## Undistorted pickup method of both virtual and real objects for integral imaging

Optics Express, Vol. 16, Issue 18, pp. 13969-13978 (2008)

http://dx.doi.org/10.1364/OE.16.013969

Acrobat PDF (449 KB)

### Abstract

Optically corrected pickup method of both virtual and real objects for integral imaging is proposed. The proposed pickup system has imbricate view volumes which are equivalent to those in the integral imaging display. Therefore, there is no distortion resulting from the discord in directions of elemental image between pickup and display. In this system, the view volumes are transformed by 4*f* optics and the directions of view are defined by lens array and telecentric lens. Without computational cost for compensation, the pickup of both real and virtual objects is confirmed experimentally.

© 2008 Optical Society of America

## 1. Introduction

3. B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” *in Digital Holography and Three-Dimensional Display*, T.-C. Poon, ed. (Springer, 2006), pp. 333–378. [CrossRef]

4. 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]

6. D.-H. Shin, B. Lee, and E.-S. Kim, “Parallax-controllable large-depth integral imaging scheme using lenslet array,” Jpn. J. Appl. Phys. **46**, 5184–5186 (2007). [CrossRef]

7. 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]

8. 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]

9. 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]

10. 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). [CrossRef] [PubMed]

11. R. Martinez-Cuenca, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted Integral image display,” Opt. Express **14**, 9657–9663 (2006). [CrossRef] [PubMed]

14. S.-W. Min, J. Hong, and B. Lee, “Analysis of an optical depth converter used in a three-dimensional integral imaging system,” Appl. Opt. **43**, 4539–4549 (2004). [CrossRef] [PubMed]

16. J.-S. Jang and B. Javidi, “Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution,” Opt. Eng. **41**, 2568–2571 (2002). [CrossRef]

17. J.-S. Jang and B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Express **12**, 1077–1083 (2004). [CrossRef] [PubMed]

18. J. Arai, H. Kawai, M. Kawakita, and F. Okano, “Depth-control method for integral imaging,” Opt. Lett. **33**, 279–281 (2008). [CrossRef] [PubMed]

19. J.-S. Jang and B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. **42**, 1869–1870 (2003). [CrossRef]

20. J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. **45**, 9066–9078 (2006). [CrossRef] [PubMed]

*et al*[22

22. M. Martinez-Corral, B. Javidi, R. Martinez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express **13**, 9175–9180 (2005). [CrossRef] [PubMed]

## 2. Distortion problem between pickup and integral imaging

*is given by*

_{display}*w*and

*f*mean the width of an elemental image and the focal length of each lens respectively. For the

*i*th lens, the corresponding sub-view volume is given by

*x*

*,*

_{ci}*z*

*) is the center position of aperture stop for the*

_{ci}*i*th lens. That is, the individual sub-view volume generated by a single lens is shaped as two equilateral triangles with the vertexes in contact. And the direction of elemental image is parallel to the optical axis.

## 3. Pickup method with imbricate view volumes

*f*optics and a telecentric lens. In this proposed system, the imbricate view volumes are transformed by 4

*f*optics and the directions of view are defined by the telecentric lens normal to the lens array plane. Therefore, pickup directions of elemental image are parallel to one another. Figure 4 shows a schematic of the proposed pickup system with imbricate view volumes. The individual sub-view volume is shaped as two equilateral triangles with the vertexes in contact and each sub-volume is overlapped with others. These view volumes are equivalent to those of InIm display. In these imbricate view volumes, the virtual and real fields are divided by the critical plane and this critical plane is located at the focal plane of the front lens in 4

*f*optics.

*f*optics and the lens array is aligned at the position where the every view gets close and contacts with adjacent others. The distance between the back lens in 4

*f*optics and the lens array is the sum of the focal lengths of two serial lenses. In Fig. 4,

*f*

_{1}and

*f*

_{2}represent the focal lengths of front and back lenses in 4

*f*optics respectively. And

*f*

_{3}is the focal length of lens array. In this proposed pickup, the viewing angle is defined by

*w*

_{3}means the width of aperture stop of an individual lens in the lens array. Therefore, in order to keep the proper relation between pickup and InIm display, two viewing angles, θ

*and θ*

_{display}*, should agree with each other.*

_{pickup}*f*optics, the rays passing through demanded elemental images are disordered when they arrive at the pickup plane. Therefore, a rotation process is necessary to organize the set of elemental images for InIm display. By the rotation process each elemental image is rotated 180 degrees around its center. This process simply changes the coordinates of an individual elemental image in reverse order and requires negligible computational costs.

*f*optics are composed of two Fresnel lenses with focal length of 152.4

*mm*, and the lens array has 1.0

*mm*periods and 3.3

*mm*focal lengths. The telecentric lens with 0.09×magnification is applied, which was manufactured by Edmund optics. The CCD is Sony XCD-SX90CR with 3.75

*µ m*pixel size. Therefore, the resolutions of each elemental image are 24×24 pixels.

## 4. Experimental results

*z*=0

*mm*is marked with a letter ‘C’. And the object with a letter ‘M’ is able to move from the virtual object position,

*z*=-30mm to the real object position,

*z*=30mm.

*f*optics is replaced with a single Fresnel lens with focal length of 152.4

*mm*. This Fresnel lens is the large convex lens controlling the position of critical plane. Figure 10 shows pickup images with the conventional method. In Figs. 10(a)–(c), the object marked with ‘M’ is positioned at

*z*=-30

*mm*,

*z*=0

*mm*, and

*z*=30

*mm*respectively. Figs. 10(d) and (e) show the elemental images of the virtual and real objects respectively. The elemental images of the movable object are shown in (f) and (g) where they are the parts of (a) and (c) respectively. In this conventional method, the letters on virtual and real objects are hard to be recognized. These phenomena result from the perspective error of a large convex lens.

*f*system shows much smaller perspective errors in elemental images than the conventional method.

*z*=-30

*mm*to

*z*=30

*mm*. On the other hand, in the proposed method, the reconstructed images show virtual and real objects with the same size. And the size of movable object is also unaffected by its position. Therefore it is proved that the distortion which occurs in the conventional pickup method cannot be found in the proposed method.

*z*=-30

*mm*, it is swinging with the constant gap between itself and the letter ‘V’. When it is positioned at

*z*=30

*mm*, it is swinging with the constant gap between itself and the letter ‘R’. As expected, the proposed pickup method provides correct perspective views according to the change of the position of the letter ‘M’.

## 5. Conclusion

*f*optics and telecentric lens and it has the same imbricate view volumes as those of InIm display. In this system, there is no distortion resulting from the discord in directions of elemental image between pickup and display. Hence additional numerical compensations are unnecessary. Even though the rotation process of each elemental image is required, this simple calculation needs negligible computational cost. Therefore, this proposed method makes real-time pickup feasible without the apparent distortion. It is expected that the proposed technique can be one of the most promising real-time pickup techniques for InIm.

## Acknowledgment

## References and links

1. | B. Javidi and F. Okano, eds., |

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

3. | B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” |

4. | 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. |

5. | 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. |

6. | D.-H. Shin, B. Lee, and E.-S. Kim, “Parallax-controllable large-depth integral imaging scheme using lenslet array,” Jpn. J. Appl. Phys. |

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

8. | 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. |

9. | 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. |

10. | 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 |

11. | R. Martinez-Cuenca, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted Integral image display,” Opt. Express |

12. | R. Martínez-Cuenca, H. Navarro, G. Saavedra, B. Javidi, and M. Martinez-Corral, “Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system,” Opt. Express |

13. | J. Hahn, Y. Kim, E.-H. Kim, and B. Lee, “Camera with inverted perspective projection view volume array for integral imaging,” The 6th International Conference on Optics-Photonics Design and Fabrication, Taipei, Taiwan , pp. 553–554, June 2008. |

14. | S.-W. Min, J. Hong, and B. Lee, “Analysis of an optical depth converter used in a three-dimensional integral imaging system,” Appl. Opt. |

15. | F. Okano and J. Arai, “Optical shifter for a three-dimensional image by use of a gradient-index lens array,” Appl. Opt. |

16. | J.-S. Jang and B. Javidi, “Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution,” Opt. Eng. |

17. | J.-S. Jang and B. Javidi, “Three-dimensional projection integral imaging using micro-convex-mirror arrays,” Opt. Express |

18. | J. Arai, H. Kawai, M. Kawakita, and F. Okano, “Depth-control method for integral imaging,” Opt. Lett. |

19. | J.-S. Jang and B. Javidi, “Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging,” Opt. Eng. |

20. | J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. |

21. | F. Okano, “Applications of Integral Photography for Real-Time Imaging,” |

22. | M. Martinez-Corral, B. Javidi, R. Martinez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.2990) Imaging systems : Image formation theory

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: June 24, 2008

Revised Manuscript: July 29, 2008

Manuscript Accepted: August 22, 2008

Published: August 25, 2008

**Citation**

Joonku Hahn, Youngmin Kim, Eun-Hee Kim, and Byoungho Lee, "Undistorted pickup method of both virtual and real objects for integral imaging," Opt. Express **16**, 13969-13978 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13969

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### References

- B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer, 2002).
- H. Liao, M. Iwahara, H. Nobuhiko, and T. Dohi, "High-quality integral videography using a multiprojector," Opt. Express 12, 1067-1076 (2004). [CrossRef] [PubMed]
- B. Lee, J.-H. Park, and S.-W. Min, "Three-dimensional display and information processing based on integral imaging," in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed. (Springer, 2006), pp. 333-378. [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]
- 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.-H. Shin, B. Lee, and E.-S. Kim, "Parallax-controllable large-depth integral imaging scheme using lenslet array," Jpn. J. Appl. Phys. 46, 5184-5186 (2007). [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]
- 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]
- 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]
- 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). [CrossRef] [PubMed]
- R. Martinez-Cuenca, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, "Optically-corrected elemental images for undistorted Integral image display," Opt. Express 14, 9657-9663 (2006). [CrossRef] [PubMed]
- R. Martínez-Cuenca, H. Navarro, G. Saavedra, B. Javidi, and M. Martinez-Corral, "Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system," Opt. Express 15, 16255-16260 (2007). [CrossRef] [PubMed]
- J. Hahn, Y. Kim, E.-H. Kim, and B. Lee, "Camera with inverted perspective projection view volume array for integral imaging," The 6th International Conference on Optics-Photonics Design and Fabrication, Taipei, Taiwan, pp. 553-554, June 2008.
- S.-W. Min, J. Hong, and B. Lee, "Analysis of an optical depth converter used in a three-dimensional integral imaging system," Appl. Opt. 43, 4539-4549 (2004). [CrossRef] [PubMed]
- F. Okano and J. Arai, "Optical shifter for a three-dimensional image by use of a gradient-index lens array," Appl. Opt. 41, 4140-4147 (2002). [CrossRef] [PubMed]
- J.-S. Jang and B. Javidi, "Two-step integral imaging for orthoscopic three-dimensional imaging with improved viewing resolution," Opt. Eng. 41, 2568-2571 (2002). [CrossRef]
- J.-S. Jang and B. Javidi, "Three-dimensional projection integral imaging using micro-convex-mirror arrays," Opt. Express 12, 1077-1083 (2004). [CrossRef] [PubMed]
- J. Arai, H. Kawai, M. Kawakita, and F. Okano, "Depth-control method for integral imaging," Opt. Lett. 33, 279-281 (2008). [CrossRef] [PubMed]
- J.-S. Jang and B. Javidi, "Formation of orthoscopic three-dimensional real images in direct pickup one-step integral imaging," Opt. Eng. 42, 1869-1870 (2003). [CrossRef]
- J. Arai, H. Kawai, and F. Okano, "Microlens arrays for integral imaging system," Appl. Opt. 45, 9066-9078 (2006). [CrossRef] [PubMed]
- F. Okano, "Applications of Integral Photography for Real-Time Imaging," in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuA1.
- M. Martinez-Corral, B. Javidi, R. Martinez-Cuenca, and G. Saavedra, "Formation of real, orthoscopic integral images by smart pixel mapping," Opt. Express 13, 9175-9180 (2005). [CrossRef] [PubMed]

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