## Holographic video at 40 frames per second for 4-million object points |

Optics Express, Vol. 19, Issue 16, pp. 15205-15211 (2011)

http://dx.doi.org/10.1364/OE.19.015205

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### Abstract

We propose a fast method for generating digital Fresnel holograms based on an interpolated wavefront-recording plane (IWRP) approach. Our method can be divided into two stages. First, a small, virtual IWRP is derived in a computational-free manner. Second, the IWRP is expanded into a Fresnel hologram with a pair of fast Fourier transform processes, which are realized with the graphic processing unit (GPU). We demonstrate state-of-the-art experimental results, capable of generating a 2048x2048 Fresnel hologram of around

© 2011 OSA

## 1. Introduction

*D*(

*x*,

*y*) on the hologram plane can be derived aswhere

*j*th’ point in

*O*and its distance to the position

*λ*is the wavelength of the light. Although the method is effective, the computation involved in generating a hologram is extremely high. In the past lots of research attempts have been conducted to overcome the above problems, such as the works developed in [2

2. 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]

12. P. W. M. Tsang, J.-P. Liu, W. K. Cheung, and T.-C. Poon, “Fast generation of Fresnel holograms based on multirate filtering,” Appl. Opt. **48**(34), H23–H30 (2009). [CrossRef] [PubMed]

13. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express **18**(19), 19504–19509 (2010). [CrossRef] [PubMed]

13. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express **18**(19), 19504–19509 (2010). [CrossRef] [PubMed]

## 2. Background of the wavefront-recording plane (WRP) method

13. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express **18**(19), 19504–19509 (2010). [CrossRef] [PubMed]

*is a vertical, 2D image that is positioned at the origin. A virtual WRP,*

*X*and

*Y*pixels, respectively, as well as identical sampling pitch

*p*. The hologram generation process can be divided into two stages. In the first stage, the complex wavefront contributed by the object points is computed aswhere

*jth*object point, and

*W*is much smaller than

*X*and

*Y*, the computation load is significantly reduced as compared with Eq. (2). In [13

**18**(19), 19504–19509 (2010). [CrossRef] [PubMed]

*α*is the arithmetic operations involved in computing the wavefront contributed by each object point. In the second stage, the WRP is expanded to the hologram aswhere

## 3. Proposed computational-free interpolated wavefront-recording plane (IWRP) method

*M*times (where

*m*and

*n*are integer values. A square support, as shown in Fig. 1a , is defined for each sample point, with the left side

## 4. Experimental results

*λ*and the distance

*z*between the WRP/IWRP and the hologram are set to 650

_{w}*nm*and 0.4m, respectively.

*M*= 8 and size of virtual window = 8x8), and applied Eqs. (5) and 6 to derive a WRP. The latter is then expand it into a hologram with Eq. (4). A real, off-axis hologram

*LCOS*) modified from the Sony VPL-HW15 Bravia projector. The projector has a horizontal and vertical resolution of 1920 and 1080, respectively. Due to the limited size and resolution of the

*LCOS*only part of the hologram (and hence the reconstructed image) can be displayed. The reconstructed images corresponding to the upper half and the lower half of the hologram are shown in Figs. 2b and 2c, respectively. We observe that the images are extremely weak and noisy. Next we repeat the above process by generating the IWRP with Eqs. (7) and 8. The reconstructed images are shown in Figs. 2d and 2e. Evidently, the reconstructed image is much clearer in appearance. To further illustrate our proposed method, we have generated a sequence of holograms of a rotating globe which is rendered with the texture of the earth image. The radius of the globe is around 0.005m, and the front tip of the globe is located at 0.01m from the IWRP. The latter is at a distance of 0.3m from the hologram. A single frame excerpt of the optical reconstructed animation clip (Media 1) is shown in Fig. 2f. It can be seen from the excerpt, as well as in the animation clip that, despite the complexity of the texture, the earth image on the globe is clearly reconstructed in every views. Next, we evaluate the computation efficiency of our proposed method. The IWRP, and its subsequent expansion to a Fresnel hologram are conducted with the PC (intel i7-950 @ 3.06GHz) and the GPU (Nvidia Geforce GTX580), respectively. The total hologram generation time and equivalent frame-rate (measure in

*fps*representing the number of hologram frames per second), versus the number of object points, are shown in Table 1 . We have assumed that the number of object points and hologram pixels are identical. From the result, it can be seen that the hologram generation time is very short as it only involves table lookup and data transfer between memory arrays. For a hologram (as well as image size) of 2048x2048 pixels, our proposed method is capable of attaining a generation speed of over 40 frames per second.

## 5. Conclusion

## Acknowledgments

## References and links

1. | T.-C. Poon, ed., “Digital holography and three-dimensional display: Principles and Applications,” Springer (2006). |

2. | 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. |

3. | 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. |

4. | 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. |

5. | H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. |

6. | T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. |

7. | H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. |

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

10. | H. Kang, F. Yaraş, and L. Onural, “Graphics processing unit accelerated computation of digital holograms,” Appl. Opt. |

11. | Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” Laser App. Chem., Sec. and Env. Ana., OSA Tech. Digest (CD) (OSA, 2008), paper JMA9. |

12. | P. W. M. Tsang, J.-P. Liu, W. K. Cheung, and T.-C. Poon, “Fast generation of Fresnel holograms based on multirate filtering,” Appl. Opt. |

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

**OCIS Codes**

(090.0090) Holography : Holography

(090.1760) Holography : Computer holography

(090.1995) Holography : Digital holography

**ToC Category:**

Holography

**History**

Original Manuscript: June 29, 2011

Manuscript Accepted: July 16, 2011

Published: July 22, 2011

**Virtual Issues**

August 12, 2011 *Spotlight on Optics*

**Citation**

Peter 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)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15205

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### References

- T.-C. Poon, ed., “Digital holography and three-dimensional display: Principles and Applications,” Springer (2006).
- 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]
- 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]
- 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(32), 5986–5995 (2008). [CrossRef] [PubMed]
- H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48(34Issue 34), H212–H221 (2009). [CrossRef] [PubMed]
- T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007). [CrossRef]
- H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001). [CrossRef]
- 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). [CrossRef] [PubMed]
- L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14(17), 7636–7641 (2006). [CrossRef] [PubMed]
- H. Kang, F. Yaraş, and L. Onural, “Graphics processing unit accelerated computation of digital holograms,” Appl. Opt. 48(34), H137–H143 (2009). [CrossRef] [PubMed]
- Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” Laser App. Chem., Sec. and Env. Ana., OSA Tech. Digest (CD) (OSA, 2008), paper JMA9.
- P. W. M. Tsang, J.-P. Liu, W. K. Cheung, and T.-C. Poon, “Fast generation of Fresnel holograms based on multirate filtering,” Appl. Opt. 48(34), H23–H30 (2009). [CrossRef] [PubMed]
- T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010). [CrossRef] [PubMed]

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