## Special-purpose computer HORN-5 for a real-time electroholography

Optics Express, Vol. 13, Issue 6, pp. 1923-1932 (2005)

http://dx.doi.org/10.1364/OPEX.13.001923

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### Abstract

In electroholography, a real-time reconstruction is one of the grand challenges. To realize it, we developed a parallelized high-performance computing board for computer-generated hologram, named HORN-5 board, where four large-scale field programmable gate array chips were mounted. The number of circuits for hologram calculation implemented to the board was 1,408. The board calculated a hologram at higher speed by 360 times than a personal computer with Pentium4 processor. A personal computer connected with four HORN-5 boards calculated a hologram of 1,408×1,050 made from a three-dimensional object consisting of 10,000 points at 0.0023 s. In other words, beyond at video rate (30 frames/s), it realized a real-time reconstruction.

© 2005 Optical Society of America

## 1. Introduction

8. M. Huebschman, B. Munjuluri, and R. G. Garner, “Dynamic holographic 3-D image projection,” Opt. Express **11**, 437–445 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-437.

*M*×

*N*, where

*M*is the number of points of a 3-D object and

*N*is the number of points of a hologram (the display resolution), whereas the cost in a two-dimensional (2-D) display system is proportional only to the display resolution. Some researchers developed the fast algorithms [9–12] which calculate CGH beyond 10 times faster than the direct calculation algorithm. At present time, however, even the fast algorithms cannot reconstruct electroholography at video rate.

*α*and

*j*show the hologram and the object respectively, the parameters

*x, y*and

*z*mean the horizontal, vertical and depth components,

*A*

_{j}is the intensity of the object point, and

*λ*is the wavelength of the reference light. In making CGH, the calculations of Eq. (1) represent almost all of the total calculation cost. If we can accelerate the calculation of Eq. (1), therefore, we can accelerate the total calculation time. The HORN computers have been designed and developed to calculate Eq. (1) by hardware. Figure 1 is the basic structure of the HORN system consisting of a host computer and a special-purpose hardware HORN. We adopt a general-purpose computer, usually a personal computer (PC), as the host computer to deal with computational tasks except for the calculation of Eq. (1).

## 2. Hardware design

*x, y≪z*in the above system, Eq. (1) can be approximated as the following expression by Fresnel approximation:

*x*

_{α}

*-x*

_{j}) and (

*y*

_{α}

*-y*

_{j}) with

*x*

_{αj}and

*y*

_{αj}. Normalizing the parameters of the positions in Eq. (2) by the pixel-pitch of hologram,

*p*(10.4 µm in the HORN-5 system), we obtain the next equation:

*X, Y*, and

*Z*are integers. Using Eq. (3), we can calculate CGH with recurrence formulas by additions. We show the schematic drawing in Fig. 3 and the equations as follows.

*I*(

*X*

_{α}

*,Y*

_{α}) at one point on the hologram by using

*Θ*

_{0}, namely, by calculating Eq. (5) directly. Next, for the points on the horizontal (

*x*-axis direction) line, we can calculate them by using Eq. (6), namely, by additions only. For the next line, we replace

*Y*

_{α}with

*Y*

_{α+1}and calculate them with the same procedure. The significant feature of this algorithm is that it requires few multiplications. It is a large advantage for hardware design because a multiplier occupies a large area of circuits.

_{0}as shown in Fig. 4 and APU (Additional Processing Unit) which calculates Θ

_{k≠0}as shown in Fig. 5. Here, we omit

*A*

_{j}as the light intensities emitted from object points are all the same value, and we rewrite

*X*

_{j}or

*Y*

_{j}means the maximum width or height of an object graphics is 2

^{14}×10.4 µm~16 cm. The 11-bit counters for

*X*

_{j}and

*Y*

_{j}mean the maximum resolution of a hologram is 2,048×2,048. Both satisfy the condition of the system described above. Moreover, a cosine function is a periodic function of 2

*π*. Using the feature, we can ignore the integer parts of Θ

_{0}and Θ

_{k}, which makes the data width short in each part of the circuits.

*I*

_{α}. Although the LCD pixels we use have 8-bit depth, a gray scale data format has little advantage as compared with a binary format (black or white) in respect of observation by today’s small-scale electroholography system and it has been shown that even a binary format hologram can produce a clear reconstructed image [6]. It is, of course, easy to change the hardware design there from 1 bit to 8 bits if necessary. For the present, therefore, we adopt the binary format in order to reduce the transferred data between HON-5 and the host PC.

*n*APUs, which calculates

*n*+1 hologram points in parallel.

## 3. Packaging and performance

^{2}/(10.4 µm)

^{2}]~10

^{10}. Therefore, we had to use double precision (64-bit) data format in this algorithm. As for the compiler, we used Microsoft Visual C++6.0 with the optimal complier option. This algorithm needed 1630 s (27 min) for generating one CGH.

## 4. Discussion and future work

*I*

_{α}from the HORN-5 boards to the host PC. Since the LCD resolution is 1,408×1,050 (1.5 Mega pixels) and the communication speed is 81.9 Mbyte/s, the communication time for

*I*

_{α}is 0.0023 s/hologram in the ideal case. If we assign 8 bits for

*I*

_{α}, it requires 0.018 s. For a LCD panel consisting of more than 3 Mega pixels, therefore, our system cannot realize a real-time reconstruction due to the communication cost.

21. T. Ito and T. Shimobaba, “One-unit system for electroholography by use of a special-purpose computational chip with a high-resolution liquid-crystal display toward a three-dimensional television”, Opt. Express , **12**, 1788–1793 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1788.

## Acknowledgments

## References and Links

1. | P. S. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE |

2. | P. S. Hilaire, S. A. Benton, M. Lucente, J. D. Sutter, and W. J. Plesniak, “Advances in holographic video,” Proc. SPIE |

3. | P. S. Hilaire, “Scalable optical architecture for electronic holography,” Opt. Eng. |

4. | G. Tricoles, “Computer generated holograms: an historical review,” Appl. Opt. |

5. | M. Lucente, “Interactive three-dimensional holographic displays: seeing the future in depth,” Comp. Graphics |

6. | T. Ito, T. Shimobaba, H. Godo, and M. Horiuchi, “Holographic reconstruction with a 10-µm pixel-pitch reflective liquid-crystal display by use of a light-emitting diode reference light,” Opt. Lett. |

7. | T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt, Express |

8. | M. Huebschman, B. Munjuluri, and R. G. Garner, “Dynamic holographic 3-D image projection,” Opt. Express |

9. | M. Lucente, “Interactive Computation of Holograms Using a Look-Up Table,” J. Electron. Imaging |

10. | H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE |

11. | K. Matsushima and M. Takai, “Fast computation of Fresnel holograms employing difference,” Appl. Opt. |

12. | T. Shimobaba and T. Ito, “An efficient computational method suitable for hardware of computer-generated hologram with phase computation by addition,” Comp. Phys. Commun. |

13. | J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove Jr., and I. Tamitani. “A hardware architecture for rapid generation of electro-holographic fringe patterns,” Proc SPIE |

14. | M. Lucente and T. A. Galyean, “Rendering interactive holographic images”, Proc. ACM SIGGRAPH |

15. | T. Yabe, T. Ito, and M. Okazaki, “Holography machine HORN-1 for computer-aided retrieval of virtual three-dimensional image,” Jpn. J. Appl. Phys. |

16. | T. Ito, T. Yabe, M. Okazaki, and M. Yanagi, “Special-purpose computer HORN-1 for reconstruction of virtual image in three dimensions,” Comp. Phys. Commun. |

17. | T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, “Special-purpose computer for holography HORN-2,” Comp. Phys. Commun. |

18. | T. Shimobaba, N. Masuda, T. Sugie, S. Hosono, S. Tsukui, and T. Ito, “Special-purpose computer for holography HORN-3 with PLD technology,” Comp. Phys. Commun. |

19. | T. Shimobaba and T. Ito, “Special-purpose computer for holography HORN-4 with recurrence algorithm,” Comp. Phys. Commun. |

20. | |

21. | T. Ito and T. Shimobaba, “One-unit system for electroholography by use of a special-purpose computational chip with a high-resolution liquid-crystal display toward a three-dimensional television”, Opt. Express , |

**OCIS Codes**

(090.1760) Holography : Computer holography

(090.2870) Holography : Holographic display

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 25, 2005

Revised Manuscript: February 25, 2005

Published: March 21, 2005

**Citation**

Tomoyoshi Ito, Nobuyuki Masuda, Kotaro Yoshimura, Atsushi Shiraki, Tomoyoshi Shimobaba, and Takashige Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express **13**, 1923-1932 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1923

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### References

- P. S. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, �??Electronic display system for computational holography,�?? Proc. SPIE 1212-20, 174�??182 (1990).
- P. S. Hilaire, S. A. Benton, M. Lucente, J. D. Sutter, and W. J. Plesniak, �??Advances in holographic video,�?? Proc. SPIE 1914-27, 188�??196 (1993)
- P. S. Hilaire, �??Scalable optical architecture for electronic holography,�?? Opt. Eng. 34, 2900�??2911 (1995).
- G. Tricoles, �??Computer generated holograms: an historical review,�?? Appl. Opt. 26, 4351�??4360 (1987)
- M. Lucente, �??Interactive three-dimensional holographic displays: seeing the future in depth,�?? Comp. Graphics 31, 63�??67 (1997)
- T. Ito, T. Shimobaba, H. Godo, and M. Horiuchi, �??Holographic reconstruction with a 10-µm pixel-pitch reflective liquid-crystal display by use of a light-emitting diode reference light,�?? Opt. Lett. 27, 1406�??1408 (2002)
- T. Ito and K. Okano, �??Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,�?? Opt. Express 12, 4320-4325 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4320">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4320</a>
- M. Huebschman, B. Munjuluri, and R. G. Garner, �??Dynamic holographic 3-D image projection,�?? Opt. Express 11, 437�??445 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-437">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-437</a>
- M. Lucente, �??Interactive Computation of Holograms Using a Look-Up Table,�?? J. Electron. Imaging 2, pp. 28-34 (1993)
- H. Yoshikawa, S. Iwase, and T. Oneda, �??Fast computation of Fresnel holograms employing difference,�?? Proc. SPIE 3956, 48�??55 (2000)
- K. Matsushima and M. Takai, �??Fast computation of Fresnel holograms employing difference,�?? Appl. Opt. 39, 6587�??6594 (2000)
- T. Shimobaba and T. Ito, �??An efficient computational method suitable for hardware of computer-generated hologram with phase computation by addition,�?? Comp. Phys. Commun. 138, 44�??52 (2001)
- J. A. Watlington, M. Lucente, C. J. Sparrell, V. M. Bove, Jr., and I. Tamitani. "A hardware architecture for rapid generation of electro-holographic fringe patterns," Proc SPIE 2406-23, 172-183 (1995)
- M. Lucente and T. A. Galyean, "Rendering interactive holographic images", Proc. ACM SIGGRAPH 95, 387-394 (1995)
- T. Yabe, T. Ito, and M. Okazaki, �??Holography machine HORN-1 for computer-aided retrieval of virtual three-dimensional image,�?? Jpn. J. Appl. Phys. 32, L1359�??L1361 (1993)
- T. Ito, T. Yabe, M. Okazaki, and M. Yanagi, �??Special-purpose computer HORN-1 for reconstruction of virtual image in three dimensions,�?? Comp. Phys. Commun. 82, 104�??110 (1994)
- T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, �??Special-purpose computer for holography HORN-2,�?? Comp. Phys. Commun. 93, 13�??20 (1996)
- T. Shimobaba, N. Masuda, T. Sugie, S. Hosono, S. Tsukui, and T. Ito, �??Special-purpose computer for holography HORN-3 with PLD technology,�?? Comp. Phys. Commun. 130, 75�??82 (2000)
- T. Shimobaba and T. Ito, �??Special-purpose computer for holography HORN-4 with recurrence algorithm,�?? Comp. Phys. Commun. 148, 160�??170 (2002).
- <a href="http://www.jvcdig.com/technology.htm">http://www.jvcdig.com/technology.htm</a>
- T. Ito and T. Shimobaba, �?? One-unit system for electroholography by use of a special-purpose computational chip with a high-resolution liquid-crystal display toward a three-dimensional television�??, Opt. Express, 12, 1788-1793 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1788">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1788</a>

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