## High-speed full analytical holographic computations for true-life scenes

Optics Express, Vol. 18, Issue 4, pp. 3345-3351 (2010)

http://dx.doi.org/10.1364/OE.18.003345

Acrobat PDF (311 KB)

### Abstract

We develop a novel method to generate hologram of three-dimensional (3D) textured triangle-mesh-model that is reconstructed from ordinary digital photos. This method allows *analytically* encoding the 3D model consisting of triangles. In contrast to other polygon based holographic computations, our full analytical method will free oneself from the numerical error that is in the angular spectrum due to the Whittaker-Shannon sampling. In order to saving the computation time, we employ the GPU platform that is remarkably superior to the CPU’s. We have rendered a true-life scene with colored textures as the first demo by our homemade software. The holographic reconstructed scene possesses high performances in many aspects such as depth cues, surface textures, shadings, and occlusions, etc. The GPU’s algorithm performs hundreds of times faster than those of CPU.

© 2010 OSA

## 1. Introduction

1. K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News **17**(7), 42–51 (2006). [CrossRef]

3. J. L. Zhao, H. Z. Jiang, and J. L. Di, “Recording and reconstruction of a color holographic image by using digital lensless Fourier transform holography,” Opt. Express **16**(4), 2514–2519 (2008). [CrossRef] [PubMed]

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

6. M. Lucente, “Interactive Computation of Holograms Using a Look-Up Table,” J. Electron. Imaging **2**(1), 28–34 (1993). [CrossRef]

7. 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]

7. 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]

8. D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. **27**(14), 3020–3024 (1988). [CrossRef] [PubMed]

10. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular sprctrum of plane waves,” J. Opt. Soc. Am. A **20**(9), 1755–1762 (2003). [CrossRef]

11. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. **47**(10), 1567–1574 (2008). [CrossRef] [PubMed]

12. 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]

13. E. Lalor, “Conditions for the Validity of the Angular Spectrun of Plane Waves,” J. Opt. Soc. Am. A **58**(9), 1235–1237 (1968). [CrossRef]

17. K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express **17**(22), 19662–19673 (2009). [CrossRef] [PubMed]

17. K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express **17**(22), 19662–19673 (2009). [CrossRef] [PubMed]

12. 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]

20. C. Petz and M. Magnor, “Fast Hologram Synthesis for 3D Geometry Models using Graphics Hardware,” Proc. SPIE **5005**, 266–275 (2003). [CrossRef]

22. 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]

## 2. Theory

### 2.1 Analytical diffraction field of 3D triangle-mesh model

*λ*is the wavelength;

*r*is a square root function with the local coordinate variables

*r*can be expanded into:where

11. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. **47**(10), 1567–1574 (2008). [CrossRef] [PubMed]

12. 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]

24. R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. **29**(3), 304–306 (1993). [CrossRef]

11. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. **47**(10), 1567–1574 (2008). [CrossRef] [PubMed]

### 2.2 Texture mapping, occlusion, and phase adjustment

10. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular sprctrum of plane waves,” J. Opt. Soc. Am. A **20**(9), 1755–1762 (2003). [CrossRef]

*z*component of mass center of each triangle (

*α*relates to the response of coherent system to sharp triangular edges, with an approximate value of 0.5 at the edge [5]. When

## 3. Parallel algorithm and implementation on CUDA

## 4. Results

25. “Autodesk® ImageModeler™,” URL http://usa.autodesk.com/adsk/servlet/index?siteID=123112&id=11390028

## 5. Conclusion

26. J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express **16**(16), 12372–12386 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News |

2. | See for example, Stanford 3D Scanning Repository, |

3. | J. L. Zhao, H. Z. Jiang, and J. L. Di, “Recording and reconstruction of a color holographic image by using digital lensless Fourier transform holography,” Opt. Express |

4. | C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer |

5. | J. W. Goodman, |

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

7. | 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. |

8. | D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. |

9. | N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” J. Opt. Soc. Am. A |

10. | K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular sprctrum of plane waves,” J. Opt. Soc. Am. A |

11. | L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. |

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

13. | E. Lalor, “Conditions for the Validity of the Angular Spectrun of Plane Waves,” J. Opt. Soc. Am. A |

14. | J. García, D. Mas, and R. G. Dorsch, “Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm,” Appl. Opt. |

15. | D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. |

16. | D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. |

17. | K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express |

18. | M. Zhang, T. S. Yeo, L. W. Li, and Y. B. Gan, “Parallel FFT Based Fast Algorithms for Solving Large Scale Electromagnetic Problems,” in |

19. | J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE |

20. | C. Petz and M. Magnor, “Fast Hologram Synthesis for 3D Geometry Models using Graphics Hardware,” Proc. SPIE |

21. | V. M. Bove, Jr., W. J. Plesniak, T. Quentmeyer, and J. Barabas, “Real-Time Holographic Video Images with Commodity PC Hardware,” Proc. SPIE Stereoscopic Displays and Applications |

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

23. | NVIDIA, “NVIDIA CUDA Compute Unified Device Architecture Programming Guide Version 2.1,” (2008). |

24. | R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. |

25. | “Autodesk® ImageModeler™,” URL http://usa.autodesk.com/adsk/servlet/index?siteID=123112&id=11390028 |

26. | J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express |

**OCIS Codes**

(090.0090) Holography : Holography

(090.1760) Holography : Computer holography

(090.2870) Holography : Holographic display

**ToC Category:**

Holography

**History**

Original Manuscript: July 31, 2009

Revised Manuscript: January 20, 2010

Manuscript Accepted: January 29, 2010

Published: February 2, 2010

**Citation**

Yuan-Zhi Liu, Jian-Wen Dong, Yi-Ying Pu, Bing-Chu Chen, He-Xiang He, and He-Zhou Wang, "High-speed full analytical holographic computations for true-life scenes," Opt. Express **18**, 3345-3351 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3345

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### References

- K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News 17(7), 42–51 (2006). [CrossRef]
- See for example, Stanford 3D Scanning Repository, and XYZ RGB Inc.
- J. L. Zhao, H. Z. Jiang, and J. L. Di, “Recording and reconstruction of a color holographic image by using digital lensless Fourier transform holography,” Opt. Express 16(4), 2514–2519 (2008). [CrossRef] [PubMed]
- C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005). [CrossRef]
- J. W. Goodman, Introduction to Fourier optics (Roberts & Company Publishers, 2004)
- M. Lucente, “Interactive Computation of Holograms Using a Look-Up Table,” J. Electron. Imaging 2(1), 28–34 (1993). [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(6), 1030–1041 (2009). [CrossRef]
- D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988). [CrossRef] [PubMed]
- N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” J. Opt. Soc. Am. A 15(4), 857–867 (1998). [CrossRef]
- K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular sprctrum of plane waves,” J. Opt. Soc. Am. A 20(9), 1755–1762 (2003). [CrossRef]
- L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008). [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]
- E. Lalor, “Conditions for the Validity of the Angular Spectrun of Plane Waves,” J. Opt. Soc. Am. A 58(9), 1235–1237 (1968). [CrossRef]
- J. García, D. Mas, and R. G. Dorsch, “Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm,” Appl. Opt. 35(35), 7013–7018 (1996). [CrossRef] [PubMed]
- D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997). [CrossRef]
- D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999). [CrossRef]
- K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17(22), 19662–19673 (2009). [CrossRef] [PubMed]
- M. Zhang, T. S. Yeo, L. W. Li, and Y. B. Gan, “Parallel FFT Based Fast Algorithms for Solving Large Scale Electromagnetic Problems,” in IEEE Antennas and Propagation Society International Symposium, pp. 3995–3998 (2006).
- J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).
- C. Petz and M. Magnor, “Fast Hologram Synthesis for 3D Geometry Models using Graphics Hardware,” Proc. SPIE 5005, 266–275 (2003). [CrossRef]
- V. M. Bove, Jr., W. J. Plesniak, T. Quentmeyer, and J. Barabas, “Real-Time Holographic Video Images with Commodity PC Hardware,” Proc. SPIE Stereoscopic Displays and Applications 5664, 255–262 (2005).
- 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]
- NVIDIA, “NVIDIA CUDA Compute Unified Device Architecture Programming Guide Version 2.1,” (2008).
- R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993). [CrossRef]
- “Autodesk® ImageModeler™,” URL http://usa.autodesk.com/adsk/servlet/index?siteID=123112&id=11390028
- J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372–12386 (2008). [CrossRef] [PubMed]

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