OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 6 — Mar. 21, 2005
  • pp: 1875–1884
« Show journal navigation

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

Jae-Hyeung Park, Joohwan Kim, Yunhee Kim, and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 13, Issue 6, pp. 1875-1884 (2005)
http://dx.doi.org/10.1364/OPEX.13.001875


View Full Text Article

Acrobat PDF (573 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

In this paper, we report on a resolution enhancement scheme for a depth-enhanced 3D/2D convertible display based on integral imaging. The proposed method utilizes an additional lens array to generate an excess of point light sources, thus permitting the resolution of the generated 3D images to be enhanced.

Fig. 1. Schematic diagram of 3D/2D convertible integral imaging (a) 2D mode (b) 3D mode

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

Figure 1 shows the concept of the 3D/2D convertible integral imaging. The 3D/2D convertible integral imaging consists of a collimated incoherent light source, a PDLC, a lens array and an SLM. Conversion between the 3D and 2D modes is achieved by controlling the diffusing rate of the PDLC. In the 2D mode, the PDLC is set to be diffusive. The collimated light is scattered by the PDLC and this scattered field is then relayed to the SLM. Each pixel in the SLM is then illuminated effectively from all directions, and consequently, 2D images are observed on the SLM plane with full resolution and viewing angle. In the 3D mode, the PDLC is set to be transparent. In this case, the collimated light rays pass through the PDLC without scattering and are imaged into an array of point light sources at the focal plane of the lens array. The light rays from each point light source are modulated according to the direction of their propagation, and finally integrated into 3D images.

In the 3D mode, the resolution is limited by the number of point light sources. Figure 2 shows this point. As shown in Fig. 2, the light rays from each point light source are modulated by the SLM. Hence, a unit comprised of one elemental lens, a point light source, and the corresponding region on the SLM is effectively one pixel that emits light rays of different colors or intensities according to the observation directions and, as a result, acts as one pixel in the generated 3D images. Since the role of the elemental lens and the SLM is merely the formation and modulation of the point light sources, the key parameter for determining the resolution of the generated 3D images is the number of point light sources. That is, the resolution of the generated 3D images is the same as the number of point light sources. In order to enhance the resolution of generated 3D images, it is necessary to generate more point light sources with a smaller spacing between them. One straightforward method for achieving this end is to use a lens array with more elemental lenses and small elemental lens pitches. Such a lens array should reach the desired size of the display panel (e.g. 12-inch or 15-inch) with uniform elemental lenses whose pitch is comparable to the pixel pitch of conventional 2D displays (e.g. 200 um) and f-number is sufficiently small to preserve a reasonable viewing angle, which is difficult to realize at this time. This high requirement stimulates research for an alternate resolution compensation method that utilizes lens arrays that can be fabricated more readily.

Fig. 2. Limitations in resolution of the 3D/2D convertible integral imaging

3. Configuration of the proposed method

Fig. 3. Schematic diagram of the proposed method

The number of second point light sources, the spacing between them, and the diverging angle of the light rays from each point light source are determined by the specifications and locations of the two lens arrays in the proposed method. The geometry for this configuration is shown in Fig. 4. The first lens array with focal length 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

ψ1=2tan1(φ12f1).
(1)

Since the position of the first point light source generated by k-th elemental lens in the first lens array, y 1,k, can be represented by y 1,k= 1, it illuminates the second lens array’s elemental lenses that satisfy

kφ1ltan(ψ12)<qφ2<kφ1+ltan(ψ12),
(2)

where 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 klkkh where kl and kh are given by

klφ1+ltan(ψ12)=qφ2=khφ1ltan(ψ12).
(3)

From Eqs. (1) and (3), kl and kh can also be represented by

kl=qφ2φ1l2f1,
(4)
kh=qφ2φ1+l2f1.
(5)

Therefore the first point light sources satisfying (klkkh) are imaged into the second point light sources by the q-th elemental lens in the second lens array at

y2,k,q=qφ2(1+gl)kφ1gl,(klkkh)
(6)

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

g=lf2lf2.
(7)

The diverging angle of each second point light source which mainly determines the viewing angle of the generated 3D images is written by

ψ2=2tan1(φ22g).
(8)

Since 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.

Fig. 4. Geometry of the generation of a point light source array using two lens arrays

The final array of the point light sources involves the collection of all of the point light sources imaged by all the elemental lenses in the second lens array. Through careful design using Eqs. (4)(8), a uniformly dense array of point light sources with parallel diverging directions can be obtained. For example, 2N×2N uniform point light sources can be generated using a second lens array consisting of N×N elemental lenses. Figure 5 shows an example of such a configuration. The parameters and locations of two lens arrays are adjusted so that each elemental lens in the second lens array images 3 point light sources at y 2,k,q=(q+0.5)φ 2, 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.

Fig. 5. Example of the generation of a uniformly dense point light source array

4. Experimental results

An was performed to verify the feasibility of the proposed method. A schematic diagram of the experimental setup is shown in Fig. 6. An incoherent white light source and a collimating lens were used to illuminate the system. The PDLC was fabricated using NOA65 polymer and an E7 liquid crystal and was operated as a transparent plate at 30 V (1kHz rectangular wave) and as a diffusing plate at 0 V. The SLM used in the experiment had a 0.036 mm pixel pitch. In the experiment, we realized the example shown in Fig. 5. The first lens array consisted of 13×13 elemental lenses with a 10 mm elemental lens pitch and a 22 mm focal length. The second lens array consisted of 70×70 elemental lenses with a 1 mm elemental lens pitch and a 3.3 mm focal length. The second lens array was located at a distance of 66 mm from the first lens array. With these specifications, the uniform point light sources with double density were achieved.

Fig. 6. Schematic diagram of the experimental setup (a) previous method (b) proposed method
Fig. 7. Part of generated point light source (a) previous method (b) proposed method
Fig. 8. 3D image observed from different directions (a) previous method (b) proposed method

The resolution enhancement of the proposed method is revealed more clearly in Fig. 9. Figure 9 shows the result of displaying flat images 30 mm in front of the SLM. The much higher fidelity of the flat images of Fig. 9(c) compared with those of Fig. 9(b) provides convincing evidence for the resolution enhancement of the proposed method.

Fig. 9. Displayed flat images in the 3D mode (a) original images (b) previous method (c) proposed method

5. Conclusion

A resolution enhancement method for a 3D/2D convertible display based on integral imaging is described. By inserting an additional lens array between the collimating lens and the PDLC, an abundant number of the point light sources is generated, far more than the number of elemental lenses in the lens array, and thus, the resolution of the 3D images is much enhanced. The experimental results support the feasibility of the proposed method.

Acknowledgment

This work was supported by the Information Display R&D Center, one of the 21st Century Frontier R&D Programs funded by the Ministry of Commerce, Industry and Energy of Korea.

References and links

1.

G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. 146, 446–451 (1908).

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]

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. 18, 1814–1821 (2001). [CrossRef]

4.

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]

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 12, 6020–6032 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-6020. [CrossRef] [PubMed]

6.

S.-H. Shin and B. Javidi, “Speckle reduced three-dimensional volume holographic display using integral imaging,” Appl. Opt. 41, 2644–2649 (2002). [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]

9.

H. Liao, M. Iwahara, N. Hata, and T. Dohi, “High-quality integral videography using a multiprojector,” Opt. Express 12, 1067–1076 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1067 [CrossRef] [PubMed]

10.

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

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, 557–563 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-557 [CrossRef] [PubMed]

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. 44, 546–552 (2005). [CrossRef] [PubMed]

13.

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

14.

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]

15.

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]

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]

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

  1. G. Lippmann, �??La photographie integrale,�?? Comptes-Rendus Acad. Sci. 146, 446-451 (1908).
  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]
  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. 18, 1814-1821 (2001). [CrossRef]
  4. 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]
  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 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]
  6. S.-H. Shin and B. Javidi, �??Speckle reduced three-dimensional volume holographic display using integral imaging,�?? Appl. Opt. 41, 2644�??2649 (2002). [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), <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]
  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]
  9. 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]
  10. B. Lee, S. Jung, and J. -H. Park, �??Viewing-angle-enhanced integral imaging using lens switching,�?? Opt. Lett. 27, 818-820 (2002). [CrossRef]
  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, 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]
  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. 44, 546-552 (2005). [CrossRef] [PubMed]
  13. J. S. Jang, and B. Javidi, �??Three dimensional synthetic aperture integral imaging,�?? Opt. Lett. 27, 1144-1146 (2002). [CrossRef]
  14. 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]
  15. 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]
  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]

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.

CrossCheck Deposited