Abstract

Computer-Generated Holograms (CGHs) can be generated from three-dimensional objects composed of point light sources by overlapping zone plates. A zone plate is a grating that can focus an incident wave and it has circular symmetry shape. In this study, we propose a fast CGH generating algorithm using the circular symmetry of zone plates and computer graphics techniques. We evaluated the proposed method by numerical simulation.

© 2012 Optical Society of America

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References

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  1. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
    [Crossref]
  2. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000).
    [Crossref]
  3. T. Shimobaba and T. Ito, “An efficient computational method suitable for hardware of computer-generated hologram with phase computation by addition,” Comput. Phys. Commun. 138, 44–52 (2001).
    [Crossref]
  4. H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8, 331–335 (2001).
    [Crossref]
  5. Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “HORN-6 special-purpose clustered computing system for electroholography,” Opt. Express 17, 13895–13902 (2009).
    [Crossref] [PubMed]
  6. 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. Express 18, 9955–9960 (2010).
    [Crossref] [PubMed]
  7. 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] [PubMed]
  8. S. -C. Kim, J. -M. Kim, and E. -S. Kim, “Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe pattern in computer-generated holograms,” Opt. Express 20, 12021–12034 (2012).
    [Crossref] [PubMed]
  9. L. Mertz and N. O. Young, “Fresnel Transformation of Images,” in Preceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London), 305–310 (1961).
  10. J. Bresenham, “A linear algorithm for incremental digital display of circular arcs,” Commun. ACM 20, 100–106 (1977).
    [Crossref]
  11. E. Andres, “Discrete circles, rings and spheres,” Comput. Graphics 18, 695–706 (1994).
    [Crossref]
  12. Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
    [Crossref]
  13. J. W. Goodman, Introduction to Fourier OpticsRoberts & Company (2004).
  14. T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 20, 3133–3135 (2009).
    [Crossref]
  15. T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509 (2010).
    [Crossref] [PubMed]
  16. P. Tsang, W. -K. Cheung, T. -C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011).
    [Crossref] [PubMed]
  17. J. Weng, T. Shimobaba, N Okada, H. Nakayma, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
    [Crossref] [PubMed]
  18. P. W. M. Tsang, K. W. K Cheung, and T.-C. Poon, “Real-time relighting of digital holograms based on wavefront recording plane method,” Opt. Express 20, 5962–5967 (2012).
    [Crossref] [PubMed]

2012 (4)

2011 (1)

2010 (2)

2009 (2)

Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “HORN-6 special-purpose clustered computing system for electroholography,” Opt. Express 17, 13895–13902 (2009).
[Crossref] [PubMed]

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 20, 3133–3135 (2009).
[Crossref]

2008 (1)

2001 (2)

T. Shimobaba and T. Ito, “An efficient computational method suitable for hardware of computer-generated hologram with phase computation by addition,” Comput. Phys. Commun. 138, 44–52 (2001).
[Crossref]

H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8, 331–335 (2001).
[Crossref]

2000 (1)

1994 (1)

E. Andres, “Discrete circles, rings and spheres,” Comput. Graphics 18, 695–706 (1994).
[Crossref]

1993 (1)

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

1977 (1)

J. Bresenham, “A linear algorithm for incremental digital display of circular arcs,” Commun. ACM 20, 100–106 (1977).
[Crossref]

Andres, E.

E. Andres, “Discrete circles, rings and spheres,” Comput. Graphics 18, 695–706 (1994).
[Crossref]

Bresenham, J.

J. Bresenham, “A linear algorithm for incremental digital display of circular arcs,” Commun. ACM 20, 100–106 (1977).
[Crossref]

Cheung, K. W. K

Cheung, W. -K.

Fan, Q.

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier OpticsRoberts & Company (2004).

Ichihashi, Y.

Ito, T.

Kim, E. -S.

Kim, J. -M.

Kim, S. -C.

Liu, J.

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

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.

Mertz, L.

L. Mertz and N. O. Young, “Fresnel Transformation of Images,” in Preceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London), 305–310 (1961).

Nakayama, H.

Nakayma, H.

Oikawa, M.

Okada, N

Poon, T. -C.

Poon, T.-C.

Shimobaba, T.

Shiraki, A.

Sugie, T.

Takada, N.

Takai, M.

Tsang, P.

Tsang, P. W. M.

Weng, J.

Yang, Z.

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

Yoshikawa, H.

H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8, 331–335 (2001).
[Crossref]

Young, N. O.

L. Mertz and N. O. Young, “Fresnel Transformation of Images,” in Preceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London), 305–310 (1961).

Zhang, Y.

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

Zhou, C.

Zhou, J.

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

Appl. Opt. (2)

Commun. ACM (1)

J. Bresenham, “A linear algorithm for incremental digital display of circular arcs,” Commun. ACM 20, 100–106 (1977).
[Crossref]

Comput. Graphics (1)

E. Andres, “Discrete circles, rings and spheres,” Comput. Graphics 18, 695–706 (1994).
[Crossref]

Comput. Phys. Commun. (1)

T. Shimobaba and T. Ito, “An efficient computational method suitable for hardware of computer-generated hologram with phase computation by addition,” Comput. Phys. Commun. 138, 44–52 (2001).
[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)

Z. Yang, Q. Fan, Y. Zhang, J. Liu, and J. Zhou, “A new method for producing computer generated holograms,” J. Opt. 14, 095702 (2012).
[Crossref]

Opt. Express (7)

Y. Ichihashi, H. Nakayama, T. Ito, N. Masuda, T. Shimobaba, A. Shiraki, and T. Sugie, “HORN-6 special-purpose clustered computing system for electroholography,” Opt. Express 17, 13895–13902 (2009).
[Crossref] [PubMed]

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. Express 18, 9955–9960 (2010).
[Crossref] [PubMed]

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509 (2010).
[Crossref] [PubMed]

P. Tsang, W. -K. Cheung, T. -C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011).
[Crossref] [PubMed]

J. Weng, T. Shimobaba, N Okada, H. Nakayma, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
[Crossref] [PubMed]

P. W. M. Tsang, K. W. K Cheung, and T.-C. Poon, “Real-time relighting of digital holograms based on wavefront recording plane method,” Opt. Express 20, 5962–5967 (2012).
[Crossref] [PubMed]

S. -C. Kim, J. -M. Kim, and E. -S. Kim, “Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe pattern in computer-generated holograms,” Opt. Express 20, 12021–12034 (2012).
[Crossref] [PubMed]

Opt. Lett. (1)

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 20, 3133–3135 (2009).
[Crossref]

Opt. Rev. (1)

H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8, 331–335 (2001).
[Crossref]

Other (2)

L. Mertz and N. O. Young, “Fresnel Transformation of Images,” in Preceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London), 305–310 (1961).

J. W. Goodman, Introduction to Fourier OpticsRoberts & Company (2004).

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Figures (5)

Fig. 1
Fig. 1 Outline of proposed method

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Fig. 2
Fig. 2 Arithmetical circle algorithm

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Fig. 3
Fig. 3 Discretization error

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Fig. 4
Fig. 4 Numerical analysis of zone plates

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Fig. 5
Fig. 5 Reconstructed images: (a) Direct calculation of Eq. (1) (b) Proposed method (c) WRP method combining the proposed method

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Tables (1)

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Table 1 Calculation times

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Equations (5)

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ϕ ( x α , y α ) = arg [ ∑ j = 0 N − 1 A j exp ( i k { x α j 2 + y α j 2 + z j 2 } 1 2 ) ] = arg [ ∑ j = 0 N − 1 I j ( θ j ( x α j , y α j ) ) ]
θ j ( x α j + n , y α j ) = θ j ( x α j + n − 1 , y α j ) + δ j ( x α j + n − 1 )
δ j ( x α j + n ) = δ j ( x α j + n − 1 ) + γ
Re [ I ( θ o + θ ɛ ) ] = cos θ o − θ ɛ sin θ o
Im [ I ( θ o + θ ɛ ) ] = sin θ o + θ ɛ cos θ o

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