Abstract

We propose a fast method for generating digital Fresnel holograms based on an interpolated wavefront-recording plane (IWRP) approach. Our method can be divided into two stages. First, a small, virtual IWRP is derived in a computational-free manner. Second, the IWRP is expanded into a Fresnel hologram with a pair of fast Fourier transform processes, which are realized with the graphic processing unit (GPU). We demonstrate state-of-the-art experimental results, capable of generating a 2048x2048 Fresnel hologram of around 4×106object points at a rate of over 40 frames per second.

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References

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  1. T.-C. Poon, ed., “Digital holography and three-dimensional display: Principles and Applications,” Springer (2006).
  2. 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(6), 1030–1041 (2009).
    [CrossRef]
  3. 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(19), D55–D62 (2008).
    [CrossRef] [PubMed]
  4. 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(32), 5986–5995 (2008).
    [CrossRef] [PubMed]
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  6. T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007).
    [CrossRef]
  7. H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
    [CrossRef]
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  11. Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” Laser App. Chem., Sec. and Env. Ana., OSA Tech. Digest (CD) (OSA, 2008), paper JMA9.
  12. P. W. M. Tsang, J.-P. Liu, W. K. Cheung, and T.-C. Poon, “Fast generation of Fresnel holograms based on multirate filtering,” Appl. Opt. 48(34), H23–H30 (2009).
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  13. 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).
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2010 (1)

2009 (4)

2008 (2)

2007 (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007).
[CrossRef]

2006 (1)

2005 (1)

2001 (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
[CrossRef]

Ahrenberg, L.

Benzie, P.

Cheung, W. K.

Ito, T.

Kang, H.

Kim, E. S.

Kim, E.-S.

Kim, S. C.

Kim, S.-C.

Liu, J.-P.

Magnor, M.

Masuda, N.

Nakayama, H.

Okabe, G.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007).
[CrossRef]

Onural, L.

Poon, T.-C.

Sakamoto, Y.

Sakata, H.

Shimobaba, T.

Shiraki, A.

Sugie, T.

Tsang, P. W. M.

Watson, J.

Yamaguchi, T.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007).
[CrossRef]

Yaras, F.

Yoon, J.-H.

Yoshikawa, H.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007).
[CrossRef]

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
[CrossRef]

Yoshimura, K.

Appl. Opt. (6)

Opt. Eng. (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007).
[CrossRef]

Opt. Express (3)

Opt. Rev. (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).
[CrossRef]

Other (2)

Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” Laser App. Chem., Sec. and Env. Ana., OSA Tech. Digest (CD) (OSA, 2008), paper JMA9.

T.-C. Poon, ed., “Digital holography and three-dimensional display: Principles and Applications,” Springer (2006).

Supplementary Material (1)

» Media 1: AVI (1173 KB)     

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Figures (2)

Fig. 1
Fig. 1

a. Sampling lattice and square support Fig. 1b. A pair of sample points, each associate with a square support and a virtual window on the scene image and the WRP, respectively. Note that the depth (i.e., z position) of the object points are not shown in the diagram.

Fig. 2
Fig. 2

a. An image divided (dotted line) into a left and right parts, positioned at z1 = 0.005m (left) and z2 = 0.01m (right) from the IWRP, respectively. The IWRP is positioned at zw = 0.4m from the hologram.Fig. 2b. Optical reconstructed image of the upper part of the hologram corresponding to the WRP derived from Eqs. (5) and 6. Fig. 2c. Optical reconstructed image of the lower part of the hologram corresponding to the WRP derived from Eqs. (5) and 6. Fig. 2d. Optical reconstructed image of the upper part of the hologram corresponding to the proposed IWRP derived from Eqs. (7) and 8. Fig. 2e. Optical reconstructed image of the lower part of the hologram corresponding to the proposed IWRP derived from Eqs. (7) and 8. Fig. 2f. Single-frame excerpts from the optical reconstructed animation clip of the hologram sequence representing a rotating earth globe located at 0.3m from the hologram. The hologram sequence is generated from the IWRP derived from Eqs. (7) and (8) (Media 1).

Tables (1)

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Table 1 Computation Time and Equivalent Frame Rate in Generating the IWRP, and Expanding the Latter to a Fresnel Hologram

Equations (9)

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D ( x , y ) = j = 0 N 1 a j r j exp ( i k r j ) = j = 0 N 1 [ a j r j cos ( k r j ) + i a j r j sin ( k r j ) ] ,
u w ( x , y ) = j = 0 N 1 ( A j / R w j ( x x j , y y j ) ) exp ( i 2 π λ R w j ( x x j , y y j ) ) ,
u w ( x , y ) = j = 0 N 1 f j ,
u ( x , y ) = K F 1 [ F [ u w ( x , y ) ] F [ h ( x , y ) ] ] ,
u w ( x , y ) | l m x < r m , b n y < t n = I ( m , n ) exp ( i 2 π R d ( m , n ) ( x x m , y y n ) / λ ) ,
u w ( x , y ) = I ( m , n ) exp ( i 2 π R d ( m , n ) ( x x m , y y n ) / λ ) = G ( x x m , y y n , I ( m , n ) , d ( m , n ) )
u w ( x , y ) | l m x < r m , t n y < b n = I ( m , n ) τ x = M 2 M 2 1 τ y = M 2 M 2 1 exp ( i 2 π R d ( m , n ) ( x x m + τ x p , y y n + τ y p ) / λ )
= G A ( x x m , y y n , I ( m , n ) , d ( m , n ) )
H ( x , y ) = R E [ u ( x , y ) R ( y ) ] ,

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