , L 4 = ( x h 2 + y h 2 + z 0 2 ) 1 / 2 [ ( z 0 sin α ) 2 + ( y h cos α ) 2 + ( z 0 cos α ) 2 ] 1 / 2 .
g skew ( x ^ , y ^ , 0 ) = g ( y ^ S x + x ^ , y ^ , 0 ) .
u h ( x h , y h , z 0 ) = j λ z 0 exp ( j k z 0 ) g skew ( x ^ , y ^ , 0 ) exp { j k z 0 [ ( x h x ^ ) 2 + ( y h y ^ ) 2 ] } d x ^ d y ^ = C 5 exp ( j k L 5 ) u b c ( α , y h cos α ) ,
C 5 = 1 , α = tan 1 ( x h z 0 ) , x h = x h , y h = y h + S x x h , L 5 = ( x h 2 + y h 2 + z 0 2 ) 1 / 2 [ ( z 0 sin α ) 2 + ( y h cos α ) 2 + ( z 0 cos α ) 2 ] 1 / 2 .
ϕ max = tan 1 n Δ d z 0 tan 1 n Δ d 2 z 0 ,
π 2 ϕ max .
2 n 2 π ϕ max .
2 π z 0 Δ d n .

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