## Depth-extended integral imaging system based on a birefringence lens array providing polarization switchable focal lengths

Optics Express, Vol. 17, Issue 21, pp. 19047-19054 (2009)

http://dx.doi.org/10.1364/OE.17.019047

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### Abstract

An integral imaging system enabling extended depth of field was proposed and demonstrated based on a birefringence lens array (BLA) whose focal length was switched via the light polarization. The lens array system was constructed by combining two different liquid crystal(LC) embedded lens arrays, BLA I and II, which were fabricated by injecting a ZLI-4119 LC and an E-7 LC in between a lens array substrate and an ITO (indium-tin-oxide) glass plate respectively. The BLA I played a role as a convex lens only for the polarization parallel to the ordinary axis of the corresponding LC, but it serves as a plain medium for that along its extraordinary one since the refractive indexes of the lens and the LC are almost identical. Meanwhile, the BLA II played a role as a concave lens only for the polarization parallel to the extraordinary axis of the LC but as a plain medium for that along its ordinary one. As a result, the focal length could be switched via the polarization, and it was measured to be 680 mm and −29 mm. For the proposed system with the prepared BLAs, both real and virtual three-dimensional (3D) images were efficiently reconstructed at the positions of z=1300 mm and z=−30 mm with no significant degradation in the resolution, indicating its depth of field range.

© 2009 OSA

## 1. Introduction

## 2. Proposed InIm system and its operation

*g*is the gap between the display panel and the BLA in effect, and

*L*denotes the distance of the resulting integrated image from the corresponding BLA, which is dependent upon the magnitude of the birefringence available the lens.

*f*

_{1}and

*f*

_{2}denote respectively the convergent and divergent focal length leading to the real and virtual integrated image, and they are given by Eq. (2). Here

*n*and

_{l}*n*are the effective refractive index of the LC and the lens respectively, and

_{p}*C*is the radius of curvature of the lens.

*n*and

_{o}*n*represent the ordinary and extraordinary refractive index of the LC and

_{e}*θ*is the tilt angle thereof. The position of the integral image plane can be adjusted by altering the focal length of the lens, which is determined by the refractive index contrast between the LC layer and the lens array substrate. Therefore the depth of field for the proposed system may be defined as the separation between the focal point where the spot size becomes ideally zero and the position where it is enlarged to be equivalent to one pixel size

*d*of the LCD, as given in Eq. (3). Finally the total depth of field is given by Δ

*z*

_{total}=Δ

*z*

_{1}+Δ

*z*

_{2}.

*n*=1.5216, Δ

_{o}*n*=0.2246 @580 nm) and the ZLI-4119 (

*n*=1.4712, Δ

_{o}*n*= 0.0603 @580 nm) were practically used to form a birefringent layer on a lens substrate, which is 10 μm thick at the center. The focal length of the BLA I and II was designed to be 630 mm and −29 mm respectively. For instance, for

*d*=0.2 mm and

*W*=4 mm, we will get Δ

*z*

_{total}=~33 mm from Δ

*z*

_{1}= 31.5 mm and Δ

*z*

_{2}=1.45 mm.

## 3. Simulation and experimental results

^{®}[16

16. J. Lee, S. Kim, and E. Kim, “Reconstruction of a three-dimensional object and system analysis using ray tracing in practical integral imaging system,” Proc. SPIE **6695**, 669519–669527 (2007). [CrossRef]

*z*

_{total}=~33 mm would be obtained for

*d*=0.2 mm,

*f*

_{1}=630,

*f*

_{2}-29mm and

*W*=4 mm. However optically Δ

*z*

_{total}is larger than computational Δ

*z*

_{total}if wave optical theory is considered. Thus, in Fig. 9(b), (c), the reconstructed image has nearly no degradation due to this effect.

## 4. Conclusion

## Acknowledgments

## References and links

1. | G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. |

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

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

4. | H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. |

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

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

7. | Y. S. Hwang, S. Hong, and B. Javidi, “Free view 3D visualization of occluded objects by using computational synthetic aperture integral imaging,” IEEE/OSA J. Disp. Tech. |

8. | Y. Frauel and B. Javidi, “Digital three-dimensional image correlation by use of computer-reconstructed integral imaging,” Appl. Opt. |

9. | B. Javidi, R. Ponce-Díaz, and S. H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. |

10. | S. H. Hong and B. Javidi, “Distortion-tolerant 3D recognition of occluded objects using computational integral imaging,” Opt. Express |

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

12. | Y. S. Hwang, T. H. Yoon, and J. C. Kim, “Design and fabrication of variable focusing lens arrays using liquid crystal for integral photography,” Jpn. J. Appl. Phys. |

13. | Y. Kim, J. H. Park, H. Choi, J. Kim, S. W. Cho, and B. Lee, “Depth-enhanced three-dimensional integral imaging by use of multilayered display devices,” Appl. Opt. |

14. | J. Park, S. Jung, H. Choi, and B. Lee, “Integral imaging with multiple image planes using a uniaxial crystal plate,” Opt. Express |

15. | Y. Kim, H. Choi, J. Kim, S.-W. Cho, Y. Kim, G. Park, and B. Lee, “Depth-enhanced integral imaging display system with electrically variable image planes using polymer-dispersed liquid-crystal layers,” Appl. Opt. |

16. | J. Lee, S. Kim, and E. Kim, “Reconstruction of a three-dimensional object and system analysis using ray tracing in practical integral imaging system,” Proc. SPIE |

**OCIS Codes**

(080.0080) Geometric optics : Geometric optics

(080.2740) Geometric optics : Geometric optical design

(220.0220) Optical design and fabrication : Optical design and fabrication

(150.2945) Machine vision : Illumination design

**History**

Original Manuscript: August 7, 2009

Revised Manuscript: September 22, 2009

Manuscript Accepted: September 24, 2009

Published: October 7, 2009

**Citation**

Chan-Kyu Park, Sang-Shin Lee, and Yong-Seok Hwang, "Depth-extended integral imaging system based on a birefringence lens array providing polarization switchable focal lengths," Opt. Express **17**, 19047-19054 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19047

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### References

- G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. 146, 446–451 (1908).
- C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58(1), 71–76 (1968). [CrossRef]
- F. Okano, J. Arai, H. Hoshino, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38(6), 1072–1077 (1999). [CrossRef]
- H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26(3), 157–159 (2001). [CrossRef]
- J.-S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27(13), 1144–1146 (2002). [CrossRef]
- S. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12(3), 483–491 (2004). [CrossRef] [PubMed]
- Y. S. Hwang, S. Hong, and B. Javidi, “Free view 3D visualization of occluded objects by using computational synthetic aperture integral imaging,” IEEE/OSA J. Disp. Tech. 3(1), 64–70 (2007). [CrossRef]
- Y. Frauel and B. Javidi, “Digital three-dimensional image correlation by use of computer-reconstructed integral imaging,” Appl. Opt. 41(26), 5488–5496 (2002). [CrossRef] [PubMed]
- B. Javidi, R. Ponce-Díaz, and S. H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. 31(8), 1106–1108 (2006). [CrossRef] [PubMed]
- S. H. Hong and B. Javidi, “Distortion-tolerant 3D recognition of occluded objects using computational integral imaging,” Opt. Express 14(25), 12085–12095 (2006). [CrossRef] [PubMed]
- H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15(8), 2059–2065 (1998). [CrossRef]
- Y. S. Hwang, T. H. Yoon, and J. C. Kim, “Design and fabrication of variable focusing lens arrays using liquid crystal for integral photography,” Jpn. J. Appl. Phys. 42(Part 1, No. 10), 6434–6438 (2003). [CrossRef]
- Y. Kim, J. H. Park, H. Choi, J. Kim, S. W. Cho, and B. Lee, “Depth-enhanced three-dimensional integral imaging by use of multilayered display devices,” Appl. Opt. 45(18), 4334–4343 (2006). [CrossRef] [PubMed]
- J. Park, S. Jung, H. Choi, and B. Lee, “Integral imaging with multiple image planes using a uniaxial crystal plate,” Opt. Express 11, 1862–1875 (2003). [CrossRef] [PubMed]
- Y. Kim, H. Choi, J. Kim, S.-W. Cho, Y. Kim, G. Park, and B. Lee, “Depth-enhanced integral imaging display system with electrically variable image planes using polymer-dispersed liquid-crystal layers,” Appl. Opt. 46(18), 3766–3773 (2007). [CrossRef] [PubMed]
- J. Lee, S. Kim, and E. Kim, “Reconstruction of a three-dimensional object and system analysis using ray tracing in practical integral imaging system,” Proc. SPIE 6695, 669519–669527 (2007). [CrossRef]

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