## Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement

Optics Express, Vol. 11, Issue 12, pp. 1346-1356 (2003)

http://dx.doi.org/10.1364/OE.11.001346

Acrobat PDF (1049 KB)

### Abstract

Integral three-dimensional (3D) imaging provides full-motion parallax, unlike other conventional stereoscopy-based techniques. To maximize this advantage, a 3D system with a wide view along all directions is required. We propose and demonstrate a new integral imaging (InIm) method to enhance the viewing angle along both horizontal and vertical directions. Elemental lens switching is performed by a combination of spatial and time multiplexing by use of double display devices and orthogonal polarizations. Experimental results show that the viewing angle of the system is enhanced along all directions without any mechanical movement or any cross talk between afterimages. We believe that the proposed method has the potential to facilitate practical use of the wide-viewing InIm system.

© 2003 Optical Society of America

## 1. Introduction

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

3. 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]

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

8. T. Naemura, T. Yoshida, and H. Harashima, “3-D computer graphics based on integral photography,” Opt. Express **8**, 255–262 (2001), http://www.opticsexpress.org/ abstract.cfm?URI=OPEX-8-4-255 [CrossRef] [PubMed]

9. F. Okano, J. Arai, H. Hoshino, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. **38**, 1072–1077 (1999). [CrossRef]

## 2. Viewing-angle-enhanced integral 3D imaging

### 2.1 Limitation of viewing angle in integral imaging system

*f*-number. This fact can be figured out easily from Fig. 1.

*w*is the width of an elemental lens and

*g*is the gap between the lens array and the elemental images. The gap is determined by the relation between the object distance and the focal length of a lens array. Assuming that

*g*is approximated by the focal length of a lens array

*f*, we can find that a lens array with small

*f*-number (

*f*/

*w*) is advantageous for increasing the viewing angle. However, as

*f*-number decreases, aberration due to short focal length also increases [10

10. S.-W. Min, S. Jung, J.-H. Park, and B. Lee, “Study for wide-viewing integral photography using an aspheric Fresnel-lens array,” Opt. Eng. **41**, 2572–2576 (2002). [CrossRef]

*f*-number. Another factor that limits the viewing angle of InIm is interference through neighboring elemental lenses. During the pickup process, the elemental images captured through the corresponding elemental lens and neighboring lenses may overlap. This is because the light rays from different points may converge at the same point. Hence they cannot be separated successfully during reconstruction because the elemental images originate from different object points. Also, in the CG InIm, a similar effect can cause image overlap during the reconstruction, and the maximum viewing angle is reduced.

### 2.2 Viewing-angle enhancement by use of elemental lens switching

12. 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]

13. B. Lee, S. Jung, and J.-H. Park, “Viewing-angle-enhanced integral imaging using lens switching,” Opt. Lett. **27**, 818–820 (2002). [CrossRef]

14. S. Jung, J.-H. Park, B. Lee, and B. Javidi, “Viewing-angle-enhanced integral 3D imaging using double display devices with masks,” Opt. Eng. **41**, 2389–2390 (2002). [CrossRef]

15. S. Jung, J.-H. Park, H. Choi, and B. Lee, “Wide-viewing integral three-dimensional imaging by use of orthogonal polarization switching,” Appl. Opt. **42**, 2513–2520 (2003). [CrossRef] [PubMed]

16. J.-S. Jang and B. Javidi, “Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,” Appl. Opt. **42**, 1996–2002 (2003). [CrossRef] [PubMed]

13. B. Lee, S. Jung, and J.-H. Park, “Viewing-angle-enhanced integral imaging using lens switching,” Opt. Lett. **27**, 818–820 (2002). [CrossRef]

15. S. Jung, J.-H. Park, H. Choi, and B. Lee, “Wide-viewing integral three-dimensional imaging by use of orthogonal polarization switching,” Appl. Opt. **42**, 2513–2520 (2003). [CrossRef] [PubMed]

14. S. Jung, J.-H. Park, B. Lee, and B. Javidi, “Viewing-angle-enhanced integral 3D imaging using double display devices with masks,” Opt. Eng. **41**, 2389–2390 (2002). [CrossRef]

## 3. System configuration of the proposed method

13. B. Lee, S. Jung, and J.-H. Park, “Viewing-angle-enhanced integral imaging using lens switching,” Opt. Lett. **27**, 818–820 (2002). [CrossRef]

15. S. Jung, J.-H. Park, H. Choi, and B. Lee, “Wide-viewing integral three-dimensional imaging by use of orthogonal polarization switching,” Appl. Opt. **42**, 2513–2520 (2003). [CrossRef] [PubMed]

*P*(

*x, y, z*) and the center of the (

*n,m*)th elemental lens (

*m*, column;

*n*, row) is

*L*(

*L*), the corresponding elemental image should be displayed on the point

_{m}, L_{n}, g*E*(

*E*, 0). Here, the plane of the display panel is located at

_{x}, E_{y}*z*=0 and the lens array is separated from the display panel by

*g*. The rays passing through the (

*n,m*)th elemental lens satisfy the following equation by simple geometric calculation:

*g*is the gap between THE lens array and THE display panel. In conventional CG InIm, the possible position of the elemental image point E is restricted by following conditions:

*W*is the horizontal width and

_{h}*W*is the vertical width of an elemental lens. These restraints on the location of elemental images are relaxed in our proposed method. The elemental image point E can exist if it satisfies the following conditions:

_{v}*f*-number of the elemental lens or the size of elemental image is not so small, the interference between elemental images for the opened neighboring lenses (across the blocked lenses) can still take place. In addition to the interference between elemental images, the cross talk between the afterimages can also occur if the opened region of the elemental lens is arranged inadequately. For example, we can assume different types of masks in two subsystems as in Fig. 5(b). In fact, this scheme is not so practical to implement because we need an electrically controllable switching device such as a LC shutter array, which is not commercially available. In this scheme, mode I is for enhancing viewing angle along the horizontal direction and mode II is for enhancing viewing angle along the vertical direction. The elemental image arrays are generated in the same way as in Fig. 3; that is, they are produced to enhance the viewing angle along one direction. The possible area for displaying elemental images is within the yellow square boxes of Fig. 5(b). If the two modes are time multiplexed with a fast speed that exceeds the eye’s response time, the observer experiences the afterimage effect. There is no cross talk between systems 1 and 2 in the same mode. One may wonder whether the elemental images for the (3,3)th elemental lens of mode II-system 1 and the (2,3)th lens of mode II-system 2 have cross talk resulting from the overlapping area in Fig. 5(b); however, the observer does not experience any cross talk, for the reason illustrated in Fig. 2.

17. J.-H. Park, S. Jung, H. Choi, and B. Lee, “Viewing-angle-enhanced integral imaging by elemental image resizing and elemental lens switching,” Appl. Opt. **41**, 6875–6883 (2002). [CrossRef] [PubMed]

*z*, we pick up the object at the distance of

*z*’ that is longer than

*z*. Here we assume

*z*’=2

*z*as a matter of convenience. To obtain four sets of elemental image arrays according to the polarization and subsystem as in Fig. 4, the original elemental image arrays are magnified by

*z*’/

*z*along both horizontal and vertical directions. Then the elemental images that correspond to opened elemental lenses in Fig. 4 are collected and rearranged by the four types of situation. In Fig. 6 the pickup images distinguishable by different colors are magnified by a factor of 2 and are reassembled. In the previous case [17

17. J.-H. Park, S. Jung, H. Choi, and B. Lee, “Viewing-angle-enhanced integral imaging by elemental image resizing and elemental lens switching,” Appl. Opt. **41**, 6875–6883 (2002). [CrossRef] [PubMed]

## 4. Experimental results

## 5. Conclusions

## Acknowledgments

## References and links

1. | M. Lippmann, “Epreuves reversible donnant la sensation du relief,” J. Phys. |

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

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

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

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

6. | J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. |

7. | 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. |

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

9. | F. Okano, J. Arai, H. Hoshino, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. |

10. | S.-W. Min, S. Jung, J.-H. Park, and B. Lee, “Study for wide-viewing integral photography using an aspheric Fresnel-lens array,” Opt. Eng. |

11. | S.-H. Shin and B. Javidi, “Viewing-angle enhancement of speckle-reduced volume holographic three-dimensional display by use of integral imaging,” Appl. Opt. |

12. | 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. |

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

14. | S. Jung, J.-H. Park, B. Lee, and B. Javidi, “Viewing-angle-enhanced integral 3D imaging using double display devices with masks,” Opt. Eng. |

15. | S. Jung, J.-H. Park, H. Choi, and B. Lee, “Wide-viewing integral three-dimensional imaging by use of orthogonal polarization switching,” Appl. Opt. |

16. | J.-S. Jang and B. Javidi, “Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,” Appl. Opt. |

17. | J.-H. Park, S. Jung, H. Choi, and B. Lee, “Viewing-angle-enhanced integral imaging by elemental image resizing and elemental lens switching,” Appl. Opt. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.2990) Imaging systems : Image formation theory

**ToC Category:**

Research Papers

**History**

Original Manuscript: March 31, 2003

Revised Manuscript: May 12, 2003

Published: June 16, 2003

**Citation**

Sungyong Jung, Jae-Hyeung Park, Heejin Choi, and Byoungho Lee, "Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement," Opt. Express **11**, 1346-1356 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-12-1346

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### References

- M. Lippmann, ???Epreuves reversible donnant la sensation du relief,??? J. Phys. 7, 821-825 (1908).
- H. E. Ives, ???Optical properties of a Lippmann lenticular 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, 1598-1603 (1997). [CrossRef] [PubMed]
- B. Lee, S. Jung, S.-W. Min, and J.-H. Park, "Three-dimensional display using integral photography with dynamically variable image planes," Opt. Lett. 26, 1481-1482 (2001). [CrossRef]
- 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]
- J.-S. Jang and B. Javidi, ???Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,??? Opt. Lett. 27, 324-326 (2002). [CrossRef]
- 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]
- F. Okano, J. Arai, H. Hoshino, and I. Yuyama, ???Three-dimensional video system based on integral photography,??? Opt. Eng. 38, 1072-1077 (1999). [CrossRef]
- S.-W. Min, S. Jung, J.-H. Park, and B. Lee, "Study for wide-viewing integral photography using an aspheric Fresnel-lens array," Opt. Eng. 41, 2572-2576 (2002). [CrossRef]
- S.-H. Shin and B. Javidi, ???Viewing-angle enhancement of speckle-reduced volume holographic three-dimensional display by use of integral imaging,??? Appl. Opt. 40, 5562-5567 (2001).
- 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]
- B. Lee, S. Jung, and J.-H. Park, ???Viewing-angle-enhanced integral imaging using lens switching,??? Opt. Lett. 27, 818-820 (2002). [CrossRef]
- S. Jung, J.-H. Park, B. Lee, and B. Javidi, "Viewing-angle-enhanced integral 3D imaging using double display devices with masks," Opt. Eng. 41, 2389-2390 (2002). [CrossRef]
- S. Jung, J.-H. Park, H. Choi, and B. Lee, ???Wide-viewing integral three-dimensional imaging by use of orthogonal polarization switching,??? Appl. Opt. 42, 2513-2520 (2003). [CrossRef] [PubMed]
- J.-S. Jang and B. Javidi, ???Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,??? Appl. Opt. 42, 1996-2002 (2003). [CrossRef] [PubMed]
- J.-H. Park, S. Jung, H. Choi, and B. Lee, "Viewing-angle-enhanced integral imaging by elemental image resizing and elemental lens switching," Appl. Opt. 41, 6875-6883 (2002). [CrossRef] [PubMed]

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