Abstract

In computer-generated hologram (CGH) calculations, a diffraction pattern needs to be calculated from all points of a 3-D object, which requires a heavy computational cost. In this paper, we propose a novel fast computer-generated hologram calculation method using sparse fast Fourier transform. The proposed method consists of two steps. First, the sparse dominant signals of CGHs are measured by calculating a wavefront on a virtual plane between the object and the CGH plane. Second, the wavefront on CGH plane is calculated by using the measured sparsity with sparse Fresnel diffraction. Experimental results proved that the proposed method is much faster than existing works while it preserving the visual quality.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  1. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012).
    [Crossref] [PubMed]
  2. C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
    [Crossref]
  3. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
    [Crossref]
  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(19), 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(6), 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 patterns in computer-generated holograms,” Opt. Express 20(11), 12021–12034 (2012).
    [Crossref] [PubMed]
  7. T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
    [Crossref] [PubMed]
  8. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39(35), 6587–6594 (2000).
    [Crossref] [PubMed]
  9. H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
    [Crossref]
  10. T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
    [Crossref] [PubMed]
  11. A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
    [Crossref] [PubMed]
  12. D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
    [Crossref] [PubMed]
  13. T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A 10(2), 299–305 (1993).
    [Crossref]
  14. 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(9), 1755–1762 (2003).
    [Crossref] [PubMed]
  15. N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
    [Crossref] [PubMed]
  16. H. Hassanieh, P. Indyk, D. Katabi, and E. Price, “Simple and practical algorithm for sparse Fourier transform,” in Proc. 23rd Annu. ACM-SIAM SODA (ACM, 2012), pp. 1183–1194.
  17. S. Pawar and K. Ramchandran, “Computing a k-sparse n-length discrete Fourier transform using at most 4k samples and O(k log k) complexity,” in Proc. Int. Symp. Information Theory (IEEE, 2013), pp. 464–468.
    [Crossref]
  18. Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
    [Crossref]
  19. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
    [Crossref] [PubMed]
  20. T. Nishitsuji, T. Shimobaba, T. Kakue, D. Arai, and T. Ito, “Simple and fast cosine approximation method for computer-generated hologram calculation,” Opt. Express 23(25), 32465–32470 (2015).
    [Crossref] [PubMed]
  21. T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
    [Crossref] [PubMed]
  22. S.-H. Hsieh, C.-S. Lu, and S.-C. Pei, “Sparse fast fourier transform by downsampling,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 5637–5641.
  23. X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
    [Crossref]
  24. A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
    [Crossref]
  25. The Stanford 3D Scanning Repository: http://graphics.stanford.edu/data/3Dscanrep/
  26. F. F. T. W. Home Page, www.fftw.org/
  27. Y. Rivenson and A. Stern, “Conditions for practicing compressive Fresnel holography,” Opt. Lett. 36(17), 3365–3367 (2011).
    [Crossref] [PubMed]
  28. H. Kang, T. Yamaguchi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47(19), D44–D54 (2008).
    [Crossref] [PubMed]
  29. K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48(34), H203–H211 (2009).
    [Crossref] [PubMed]
  30. T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
    [Crossref]
  31. H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
    [Crossref]

2015 (5)

2014 (1)

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

2013 (1)

2012 (3)

2011 (2)

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
[Crossref]

Y. Rivenson and A. Stern, “Conditions for practicing compressive Fresnel holography,” Opt. Lett. 36(17), 3365–3367 (2011).
[Crossref] [PubMed]

2010 (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

2009 (4)

2008 (2)

2005 (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

2003 (1)

2000 (2)

K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39(35), 6587–6594 (2000).
[Crossref] [PubMed]

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
[Crossref]

1993 (2)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

T. Tommasi and B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A 10(2), 299–305 (1993).
[Crossref]

Abbeel, P.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
[Crossref]

Achim, T.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
[Crossref]

Arai, D.

Bianco, B.

Blinder, D.

Brady, D. J.

Cameron, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

Choi, K.

Endo, Y.

Fang, B.

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

Hirayama, R.

Hiyama, D.

Horisaki, R.

Hsieh, S.-H.

S.-H. Hsieh, C.-S. Lu, and S.-C. Pei, “Sparse fast fourier transform by downsampling,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 5637–5641.

Ichihashi, Y.

Ichikawa, T.

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
[Crossref]

Ito, T.

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
[Crossref] [PubMed]

T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
[Crossref] [PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
[Crossref] [PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, D. Arai, and T. Ito, “Simple and fast cosine approximation method for computer-generated hologram calculation,” Opt. Express 23(25), 32465–32470 (2015).
[Crossref] [PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[Crossref] [PubMed]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012).
[Crossref] [PubMed]

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
[Crossref] [PubMed]

Iwase, S.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
[Crossref]

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Kakue, T.

Kang, H.

Kim, E.-S.

Kim, J.-M.

Kim, S.-C.

Lim, S.

Liu, L.

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

Lu, C.-S.

S.-H. Hsieh, C.-S. Lu, and S.-C. Pei, “Sparse fast fourier transform by downsampling,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 5637–5641.

Luan, X.

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Marks, D. L.

Masuda, N.

Matsushima, K.

Munteanu, A.

Murano, K.

Nakahara, S.

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

Nakayama, H.

Narayan, K. S.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
[Crossref]

Nishi, H.

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

Nishitsuji, T.

Oi, R.

Oikawa, M.

Okada, N.

Oneda, T.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
[Crossref]

Pawar, S.

S. Pawar and K. Ramchandran, “Computing a k-sparse n-length discrete Fourier transform using at most 4k samples and O(k log k) complexity,” in Proc. Int. Symp. Information Theory (IEEE, 2013), pp. 464–468.
[Crossref]

Pei, S.-C.

S.-H. Hsieh, C.-S. Lu, and S.-C. Pei, “Sparse fast fourier transform by downsampling,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 5637–5641.

Qian, J.

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

Ramchandran, K.

S. Pawar and K. Ramchandran, “Computing a k-sparse n-length discrete Fourier transform using at most 4k samples and O(k log k) complexity,” in Proc. Int. Symp. Information Theory (IEEE, 2013), pp. 464–468.
[Crossref]

Rivenson, Y.

Y. Rivenson and A. Stern, “Conditions for practicing compressive Fresnel holography,” Opt. Lett. 36(17), 3365–3367 (2011).
[Crossref] [PubMed]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Sakamoto, Y.

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
[Crossref]

K. Yamaguchi and Y. Sakamoto, “Computer generated hologram with characteristics of reflection: reflectance distributions and reflected images,” Appl. Opt. 48(34), H203–H211 (2009).
[Crossref] [PubMed]

Schelkens, P.

Schimmel, H.

Sha, J.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
[Crossref]

Shimobaba, T.

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
[Crossref] [PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, D. Arai, and T. Ito, “Simple and fast cosine approximation method for computer-generated hologram calculation,” Opt. Express 23(25), 32465–32470 (2015).
[Crossref] [PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
[Crossref] [PubMed]

T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
[Crossref] [PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[Crossref] [PubMed]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012).
[Crossref] [PubMed]

T. Shimobaba, N. Masuda, and T. Ito, “Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane,” Opt. Lett. 34(20), 3133–3135 (2009).
[Crossref] [PubMed]

Singh, A.

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
[Crossref]

Slinger, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

Stern, A.

Y. Rivenson and A. Stern, “Conditions for practicing compressive Fresnel holography,” Opt. Lett. 36(17), 3365–3367 (2011).
[Crossref] [PubMed]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Subagyo, A.

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
[Crossref]

Sueoka, K.

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
[Crossref]

Symeonidou, A.

Takai, M.

Tommasi, T.

Weng, J.

Wyrowski, F.

Yamaguchi, K.

Yamaguchi, T.

Yamamoto, K.

Yang, W.

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

Yoshikawa, H.

H. Kang, T. Yamaguchi, and H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47(19), D44–D54 (2008).
[Crossref] [PubMed]

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
[Crossref]

Appl. Opt. (5)

Computer (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Express (9)

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[Crossref] [PubMed]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012).
[Crossref] [PubMed]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated holograms by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23(17), 22149–22161 (2015).
[Crossref] [PubMed]

D. Arai, T. Shimobaba, K. Murano, Y. Endo, R. Hirayama, D. Hiyama, T. Kakue, and T. Ito, “Acceleration of computer-generated holograms using tilted wavefront recording plane method,” Opt. Express 23(2), 1740–1747 (2015).
[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 patterns in computer-generated holograms,” Opt. Express 20(11), 12021–12034 (2012).
[Crossref] [PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
[Crossref] [PubMed]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
[Crossref] [PubMed]

T. Nishitsuji, T. Shimobaba, T. Kakue, D. Arai, and T. Ito, “Simple and fast cosine approximation method for computer-generated hologram calculation,” Opt. Express 23(25), 32465–32470 (2015).
[Crossref] [PubMed]

T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
[Crossref] [PubMed]

Opt. Lett. (2)

Pattern Recognit. (1)

X. Luan, B. Fang, L. Liu, W. Yang, and J. Qian, “Extracting sparse error of robust PCA for face recognition in the presence of varying illumination and occlusion,” Pattern Recognit. 47(2), 495–508 (2014).
[Crossref]

Proc. SPIE (3)

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “A method of calculating reflectance distributions for CGH with FDTD using the structure of actual surfaces,” Proc. SPIE 7957, 795707 (2011).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48–55 (2000).
[Crossref]

Other (6)

H. Hassanieh, P. Indyk, D. Katabi, and E. Price, “Simple and practical algorithm for sparse Fourier transform,” in Proc. 23rd Annu. ACM-SIAM SODA (ACM, 2012), pp. 1183–1194.

S. Pawar and K. Ramchandran, “Computing a k-sparse n-length discrete Fourier transform using at most 4k samples and O(k log k) complexity,” in Proc. Int. Symp. Information Theory (IEEE, 2013), pp. 464–468.
[Crossref]

A. Singh, J. Sha, K. S. Narayan, T. Achim, and P. Abbeel, “Bigbird: A large-scale 3d database of object instances,” in Proc. Int. Conf. Robotics and Automation (IEEE, 2014), pp. 509–516.
[Crossref]

The Stanford 3D Scanning Repository: http://graphics.stanford.edu/data/3Dscanrep/

F. F. T. W. Home Page, www.fftw.org/

S.-H. Hsieh, C.-S. Lu, and S.-C. Pei, “Sparse fast fourier transform by downsampling,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (IEEE, 2013), pp. 5637–5641.

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Figures (8)

Fig. 1
Fig. 1 Examples of numerical reconstructed images of sampled CGH signals, where 10% of the signals were used. (a) 3-D object point cloud for Bunny. (b) Holographic fringe pattern (i.e., CGH) (c) The numerical reconstructed result from randomly selected 10% of CGH signals. (d) The numerical reconstructed result from the top 10% magnitude of CGH signals.
Fig. 2
Fig. 2 The quality of the numerical reconstruction according to the sampling ratio. The visual quality is measured by PSNR.
Fig. 3
Fig. 3 Overview of the proposed fast CGH calculation for 3-D objects. In the first step, the wavefront on the virtual plane is calculated using multiple ray tracing for each object point cluster. In the second step, the wavefront on the CGH plane is calculated using sparse Fresnel diffraction with sFFT. Note that the red dots indicate a small number of dominant signals on the virtual plane. For sFFT, the number of dominant signals (i.e, sparsity) is measured based on the magnitude. z1 represents the distance between the object and the virtual plane. z2 represents the distance between the virtual plane and the CGH plane.
Fig. 4
Fig. 4 Proposed fast calculation of wavefront on the virtual plane using multiple ray tracing. The red dots and the green dots represent the object points belonging to the first and second clusters, C1 and C2, respectively. The blue dots represent the object points belonging to the S-th cluster, CS. Notably, multiple wavefronts of each cluster on the virtual plane are calculated using ray tracing in parallel. Note that the radius of small area traversed by i-th point light in the Ct is defined as Wti = |zti|tanθ = |zti|tan(sin−1(λ/2p)), as reported in [10]. zti represents the distance between i-th point in the Ct and the virtual plane. p is the sampling pitch, which is 8.5 μm in this paper.
Fig. 5
Fig. 5 Schematic diagram of the proposed fast CGH calculation using sparse Fresnel diffraction with sFFT. The wavefront on the CGH plane is calculated from the wavefront on a virtual plane using sFFT. To that end, the sparsity of the wavefront is measured by counting the dominant signals based on the magnitude.
Fig. 6
Fig. 6 Examples of the distributions of the CGH fringe pattern for Bunny. (a) Original signal distribution of the CGH fringe pattern in Fourier domain. (b) Sparse distribution of the CGH fringe pattern in Fourier domain after the selection process.
Fig. 7
Fig. 7 Visual results of the numerical reconstruction from the CGHs generated by four existing methods and the proposed method for each data set. (a) Results of the ray tracing, (b) Results of the LUT based method [3], (c) Results of the recurrence based method [8], (d) Results of the WRP based method [10], (e) Results of the proposed method.
Fig. 8
Fig. 8 The quality and the computation time (step 2) as a function of k for Bunny.

Tables (4)

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Table 1 Data sets in our experiments.

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Table 2 CGH calculation conditions in our experiments.

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Table 3 Computational times [seconds (s)] of CGH calculation for each data set.

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Table 4 PSNR [dB] for visual quality of the numerical reconstruction from the generated CGH.

Equations (2)

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u VP (x,y)= t=1 S i=1 N t A t i R t i exp(jk R t i ) .
u(ξ,η)= exp( j 2π λ z 2 ) jλ z 2 u VP (x,y)exp( j π λ z 2 ( ( ξx ) 2 + ( ηy ) 2 ) )dxdy exp( j 2π λ z 2 ) jλ z 2 S 1 [ S[ u VP (ξ,η) ]S[ h(ξ,η) ] ] .

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