Abstract

Computer-Generated Holograms (CGHs) can be generated by superimposing zoneplates. A zoneplate is a grating that can concentrate an incident light into a point. Since a zoneplate has a circular symmetry, we reported an algorithm that rapidly generates a zoneplate by drawing concentric circles using computer graphic techniques. However, random memory access was required in the algorithm and resulted in degradation of the computational efficiency. In this study, we propose a fast CGH generation algorithm without random memory access using run-length encoding (RLE) based recurrence relation. As a result, we succeeded in improving the calculation time by 88 %, compared with that of the previous work.

© 2015 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. N. Takada, T. Shimobaba, H. Nakayama, A. Shiraki, N. Okada, M. Oikawa, N. Masuda, and T. Ito, “Fast high-resolution computer-generated hologram computation using multiple graphics processing unit cluster system,” Appl. Opt. 51, 7303–7307 (2012).
    [Crossref] [PubMed]
  3. H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, and T. Ito, “Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features,” Opt. Express 22, pp.28052–28057 (2014).
    [Crossref] [PubMed]
  4. 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]
  5. 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] [PubMed]
  6. 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]
  7. T. Nishitsuji, T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Fast calculation of computer-generated hologram using the circular symmetry of zone plates,” Opt. Express 20, 27496–27502 (2012).
    [Crossref] [PubMed]
  8. L. Mertz and N. O. Young, “Fresnel Transformation of Images,” in Proceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, ed. (Chapman & Hall, London), 305–310 (1961).
  9. S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).
  10. 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]
  11. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

2014 (1)

2012 (4)

2009 (1)

2008 (1)

1993 (1)

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

Araki, H.

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 Optics (Roberts & Company, 2004).

Ito, T.

Kakue, T.

Kim, C. Y.

S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).

Kim, E.-S.

Kim, J.-M.

Kim, S.-C.

Lee, S.

S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).

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.

Mertz, L.

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

Nakayama, H.

Nam, D. K.

S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).

Nishitsuji, T.

Niwase, H.

Oikawa, M.

Okada, N.

Park, D. S.

S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).

Shimobaba, T.

Shiraki, A.

Sugiyama, A.

Takada, N.

Wey, H. C.

S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).

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]

Young, N. O.

L. Mertz and N. O. Young, “Fresnel Transformation of Images,” in Proceedings, 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, 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. (3)

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 (3)

Other (3)

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

S. Lee, H. C. Wey, D. K. Nam, D. S. Park, and C. Y. Kim, “Fast hologram pattern generation by radial symmetric interpolation,” Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980O (2012).

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

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Figures (4)

Fig. 1
Fig. 1 Outline of proposed method.
Fig. 2
Fig. 2 Calculation of the length of groups.
Fig. 3
Fig. 3 Discretization error compensation.
Fig. 4
Fig. 4 Reconstructed images (numerical simulation): (a)(d) Direct calculation of Eq. (1); (b)(e) Our previous method; (c)(f) Proposed method with error compensation.

Tables (1)

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Table 1 Calculation times

Equations (16)

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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 u j ( θ j ( x α j , y α j ) ) ] ,
l n = f l o o r ( b n ) c e i l ( a n ) + 1 ,
a n = { Y 2 + ( Y + n 0.5 ) 2 } 1 2 ,
b n = { Y 2 + ( Y + n + 0.5 ) 2 } 1 2 .
b n 2 = a n 2 + 2 ( Y + n ) ,
= a n 2 + d n ,
b n = ( a n 2 + d n ) 1 2 ,
d n = 2 ( Y + n ) ,
a 0 = 0 ,
b 0 = ( Y + 0.25 ) 1 2 .
a n + 1 = b n ,
d n + 1 = d n + 2.
R e [ I ( θ o + θ ε ) ] = cos θ o θ ε sin θ o ,
I m [ I ( θ o + θ ε ) ] = sin θ o + θ ε cos θ o .
θ ε ( x + 1 , r ) θ ε ( x , r ) = k p z j ( 2 x + 1 ) ,
θ ε ( x , r + 1 ) θ ε ( x , r ) = k p z j ( 2 r + 1 ) .

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