## Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display |

Applied Optics, Vol. 52, Issue 7, pp. 1404-1412 (2013)

http://dx.doi.org/10.1364/AO.52.001404

Acrobat PDF (869 KB)

### Abstract

A fast algorithm with low memory usage is proposed to generate the hologram for full-color 3D display based on a compressed look-up table (C-LUT). The C-LUT is described and built to reduce the memory usage and speed up the calculation of the computer-generated hologram (CGH). Numerical simulations and optical experiments are performed to confirm this method, and several other algorithms are compared. The results show that the memory usage of the C-LUT is kept low when number of depth layers of the 3D object is increased, and the time for building the C-LUT is independent of the number of depth layers of the 3D object. The algorithm based on C-LUT is an efficient method for saving memory usage and calculation time, and it is expected that it could be used for realizing real-time and full-color 3D holographic display in the future.

© 2013 Optical Society of America

## 1. Introduction

1. A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a
simplified ray-tracing approach,” Comput.
Phys. **6**, 389–392
(1992). [CrossRef]

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

5. M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an
approximate Fresnel integral,” J.
Opt. **13**, 075405 (2011). [CrossRef]

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

7. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel
computer-generated-hologram using look-up table and wave front-recording
plane methods for three-dimensional display,”
Opt. Express **18**, 19504–19509(2010). [CrossRef]

8. 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]

11. S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of
the novel look-up table memory
size based on a relationship between the pixel pitch and reconstruction
distance of a
computer-generated
hologram,” Appl. Opt. **50**, 3375–3382
(2011). [CrossRef]

*et al.*[12

12. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on
GPU,” Opt. Express **17**, 18543–18555
(2009). [CrossRef]

13. Y. Z. Liu, J. W. Dong, Y. Y. Pu, H. X. He, B. C. Chen, H. Z. Wang, H. Zheng, and Y. Yu, “Fraunhofer computer-generated
hologram for diffused 3D scene
in Fresnel region,” Opt. Lett. **36**, 2128–2130
(2011). [CrossRef]

14. F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic
video display system using LED illumination,”
Appl. Opt. **48**, H48–H53
(2009). [CrossRef]

## 2. Conventional CRT and LUT Algorithms

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

*et al.*[12

12. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on
GPU,” Opt. Express **17**, 18543–18555
(2009). [CrossRef]

## 3. New Method Based on C-LUT

15. 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**, 5993–5996
(2010). [CrossRef]

## 4. Errors of the New Method and Corresponding Correction

## 5. Implementations and Results

17. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced
by a pixelated spatial light modulator for holographic
projection,” Appl. Opt. **48**, 5834–5841
(2009). [CrossRef]

## 6. Conclusions

18. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a
graphics processing unit,” Opt.
Express **14**, 603–608
(2006). [CrossRef]

21. 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]

## References

1. | A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a
simplified ray-tracing approach,” Comput.
Phys. |

2. | K. Matsushima and M. Takai, “Recurrence formulas for fast creation of
synthetic three-dimensional holograms,” Appl.
Opt. |

3. | H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for
real-time holographic display,” Opt.
Eng. |

4. | H. Kang, T. Yamaguchi, and A. H. Yoshikawa, “Accurate phase-added stereogram to
improve the coherent stereogram,” Appl.
Opt. |

5. | M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an
approximate Fresnel integral,” J.
Opt. |

6. | M. Lucente, “Interactive computation of holograms
using a look-up table,” J. Electron.
Imaging |

7. | T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel
computer-generated-hologram using look-up table and wave front-recording
plane methods for three-dimensional display,”
Opt. Express |

8. | 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. |

9. | 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. |

10. | 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. |

11. | S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of
the novel look-up table memory
size based on a relationship between the pixel pitch and reconstruction
distance of a
computer-generated
hologram,” Appl. Opt. |

12. | Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on
GPU,” Opt. Express |

13. | Y. Z. Liu, J. W. Dong, Y. Y. Pu, H. X. He, B. C. Chen, H. Z. Wang, H. Zheng, and Y. Yu, “Fraunhofer computer-generated
hologram for diffused 3D scene
in Fresnel region,” Opt. Lett. |

14. | F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic
video display system using LED illumination,”
Appl. Opt. |

15. | 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. |

16. | J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional
optical image without distortion in dynamic holographic
projection,” Opt. Eng. |

17. | H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced
by a pixelated spatial light modulator for holographic
projection,” Appl. Opt. |

18. | N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a
graphics processing unit,” Opt.
Express |

19. | A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color
reconstruction system using
graphics processing unit and
liquid crystal display
projector,” Opt. Express |

20. | 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 |

21. | 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 |

**OCIS Codes**

(090.1760) Holography : Computer holography

(090.2870) Holography : Holographic display

(090.1705) Holography : Color holography

(090.5694) Holography : Real-time holography

**ToC Category:**

Holography

**History**

Original Manuscript: December 17, 2012

Revised Manuscript: January 16, 2013

Manuscript Accepted: January 16, 2013

Published: February 22, 2013

**Citation**

Jia Jia, Yongtian Wang, Juan Liu, Xin Li, Yijie Pan, Zhumei Sun, Bin Zhang, Qing Zhao, and Wei Jiang, "Reducing the memory usage for effectivecomputer-generated hologram calculation using compressed look-up table in full-color holographic display," Appl. Opt. **52**, 1404-1412 (2013)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-7-1404

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### References

- A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992). [CrossRef]
- K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000). [CrossRef]
- H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007). [CrossRef]
- H. Kang, T. Yamaguchi, and A. H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44–D54 (2008). [CrossRef]
- M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an approximate Fresnel integral,” J. Opt. 13, 075405 (2011). [CrossRef]
- M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993). [CrossRef]
- T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wave front-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509(2010). [CrossRef]
- 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]
- 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, 5986–5995 (2008). [CrossRef]
- 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]
- S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50, 3375–3382 (2011). [CrossRef]
- Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009). [CrossRef]
- Y. Z. Liu, J. W. Dong, Y. Y. Pu, H. X. He, B. C. Chen, H. Z. Wang, H. Zheng, and Y. Yu, “Fraunhofer computer-generated hologram for diffused 3D scene in Fresnel region,” Opt. Lett. 36, 2128–2130 (2011). [CrossRef]
- F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic video display system using LED illumination,” Appl. Opt. 48, H48–H53 (2009). [CrossRef]
- 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, 5993–5996 (2010). [CrossRef]
- J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011). [CrossRef]
- H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009). [CrossRef]
- N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14, 603–608 (2006). [CrossRef]
- A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express 17, 16038–16045 (2009). [CrossRef]
- 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]
- 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]

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