## Resolution-enhanced three-dimension/two-dimension convertible display based on integral imaging

Optics Express, Vol. 13, Issue 6, pp. 1875-1884 (2005)

http://dx.doi.org/10.1364/OPEX.13.001875

Acrobat PDF (573 KB)

### Abstract

A scheme for the resolution-enhancement of a three-dimension/two-dimension convertible display based on integral imaging is proposed. The proposed method uses an additional lens array, located between the conventional lens array and a collimating lens. Using the additional lens array, the number of the point light sources is increased far beyond the number of the elemental lenses constituting the lens array, and, consequently, the resolution of the generated 3D image is enhanced. The principle of the proposed method is described and verified experimentally.

© 2005 Optical Society of America

## 1. Introduction

2. 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**, 1598–1603 (1997). [CrossRef] [PubMed]

7. S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express **12**, 483–491 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483. [CrossRef] [PubMed]

8. L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. **40**, 5592–5599 (2001). [CrossRef]

16. 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**, 1924–1926 (2003). [CrossRef] [PubMed]

17. J.-H. Park, H.-R. Kim, Y. Kim, J. Kim, J. Hong, S.-D. Lee, and B. Lee, “Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging,” Opt. Lett. **29**, 2734–2736 (2004). [CrossRef] [PubMed]

17. J.-H. Park, H.-R. Kim, Y. Kim, J. Kim, J. Hong, S.-D. Lee, and B. Lee, “Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging,” Opt. Lett. **29**, 2734–2736 (2004). [CrossRef] [PubMed]

## 2. 3D/2D convertible integral imaging and resolution limitation

## 3. Configuration of the proposed method

17. J.-H. Park, H.-R. Kim, Y. Kim, J. Kim, J. Hong, S.-D. Lee, and B. Lee, “Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging,” Opt. Lett. **29**, 2734–2736 (2004). [CrossRef] [PubMed]

*f*

_{1}and elemental lens pitch

*φ*

_{1}forms the first point light source array at its focal plane. Each elemental lens with pitch

*φ*

_{2}and focal length

*f*

_{2}in the second lens array images these first point light sources at its image plane. Note that not all of the first point light sources are imaged by each elemental lens in the second lens array because the diverging angle of the light rays from each first point light source is limited. The diverging angle of each first point light source,

*ψ*

_{1}, is given by

*k*-th elemental lens in the first lens array,

*y*

_{1,k}, can be represented by

*y*

_{1,k}=

*kφ*

_{1}, it illuminates the second lens array’s elemental lenses that satisfy

*l*is the distance between the second lens array and the focal plane of the first lens array, and

*q*is the index of the elemental lenses in the second lens array. Or equivalently, the

*q*-th elemental lens in the second lens array is illuminated by the first point light sources whose index

*k*satisfies

*k*≤

_{l}*k*≤

*k*where

_{h}*k*and

_{l}*k*are given by

_{h}*k*≤

_{l}*k*≤

*k*) are imaged into the second point light sources by the

_{h}*q*-th elemental lens in the second lens array at

*g*is the location of the image plane of the second lens array which is given by

*g*is slightly larger than

*f*

_{2}as indicated by Eq. (7), the viewing angle of the proposed method can be somewhat narrower than conventional method where

*g*=

*f*. Note that the diverging directions of the second point light sources are, in general, not parallel but vary depending on the relative position between the optic axis of the corresponding elemental lens in the second lens array and the second point light sources, as shown in Fig. 4 (shaded region). This non-parallel diverging direction is another factor in reducing the viewing angle of the proposed method.

*y*

_{2,k,q}=(

*q*+0.5)

*φ*

_{2},

*qφ*

_{2}, (

*q*-0.5)

*φ*

_{2}. As a result, at every position of (

*q*±0.5)

*φ*

_{2}, the point light sources imaged by two neighboring elemental lenses in the second lens array are overlapped. Therefore a uniform point light source array can be obtained that is twice as dense. Note that at the overlapping point light sources the diverging regions (shaded region in Fig. 5) are not overlapped but are patched constructively. Therefore the reduction in viewing angle due to non-parallel diverging directions is effectively alleviated.

## 4. Experimental results

**29**, 2734–2736 (2004). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgment

## References and links

1. | G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. |

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

3. | S. Manolache, A. Aggoun, M. McCormick, N. Davies, and S. Y. Kung, “Analytical model of a three-dimensional integral image recording system that uses circular and hexagonal-based spherical surface microlenses,” J. Opt. Soc. Am. A. |

4. | T. Naemura, T. Yoshida, and H. Harashima, “3-D computer graphics based on integral photography,” Opt. Express |

5. | J.-H. Park, Y. Kim, J. Kim, S.-W. Min, and B. Lee, “Three-dimensional display scheme based on integral imaging with three-dimensional information processing,” Opt. Express |

6. | S.-H. Shin and B. Javidi, “Speckle reduced three-dimensional volume holographic display using integral imaging,” Appl. Opt. |

7. | S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express |

8. | L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. |

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

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

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

12. | Y. Kim, J.-H. Park, S.-W. Min, S. Jung, H. Choi, and B. Lee, “Wide-viewing-angle integral three-dimensional imaging system by curving a screen and a lens array,” Appl. Opt. |

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

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

15. | J. Hong, J.-H. Park, S. Jung, and B. Lee, “A depth-enhanced integral imaging by use of optical path control,” Opt. Lett. |

16. | 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. |

17. | J.-H. Park, H.-R. Kim, Y. Kim, J. Kim, J. Hong, S.-D. Lee, and B. Lee, “Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging,” Opt. Lett. |

**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: January 11, 2005

Revised Manuscript: February 24, 2005

Published: March 21, 2005

**Citation**

Jae-Hyeung Park, Joohwan Kim, Yunhee Kim, and Byoungho Lee, "Resolution-enhanced three-dimension / two-dimension convertible display based on integral imaging," Opt. Express **13**, 1875-1884 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1875

Sort: Journal | Reset

### References

- G. Lippmann, �??La photographie integrale,�?? Comptes-Rendus Acad. Sci. 146, 446-451 (1908).
- 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, 1598-1603 (1997). [CrossRef] [PubMed]
- S. Manolache, A. Aggoun, M. McCormick, N. Davies, and S. Y. Kung, �??Analytical model of a three-dimensional integral image recording system that uses circular and hexagonal-based spherical surface microlenses,�?? J. Opt. Soc. Am. A. 18, 1814-1821 (2001). [CrossRef]
- T. Naemura, T. Yoshida, and H. Harashima, �??3-D computer graphics based on integral photography,�?? Opt. Express 8, 255-262 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-4-255">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-4-255</a>. [CrossRef] [PubMed]
- J.-H. Park, Y. Kim, J. Kim, S.-W. Min, and B. Lee, "Three-dimensional display scheme based on integral imaging with three-dimensional information processing," Opt. Express 12, 6020-6032 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-6020">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-6020</a>. [CrossRef] [PubMed]
- S.-H. Shin and B. Javidi, �??Speckle reduced three-dimensional volume holographic display using integral imaging,�?? Appl. Opt. 41, 2644�??2649 (2002). [CrossRef] [PubMed]
- S.-H. Hong, J.-S. Jang, and B. Javidi, "Three-dimensional volumetric object reconstruction using computational integral imaging," Opt. Express 12, 483-491 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-483</a>. [CrossRef] [PubMed]
- L. Erdmann and K. J. Gabriel, �??High-resolution digital integral photography by use of a scanning microlens array,�?? Appl. Opt. 40, 5592-5599 (2001). [CrossRef]
- 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]
- B. Lee, S. Jung, and J. -H. Park, �??Viewing-angle-enhanced integral imaging using lens switching,�?? Opt. Lett. 27, 818-820 (2002). [CrossRef]
- J. S. Jang, Y.-S. Oh, and B. Javidi, �??Spatiotemporally multiplexed integral imaging projector for large-scale high resolution three-dimensional display,�?? Opt. Express 12, 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]
- Y. Kim, J.-H. Park, S.-W. Min, S. Jung, H. Choi, and B. Lee, "Wide-viewing-angle integral three-dimensional imaging system by curving a screen and a lens array," Appl. Opt. 44, 546-552 (2005). [CrossRef] [PubMed]
- J. S. Jang, and B. Javidi, �??Three dimensional synthetic aperture integral imaging,�?? Opt. Lett. 27, 1144-1146 (2002). [CrossRef]
- J. S. Jang, and B. Javidi, �??Improved viewing resolution of 3-D integral imaging with nonstationary micro-optics,�?? Opt. Lett. 27, 324-326 (2002). [CrossRef]
- J. Hong, J.-H. Park, S. Jung and B. Lee, "A depth-enhanced integral imaging by use of optical path control," Opt. Lett. 29, 1790-1792 (2004). [CrossRef] [PubMed]
- 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, 1924-1926 (2003). [CrossRef] [PubMed]
- J.-H. Park, H.-R. Kim, Y. Kim, J. Kim, J. Hong, S.-D. Lee, and B. Lee, "Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging," Opt. Lett. 29, 2734-2736 (2004). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.