## Fast reconfiguration algorithm of computer generated holograms for adaptive view direction change in holographic three-dimensional display |

Optics Express, Vol. 20, Issue 27, pp. 28282-28291 (2012)

http://dx.doi.org/10.1364/OE.20.028282

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### Abstract

Reconfiguration is a computational algorithm of adaptively updating computer generated holograms (CGHs) for the positional change of an observer’s viewing window with low computational load by efficiently using pre-calculated elementary CGHs. A fast reconfiguration algorithm of CGHs for three-dimensional mesh objects is proposed. Remarkable improvement is achieved in the computation speed of CGHs, which is at least 20-times faster than repetitive re-computation of CGHs. The image quality of reconfigured CGHs is analyzed.

© 2012 OSA

## 1. Introduction

8. T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express **13**(6), 1923–1932 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1923. [CrossRef] [PubMed]

9. E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE **7690**, 76900E, 76900E-13 (2010). [CrossRef]

10. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express **14**(17), 7636–7641 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7636. [CrossRef] [PubMed]

12. H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. **49**(31), 5993–5996 (2010). [CrossRef]

13. M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging **2**(1), 28–34 (1993). [CrossRef]

14. 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]

15. Y. Sando, D. Barada, and T. Yatagai, “Fast calculation of computer-generated holograms based on 3-D Fourier spectrum for omnidirectional diffraction from a 3-D voxel-based object,” Opt. Express **20**(19), 20962–20969 (2012). [CrossRef] [PubMed]

## 2. Viewing characteristics of mesh object CGHs

11. 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**(10), 9955–9960 (2010). [CrossRef] [PubMed]

*k*th single triangle facet to the VW, we have to use a directional carrier wave in the design of a CGH represented by the form of a local plane wave,where the direction of the wavevector,

*k*th triangle facet is placed on an infinite plane

*k*th single triangle facet is expressed by the angular spectrum form:where the exponential function of the carrier wave in Eq. (1) is immersed in the angular spectrum representation. In Eq. (2a), the localization operator

## 3. Reconfiguration algorithm of CGH

*x*-

*y*plane,

*x*-

*y*plane and a triangle tilted 45 degrees relative to the

*x*-

*y*plane, respectively. The RMSEs for the horizontal shift (

*x*-axis distance) of the VW and the axial shift of the triangle object are plotted. The reference ASCGHs for reconfiguration are computed at the reference VW position that is positioned on the optical axis with

*x*-directional horizontal shift of VW and the error due to the reconfiguration is inversely proportional to the effective projection area of the triangle to the observer at a specified horizontal shift. In the case of the non-tilted triangle, the effective projection area of the triangle for the VW position decreases as the triangle approaches the observer, and as a result, increase of the RMSE is observed, while for the 45 deg. tilted triangle, the effective projection area of the triangle increases as the triangle approaches the observer, so decreasing behavior of the RMSE clearly appears in Fig. 6(b). In this analysis, the overall RMSE is less than 20%.

## 4. Conclusion

## Acknowledgment

## References and links

1. | A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A |

2. | M. A. Neifeld, “Information, resolution, and space-bandwidth product,” Opt. Lett. |

3. | J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. |

4. | R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE |

5. | N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE |

6. | Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. |

7. | T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. |

8. | T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express |

9. | E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE |

10. | L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express |

11. | 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 |

12. | H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. |

13. | M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging |

14. | 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 |

15. | Y. Sando, D. Barada, and T. Yatagai, “Fast calculation of computer-generated holograms based on 3-D Fourier spectrum for omnidirectional diffraction from a 3-D voxel-based object,” Opt. Express |

16. | H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. |

**OCIS Codes**

(090.2870) Holography : Holographic display

(090.1995) Holography : Digital holography

**ToC Category:**

Holography

**History**

Original Manuscript: September 12, 2012

Revised Manuscript: November 15, 2012

Manuscript Accepted: November 16, 2012

Published: December 6, 2012

**Citation**

Jaebum Cho, Joonku Hahn, and Hwi Kim, "Fast reconfiguration algorithm of computer generated holograms for adaptive view direction change in holographic three-dimensional display," Opt. Express **20**, 28282-28291 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28282

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### References

- A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A13(3), 470–473 (1996). [CrossRef]
- M. A. Neifeld, “Information, resolution, and space-bandwidth product,” Opt. Lett.23(18), 1477–1479 (1998). [CrossRef] [PubMed]
- J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt.50(34), H87–H115 (2011). [CrossRef] [PubMed]
- R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic displays as an alternative to stereoscopic displays,” Proc. SPIE6803, 68030M, 68030M-9 (2008). [CrossRef]
- N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE6911, 69110V, 69110V-10 (2008). [CrossRef]
- Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt.47(19), D6–D11 (2008). [CrossRef] [PubMed]
- T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt.41(8), 1489–1499 (2002). [CrossRef] [PubMed]
- T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express13(6), 1923–1932 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1923 . [CrossRef] [PubMed]
- E. Zschau, R. Missbach, A. Schwerdtner, and H. Stolle, “Generation, encoding, and presentation of content on holographic displays in real time,” Proc. SPIE7690, 76900E, 76900E-13 (2010). [CrossRef]
- L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express14(17), 7636–7641 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7636 . [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. Express18(10), 9955–9960 (2010). [CrossRef] [PubMed]
- H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt.49(31), 5993–5996 (2010). [CrossRef]
- M. Lucente, “Interactive Computation of holograms using a Look-up Table,” J. Electron. Imaging2(1), 28–34 (1993). [CrossRef]
- 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. Express20(4), 4018–4023 (2012). [CrossRef] [PubMed]
- Y. Sando, D. Barada, and T. Yatagai, “Fast calculation of computer-generated holograms based on 3-D Fourier spectrum for omnidirectional diffraction from a 3-D voxel-based object,” Opt. Express20(19), 20962–20969 (2012). [CrossRef] [PubMed]
- H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt.47(19), D117–D127 (2008). [CrossRef] [PubMed]

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