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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 21 — Oct. 12, 2009
  • pp: 19047–19054
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Depth-extended integral imaging system based on a birefringence lens array providing polarization switchable focal lengths

Chan-Kyu Park, Sang-Shin Lee, and Yong-Seok Hwang  »View Author Affiliations


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

In this paper an InIm system exploiting a birefringence lens array (BLA) allowing two different focal lengths was proposed and implemented. The BLAs were fabricated by placing two different types of LC in between a lens array substrate and a glass plate, and their focal length was varied by switching the light polarization. The real and imaginary 3D images for an object were reconstructed at two different locations with a certain depth of field respectively, supporting that the depth of field for the reconstructed images could be readily extended by combining them properly.

2. Proposed InIm system and its operation

Figure 2
Fig. 2 Proposed InIm system using a BLA with polarization selective focal lengths.
illustrates the configuration of the proposed InIm system involving a polarization selective lens array composed of BLA I and II and an LCD providing pickup elemental images. The BLA I and II are first aligned in such a way that their principal axes, the ordinary and extraordinary axis, are matched together. A polarizer is used to dynamically change the polarization of the incident light. Dynamically changing polarizer means a temporally rotating polarizer. Either of the two BLAs whose axis matches that of the polarizer is selected to play a role as lens. For the polarization parallel to its ordinary axis, the BLA I acts as a convex lens and thus a real integrated image is obtained in front of it. Meanwhile, for the polarization parallel to its extraordinary axis the BLA II functions as a concave lens generating a virtual integrated image at the back of it. The propagation of rays for the two BLAs is depicted in Fig. 3
Fig. 3 Propagation of rays through a pair of cascaded BLAs. Here z=0 corresponds to the position at the top of ITO glass plate of either BLA I or BLA II.
depending on the light polarization. Here the BLA I and II were made by placing ZLI-4119 and E-7 nematic LCs in between a lens array substrate and an indium-tin-oxide (ITO) glass plate respectively. As shown in Fig. 3, the incident light polarized in the extraordinary direction is refracted by the BLA II alone but bypasses the BLA I working as a plain retarder. On the contrary, for the light polarized in the ordinary direction only the BLA I plays a role as a convex lens.

An enlarged view of the proposed BLA is given in Fig. 4
Fig. 4 Detailed structure of a unit element of the proposed BLA.
. Its focal length may be estimated by taking into account the distribution of the refractive index profile along the light propagation direction. To extend the depth of field of the integrated images without degrading the resolution the focal length of the BLAs used is to vary over a wide range as long as the light polarization is switched instantly.

The position of the center of the reconstructed image can be expressed as Eq. (1). Here 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 nl and np are the effective refractive index of the LC and the lens respectively, and C is the radius of curvature of the lens. no and ne represent the ordinary and extraordinary refractive index of the LC and 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 Δz totalz 1z 2.

1g+1Li=1fifori=1or2
(1)
fi=1(nlinp)Cwherei=1or2andnli(θ)=noineinoi2sin2θ+nei2cos2θ.
(2)
Δzi=(d/W)fifori=1or2
(3)

In this work two kinds of LCs including the E-7 (no=1.5216, Δn=0.2246 @580 nm) and the ZLI-4119 (no =1.4712, Δn= 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 Δz total=~33 mm from Δz 1= 31.5 mm and Δz 2=1.45 mm.

3. Simulation and experimental results

A conventional InIm system employing a plain non-birefringent lens array was first designed and analyzed by using the LightTools® [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]

]. The elemental image for the two objects of letters ‘I’ and ‘P’, which were located at z=9 mm and z=30 mm respectively, was produced with the resolution of 609 x 609 pixels as shown in Fig. 5(a)
Fig. 5 Performance of a conventional InIm system with a plain lens array (a) elemental image of the two objects (b) reconstructed image at z=9 mm (c) reconstructed image at z=30 mm.
. They were reconstructed at z=9 mm and z=30 mm respectively as displayed in Fig. 5(b) and 5(c). At each of the reconstruction image planes one object is shown to be clearly imaged but the other blurred severely, reflecting the limited depth of field for the current system as anticipated. This problem may be however addressed by adaptively controlling the focal length of the lens arrays in accordance with the reconstruction position of each object.

4. Conclusion

An InIm system taking advantaging of a BLA with polarization selective focal lengths was presented. Both real and virtual images of a 3D object were decently reconstructed at two widely separated positions with no remarkable degradation in the resolution. In the future an InIm system exhibiting a continuously varying reconstructed image will be attempted. A lens with shorter focal lengths might be required to overcome the narrow viewing angle resulting from the limited amount of birefringence available from BLAs. The aberration of the BLAs and the range of depth enhancement should be also considered.

Acknowledgments

This research was supported by the MKE (Ministry of Knowledge Economy), Korea under the ITRC (Information Technolgy Research Center) Support program supervised by the IITA (Institute of Information Technology Advancement) (IITA-2008-C1090-0801-0018).

References and links

1.

G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. 146, 446–451 (1908).

2.

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58(1), 71–76 (1968). [CrossRef]

3.

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]

4.

H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26(3), 157–159 (2001). [CrossRef]

5.

J.-S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27(13), 1144–1146 (2002). [CrossRef]

6.

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]

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. 3(1), 64–70 (2007). [CrossRef]

8.

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]

9.

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]

10.

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]

11.

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]

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. 42(Part 1, No. 10), 6434–6438 (2003). [CrossRef]

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. 45(18), 4334–4343 (2006). [CrossRef] [PubMed]

14.

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]

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. 46(18), 3766–3773 (2007). [CrossRef] [PubMed]

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]

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

  1. G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. 146, 446–451 (1908).
  2. C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58(1), 71–76 (1968). [CrossRef]
  3. 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]
  4. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26(3), 157–159 (2001). [CrossRef]
  5. J.-S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27(13), 1144–1146 (2002). [CrossRef]
  6. 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]
  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. 3(1), 64–70 (2007). [CrossRef]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  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. 42(Part 1, No. 10), 6434–6438 (2003). [CrossRef]
  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. 45(18), 4334–4343 (2006). [CrossRef] [PubMed]
  14. 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]
  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. 46(18), 3766–3773 (2007). [CrossRef] [PubMed]
  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]

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