## Three-dimensional electro-floating display system using an integral imaging method

Optics Express, Vol. 13, Issue 12, pp. 4358-4369 (2005)

http://dx.doi.org/10.1364/OPEX.13.004358

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### Abstract

A new-type of three-dimensional (3D) display system based on two different techniques, image floating and integral imaging, is proposed. The image floating is an antiquated 3D display technique, in which a large convex lens or a concave mirror is used to display the image of a real object to observer. The electro-floating system, which does not use a real object, requires a volumetric display part in order to present 3D moving pictures. Integral imaging is an autostereoscopic technique consisting of a lens array and a two-dimensional display device. The integral imaging method can be adapted for use in an electro-floating display system because the integrated image has volumetric characteristics within the viewing angle. The proposed system combines the merits of the two techniques such as an impressive feel of depth and the facility to assemble. In this paper, the viewing characteristics of the two techniques are defined and analyzed for the optimal design of the proposed system. The basic experiments for assembling the proposed system were performed and the results are presented. The proposed system can be successfully applied to many 3D applications such as 3D television.

© 2005 Optical Society of America

## 1. Introduction

1. T. Okoshi, “Three-dimensional displays,” Proc. IEEE **68**, pp. 548–564 (1980). [CrossRef]

5. J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. **37**, 2034–2045 (1998). [CrossRef]

## 2. Concepts of adopted display techniques

### 2.1 Image floating

_{fl_whole}is given by:

*w*is the aperture size of the floating lens,

*L*

_{fl}the floating distance and

*s*

_{fl}the size of the floating image. The reference point of the viewing angle of whole view,

*A*

_{rf}, is changed in accordance with the floating distance and the sizes of the floating lens and the floating image. The variation in the reference point makes comparisons with different systems difficult. The viewing angle with a fixed reference point can be approximately defined under the assumption that the size of floating image can be ignored and is determined by:

_{fl}is the approximate viewing angle of the floating system, the reference point of which is fixed on the floating image. In the actual system, the viewing angle obtained by Eq. (2) denotes the angular region where the observer can see more than half of the floating image.

*s*

_{ob}is the size of the object,

*M*

_{fl}the magnification factor of the floating lens,

*f*

_{fl}the focal length of the floating lens and

*L*

_{ob}the object distance. According to Eq. (3), the magnification factor is set to 1 when the object distance and the floating distance are equal and twice the focal length. When the objects are plural and their longitudinal locations are different, the magnification factor for each object is determined individually according to Eq. (3). In the floating display system, the distance between the floating images can be changed from that between the objects, but the sequence of the floating images is identical with that of the objects.

### 2.2 Integral imaging

7. H. Liao, M. Iwahara, N. Hata, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express **12**, 1067–1076 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1067. [CrossRef] [PubMed]

3. H. E. Ives, “Optical properties of a Lippmann lenticulated sheet,” J. Opt. Soc. Am. **21**, 171–176 (1931). [CrossRef]

5. J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. **37**, 2034–2045 (1998). [CrossRef]

*z*

_{m}can be expressed as [9

9. S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Japanese J. Appl. Phys. **44**, pp. L71–L74 (2005). [CrossRef]

*l*is the position of the central depth plane of the integrated image,

*g*the gap between the lens array and the display device,

*P*

_{L}the elemental lens pitch, and

*P*

_{X}the pixel size of the display device.

10. H. Choi, Y. Kim, J.-H. Park, S. Jung, and B. Lee, “Improved analysis on the viewing angle of integral imaging,” Appl. Opt. **44**, pp. 2311–2317 (2005). [CrossRef] [PubMed]

11. J.-H. Park, S.-W. Min, S. Jung, and B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. **40**, pp. 5217–5232 (2001). [CrossRef]

_{ii}is the viewing angle of the integral imaging system. The tendency of the actual viewing angle corresponds to the result of Eq. (5).

9. S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Japanese J. Appl. Phys. **44**, pp. L71–L74 (2005). [CrossRef]

11. J.-H. Park, S.-W. Min, S. Jung, and B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. **40**, pp. 5217–5232 (2001). [CrossRef]

13. J.-S. Jang, F. Jin, and B. Javidi, “Three-dimensional integral imaging with large depth of focus by use of real and virtual image fields,” Opt. Lett. **28**, pp. 1421–1423 (2003). [CrossRef] [PubMed]

9. S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Japanese J. Appl. Phys. **44**, pp. L71–L74 (2005). [CrossRef]

12. B. Lee, S. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. **26**, pp. 1481–1482 (2001). [CrossRef]

19. J. S. Jang, Yong-Seok Oh, and B. Javidi, “Spatiotemporally multiplexed integral imaging projector for large-scale high resolution three-dimensional display,” Opt. Express **12**, pp. 557–563 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-557 [CrossRef] [PubMed]

20. H. Choi, J.-H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in *Technical Digest of The 16th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2003)*, Tucson, Arizona, USA, Oct.2003, vol. 2, pp. 730–731. [CrossRef]

24. H. Choi, J.-H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” Japanese J. Appl. Phys. **43**, pp. 5330–5336 (2004). [CrossRef]

## 3. Electro-floating display system using integral imaging method

### 3.1 Experimental setup

7. H. Liao, M. Iwahara, N. Hata, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express **12**, 1067–1076 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1067. [CrossRef] [PubMed]

### 3.2 Experimental results

*t*

_{fl}can be obtained by:

*M*is the magnification factor for the central depth plane. The variations in image depth are different for the images in front of and behind the central depth plane, as shown in Fig. 9. The distance between the front image and the center image, Δ

*t*

_{2}, is greater than that between the center image and the rear image, Δ

*t*

_{1}. In the experiment described in Fig. 8, the image depth of the integrated image is about 40 mm. As a result, the thickness of the floating image is about 40.5 mm according to Eq. (6). In this case, the thickness of the floating image is not greatly changed from the image depth of the integrated image because the magnification factor is 1.

*f*-number of the elemental lens and the central depth plane of the integral imaging system. The flipping distance

*d*, as shown in Fig. 10, is obtained by:

*f*

_{ii}is the focal length of the lens array. Because the flipping distance is not affected by the size of the integrated image, the location of the flipped image is also independent of image size.

## 4. Conclusions

## Acknowledgments

## References and links

1. | T. Okoshi, “Three-dimensional displays,” Proc. IEEE |

2. | G. Lippmann, “La photographie integrale,” Comptes-Rendus |

3. | H. E. Ives, “Optical properties of a Lippmann lenticulated sheet,” J. Opt. Soc. Am. |

4. | F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. |

5. | J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. |

6. | S.-W. Min, J. Kim, and B. Lee, “Three-dimensional electro-floating display system based on integral imaging technique,” in |

7. | H. Liao, M. Iwahara, N. Hata, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express |

8. | S.-W. Min, S. Jung, J.-H. Park, and B. Lee, “Computer-generated integral photography,” in |

9. | S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Japanese J. Appl. Phys. |

10. | H. Choi, Y. Kim, J.-H. Park, S. Jung, and B. Lee, “Improved analysis on the viewing angle of integral imaging,” Appl. Opt. |

11. | J.-H. Park, S.-W. Min, S. Jung, and B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. |

12. | B. Lee, S. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. |

13. | J.-S. Jang, F. Jin, and B. Javidi, “Three-dimensional integral imaging with large depth of focus by use of real and virtual image fields,” Opt. Lett. |

14. | B. Lee, S. Jung, J. H. Park, and S. W. Min, “Viewing-angle-enhanced integral imaging using lens switching,” in |

15. | J. S. Jang and B. Javidi, “Improved viewing resolution of 3-D integral imaging with nonstationary micro-optics,” Opt. Lett. |

16. | B. Lee, S. Jung, and J.-H. Park, “Viewing-angle-enhanced integral imaging by lens switching,” Opt. Lett. |

17. | J. S. Jang and B. Javidi, “Three dimensional synthetic aperture integral imaging,” Opt. Lett. |

18. | H. Choi, S.-W. Min, S. Jung, J.-H. Park, and B. Lee, “Multiple-viewing-zone integral imaging using a dynamic barrier array for three-dimensional displays,” Opt. Express |

19. | J. S. Jang, Yong-Seok Oh, and B. Javidi, “Spatiotemporally multiplexed integral imaging projector for large-scale high resolution three-dimensional display,” Opt. Express |

20. | H. Choi, J.-H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” in |

21. | J. S. Jang and B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes,” Opt. Lett. |

22. | Y. Kim, J.-H. Park, H. Choi, S. Jung, S.-W Min, and B. Lee, “Viewing-angle-enhanced integral imaging system using a curved lens array,” Opt. Express |

23. | S.-W. Min, J. Kim, and B. Lee, “Wide-viewing projection-type integral imaging system with an embossed screen,” Opt. Lett. |

24. | H. Choi, J.-H. Park, J. Hong, and B. Lee, “Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display,” Japanese J. Appl. Phys. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.2990) Imaging systems : Image formation theory

(220.2740) Optical design and fabrication : Geometric optical design

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 6, 2005

Revised Manuscript: May 12, 2005

Published: June 13, 2005

**Citation**

Sung-Wook Min, Minsoo Hahn, Joohwan Kim, and Byoungho Lee, "Three-dimensional electro-floating display system using an integral imaging method," Opt. Express **13**, 4358-4369 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-12-4358

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### References

- T. Okoshi, "Three-dimensional displays," Proc. IEEE 68, pp. 548-564 (1980). [CrossRef]
- G. Lippmann, "La photographie integrale," Comptes-Rendus 146, 446-451, Academie des Sciences (1908).
- H. E. Ives, "Optical properties of a Lippmann lenticulated sheet," J. Opt. Soc. Am. 21, 171-176 (1931). [CrossRef]
- F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Real-time pickup method for a three-dimensional image based on integral photography," Appl. Opt. 36, pp. 1598-1603 (1997). [CrossRef] [PubMed]
- J. Arai, F. Okano, H. Hoshino, and I. Yuyama, "Gradient-index lens-array method based on real-time integral photography for three-dimensional images," Appl. Opt. 37, 2034�??2045 (1998). [CrossRef]
- S.-W. Min, J. Kim, and B. Lee, "Three-dimensional electro-floating display system based on integral imaging technique," in Stereoscopic Displays and Applications XVI, Electronics Imaging, paper 5664A-37, San Jose, CA (2005).
- H. Liao, M. Iwahara, N. Hata, and T. Dohi, "High-quality integral videography using a multiprojector," Opt. Express 12, 1067-1076 (2004), <a href = "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1067.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1067.<a/> [CrossRef] [PubMed]
- S.-W. Min, S. Jung, J.-H. Park, and B. Lee, "Computer-generated integral photography," in Proceedings of The 6th International Workshop on 3-D Imaging Media Technology, Seoul, Korea, July 2000, pp. 21-28.
- S.-W. Min, J. Kim, and B. Lee, "New characteristic equation of three-dimensional integral imaging system and its applications," Japanese J. Appl. Phys. 44, pp. L71-L74 (2005). [CrossRef]
- H. Choi, Y. Kim, J.-H. Park, S. Jung, and B. Lee, "Improved analysis on the viewing angle of integral imaging," Appl. Opt. 44, pp. 2311-2317 (2005). [CrossRef] [PubMed]
- J.-H. Park, S.-W. Min, S. Jung, and B. Lee, "Analysis of viewing parameters for two display methods based on integral photography," Appl. Opt. 40, pp. 5217-5232 (2001). [CrossRef]
- B. Lee, S. Jung, S.-W. Min, and J.-H. Park, "Three-dimensional display by use of integral photography with dynamically variable image planes," Opt. Lett. 26, pp. 1481-1482 (2001). [CrossRef]
- J.-S. Jang, F. Jin, and B. Javidi, "Three-dimensional integral imaging with large depth of focus by use of real and virtual image fields," Opt. Lett. 28, pp. 1421-1423 (2003). [CrossRef] [PubMed]
- B. Lee, S. Jung, J. H. Park, and S. W. Min, "Viewing-angle-enhanced integral imaging using lens switching," in Stereoscopic Displays and Virtual Reality Systems IX, A. J. Woods, J. O. Merritt, S. A. Benton, and M. T. Bolas, eds., Proc. SPIE 4660, pp. 146-154 (2002).
- J. S. Jang and B. Javidi, "Improved viewing resolution of 3-D integral imaging with nonstationary micro-optics," Opt. Lett. 27, pp. 324-326 (2002). [CrossRef]
- B. Lee, S. Jung, and J.-H. Park, "Viewing-angle-enhanced integral imaging by lens switching," Opt. Lett. 27, pp. 818-820 (2002). [CrossRef]
- J. S. Jang and B. Javidi, "Three dimensional synthetic aperture integral imaging," Opt. Lett. 27, pp. 1144-1146 (2002). [CrossRef]
- H. Choi, S.-W. Min, S. Jung, J.-H. Park, and B. Lee, "Multiple-viewing-zone integral imaging using a dynamic barrier array for three-dimensional displays," Opt. Express 11, pp. 927-932 (2003), <a href ="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-927.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-927.<a/> [CrossRef] [PubMed]
- J. S. Jang, Yong-Seok Oh, and B. Javidi, "Spatiotemporally multiplexed integral imaging projector for large-scale high resolution three-dimensional display," Opt. Express 12, pp. 557 - 563 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-557.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-557.<a/> [CrossRef] [PubMed]
- H. Choi, J.-H. Park, J. Hong, and B. Lee, "Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display," in Technical Digest of The 16th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2003), Tucson, Arizona, USA, Oct. 2003, vol. 2, pp. 730-731. [CrossRef]
- J. S. Jang and B. Javidi, " Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes," Opt. Lett. 28, pp. 1924-1926 (2003). [CrossRef] [PubMed]
- Y. Kim, J.-H. Park, H. Choi, S. Jung, S.-W, Min, and B. Lee, "Viewing-angle-enhanced integral imaging system using a curved lens array," Opt. Express 12, pp. 421-429 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-421.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-421.<a/> [CrossRef] [PubMed]
- S.-W. Min, J. Kim, and B. Lee, "Wide-viewing projection-type integral imaging system with an embossed screen," Opt. Lett. 29, pp. 2420-2422 (2004). [CrossRef] [PubMed]
- H. Choi, J.-H. Park, J. Hong, and B. Lee, "Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display," Japanese J. Appl. Phys. 43, pp. 5330-5336 (2004). [CrossRef]

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