## Floated image mapping for integral floating display

Optics Express, Vol. 16, Issue 12, pp. 8549-8556 (2008)

http://dx.doi.org/10.1364/OE.16.008549

Acrobat PDF (454 KB)

### Abstract

A computer generation method of elemental image for integral floating display, named as floated image mapping, is proposed. The concept of floated integral imaging system is introduced to overcome the problems coming from the conventional viewpoint of the integral floating display. Both analysis and experimental results which support and verify the functional contributions of the floated image mapping are presented. The expansion of expressible depth range and the reduction of computation time for the real time processing are main contributions of the proposed algorithm.

© 2008 Optical Society of America

## 1. Introduction

1. S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Express **13**, 4358–4369 (2005). [CrossRef]

7. Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. **17**, 1683–1684, (1978). [CrossRef]

12. S.-W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, “Enhanced image mapping algorithm for computer-generated integral imaging system,” Jpn. J. Appl. Phys. **45**, L744–L747 (2006). [CrossRef]

13. K. S. Park, S.-W. Min, and Y. Cho, “Viewpoint vector rendering for efficient elemental image generation,” IEICE Trans. Inf. & Syst. **E90-D**, 233–241 (2007). [CrossRef]

## 2. Computer generation of elemental image of integral floating display

### 2.1. Principle of the method

12. S.-W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, “Enhanced image mapping algorithm for computer-generated integral imaging system,” Jpn. J. Appl. Phys. **45**, L744–L747 (2006). [CrossRef]

*d*and

_{di}*d*are the distance from the 2D display of the integral imaging to the floating device and that from the 2D display of the floated integral imaging system to the floating device, while

_{df}*φ*and

_{pi}*φ*are the pixel pitch of the 2D display of the integral imaging and that of the floated integral imaging system, respectively. The image of the 2D display is named as a floated 2D display and is located between the floating device and the floated lens array. The floated lens array and the floated 2D display together are named as a floated integral imaging system. An elemental image of the floating image can be generated using this floated integral imaging system.

_{pf}### 2.2. Merits of the proposed method

## 3. Experimental results

*z*-value in the animation indicates the distance from the floating device. Notice that the yellow fish is well integrated although it is located 150mm away from the floating lens, thus in the retro-floating range. Figure 9 shows the still images when the diffuser is placed at the distance of 150mm, 175mm and 200mm from the floating lens, which shows that all the fishes are integrated at the desired locations.

## 4. Conclusion

## References and links

1. | S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Express |

2. | J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Express |

3. | G. Lippmann, “La photographie integrale,” C. -R. Acad. Sci. |

4. | C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. |

5. | H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A |

6. | H. Liao, T. Dohi, and M. Iwahara, “Improved viewing resolution of integral videography by use of rotated prism sheets,” Opt. Express |

7. | Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. |

8. | S.-W. Min, S. Jung, J.-H. Park, and B. Lee “Three-dimensional display system based on computergenerated integral photography,” Stereoscopic Displays and Virtual Reality Systems VIII, Photonics West, San Jose, CA, USA, Proc. SPIE. |

9. | S. Nakajima, K. Nakamura, K. Masamune, I. Sakuma, and T. Dohi, “Three-dimensional medical imaging display with computer-generated integral photography,” Comput. Med. Image Graph. |

10. | D.-H. Shin, E.-S. Kim, and B. Lee, “Computational Reconstruction of Three-Dimensional Objects in Integral Imaging using Lenslet Array,” Jpn. J. Appl. Phys. |

11. | J.-B. Hyun, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Curved computational integral imaging reconstruction technique for resolution-enhanced display of three-dimensional object images,” Appl. Opt. |

12. | S.-W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, “Enhanced image mapping algorithm for computer-generated integral imaging system,” Jpn. J. Appl. Phys. |

13. | K. S. Park, S.-W. Min, and Y. Cho, “Viewpoint vector rendering for efficient elemental image generation,” IEICE Trans. Inf. & Syst. |

14. | G. Park, S.-W Cho, J. Kim, Y. Kim, H. Choi, J. Hahn, and B. Lee, “Pickup method from OpenGL by reverse projection matrix for real-orthoscopic integral imaging,” Digital Holography and Three-Dimensional Imaging, Vancouver, Canada, paper DTuA8, June 2007. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.2990) Imaging systems : Image formation theory

**ToC Category:**

Image Processing

**History**

Original Manuscript: April 8, 2008

Revised Manuscript: May 19, 2008

Manuscript Accepted: May 23, 2008

Published: May 27, 2008

**Citation**

Joohwan Kim, Sung-Wook Min, and Byoungho Lee, "Floated image mapping for integral floating display," Opt. Express **16**, 8549-8556 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8549

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### References

- S.-W. Min, M. Hahn, J. Kim, and B. Lee, "Three-dimensional electro-floating display system using an integral imaging method," Opt. Express 13, 4358-4369 (2005). [CrossRef]
- J. Kim, S.-W. Min, and B. Lee, "Viewing region maximization of an integral floating display through location adjustment of viewing window," Opt. Express 15, 13023-13034 (2007). [CrossRef] [PubMed]
- G. Lippmann, "La photographie integrale," C. -R. Acad. Sci. 146, 446-451 (1908).
- C. B. Burckhardt, "Optimum parameters and resolution limitation of integral photography," J. Opt. Soc. Am. 58, 71-76 (1967). [CrossRef]
- H. Hoshino, F. Okano, H. Isono, and I. Yuyama, "Analysis of resolution limitation of integral photography," J. Opt. Soc. Am. A 15, 2059-2065 (1998). [CrossRef]
- H. Liao, T. Dohi, and M. Iwahara, "Improved viewing resolution of integral videography by use of rotated prism sheets," Opt. Express 15, 4814-4822 (2007). [CrossRef] [PubMed]
- Y. Igarashi, H. Murata, and M. Ueda, "3D display system using a computer generated integral photography," Jpn. J. Appl. Phys. 17, 1683-1684, (1978). [CrossRef]
- S.-W. Min, S. Jung, J.-H. Park, and B. Lee "Three-dimensional display system based on computer-generated integral photography," Stereoscopic Displays and Virtual Reality Systems VIII, Photonics West, San Jose, CA, USA, Proc. SPIE. 4297, 187-195, Jan. 2001. [CrossRef]
- S. Nakajima, K. Nakamura, K. Masamune, I. Sakuma, and T. Dohi, "Three-dimensional medical imaging display with computer-generated integral photography," Comput. Med. Image Graph. 25, 235-241 (2001). [CrossRef]
- D.-H. Shin, E.-S. Kim, and B. Lee, "Computational Reconstruction of Three-Dimensional Objects in Integral Imaging using Lenslet Array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005). [CrossRef]
- J.-B. Hyun, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Curved computational integral imaging reconstruction technique for resolution-enhanced display of three-dimensional object images," Appl. Opt. 46, 7697-7708 (2007). [CrossRef] [PubMed]
- S.-W. Min, K. S. Park, B. Lee, Y. Cho, and M. Hahn, "Enhanced image mapping algorithm for computer-generated integral imaging system," Jpn. J. Appl. Phys. 45, L744-L747 (2006). [CrossRef]
- K. S. Park, S.-W. Min, and Y. Cho, "Viewpoint vector rendering for efficient elemental image generation," IEICE Trans. Inf. & Syst.E 90-D, 233-241 (2007). [CrossRef]
- G. Park, S.-W Cho J. Kim, Y. Kim, H. Choi, J. Hahn, and B. Lee, "Pickup method from OpenGL by reverse projection matrix for real-orthoscopic integral imaging," Digital Holography and Three-Dimensional Imaging, Vancouver, Canada, paper DTuA8, June 2007.

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