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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 12 — Jun. 6, 2011
  • pp: 11007–11017
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Design and fabrication of optical system for time-multiplex autostereoscopic display

Jian-Chiun Liou and Fo-Hau Chen  »View Author Affiliations


Optics Express, Vol. 19, Issue 12, pp. 11007-11017 (2011)
http://dx.doi.org/10.1364/OE.19.011007


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Abstract

We propose and experimentally demonstrate a novel time-multiplexed autostereoscopic multi-view full resolution 3D display based on the lenticular lens array in association with the control of the active dynamic LED backlight. The lenticular lenses of the lens array optical system receive the light and deflect the light into each viewing zone in a time sequence.

© 2011 OSA

1. Introduction

Currently, several 2D/3D switched displays had been proposed [5

5. H.-K. Hong, S.-M. Jung, B.-J. Lee, and H.-H. Shin, “Electric-field-driven LC lens for 3-D/2-D autostereoscopic display,” J. Soc. Inf. Disp. 17(5), 399–406 (2009). [CrossRef]

,6

6. G. J. Woodgate and J. Harrold, “Efficiency analysis for multiview spatially multiplexed autostereoscopic 2D/3D display,” J. Soc. Inf. Disp. 15(11), 873–881 (2007). [CrossRef]

] such as switched barrier and LC-lens. However, both of the parallax barrier [7

7. O. H. Willemsen, S. T. de Zwart, M. G. H. Hiddink, D. K. G. de Boer, and M. P. C. M. Krijin, “Multi-view 3D Displays,” in Proceedings of Society for Information Display 2007 (Society for Information Display, 2007), pp. 1154–1157.

] and the cylindrical lens arrays [8

8. O. H. Willemsen, S. T. De Zwart, M. G. H. Hiddink, and O. Willemsen, “2D/3D switching displays,” J. Soc. Inf. Disp. 14(8), 715–722 (2006). [CrossRef]

10

10. J.-Y. Son and B. Javidi, “Three-dimensional image methods based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005). [CrossRef]

] still has the issues of narrow viewing angle and low resolution when displaying the 3D images. Besides, in order to balance the horizontal versus vertical resolution of an autostereoscopic displays, a slanted lens array is used [11

11. C. van Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999). [CrossRef]

]. This causes the high crosstalk of stereo display and the subpixels of a view to appear on nonrectangular grid. This paper describes our work aimed at developing optical system; active barrier dynamic backlight slit multi-view full resolution and lower crosstalk 3D panel. The panel of 240Hz displays the corresponding images of the four viewing zones by the same time sequence according to temporal multiplexed mechanism.

The time multiplexed stereo display consists of a liquid-crystal display (LCD) panel with an active barrier dynamic backlight slit unit and a lens plate, commonly referred to as a lenticular. The lenticular consists of an array of cylinder lenses that extend in the direction perpendicular to the plane of the drawing. The focal plane of these lenses is positioned at (or close to) the pixel plane of the LCD panel and in this way light from the pixels is collimated towards the viewer into different directions and viewing angle. This viewing angle is preserved in the multi-view full resolution stereo image design, which allows for simultaneous, multiple-user perception of stereo. The design of the monitor is intended to accommodate a combination of standing and seated viewers. The stereo viewing angle is primarily limited by the viewer’s ability to see the lower monitor through the mirror. Unlike most of the current autostereo monitors, there is no restrictive “sweet spot” requiring precise head placement. This adds to the stereo viewing comfort. The look-around capability is an ancillary benefit of the fact that such displays allow the user to view them from a relatively wide range of viewing positions.

2. Architecture

All modern multiview displays use TFT screens for image formation. The light generated by the TFT is separated into multiple directions by the means of special layer additionally mounted on the screen surface. Such layer is called “optical layer”, “lens plate” and “optical filter”. Since PMMA possesses advantages of stability in size and being inexpensive in price, the micro-prism array plate is also adopted as the light guiding plate for the display board [12

12. D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light-guide plates for liquid crystal display backlight,” J. Opt. A, Pure Appl. Opt. 7(3), 111–117 (2005). [CrossRef]

]. A characteristic of all 3D displays is the tradeoff between pixel resolution (or brightness [13

13. C.-Y. Chen, T.-T. Yang, and W.-S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16(20), 15495–15505 (2008). [CrossRef] [PubMed]

,14

14. B. Kim, J. Kim, W.-S. Ohm, and S. Kang, “Eliminating hotspots in a multi-chip LED array direct backlight system with optimal patterned reflectors for uniform illuminanceand minimal system thickness,” Opt. Express 18(8), 8595–8604 (2010). [CrossRef] [PubMed]

] or temporal frequency) and depth. In a scene viewed in 3D, pixels that in 2D would have contributed to high resolution are used instead to show depth. If the slanted lenticular sheet were placed vertically atop the LCD, then vertical and horizontal resolution would drop by a factor equal to the number of views. A sheet of slanted lenticules as shown in Fig. 1
Fig. 1 5-view slanted lenticular sheet.
, by contrast, distributes the resolution loss in the vertical and horizontal planes. A 5-view slanted lenticular sheet, for example, original 10 pixels (5 × 2) causes a two-fold decrease in both vertical and horizontal resolution. This causes the high crosstalk of stereo display and the subpixels of a view to appear on nonrectangular grid.

This paper addresses the specific technological challenges of autostereoscopic 3D displays and presents a novel optical system that integrates a real-time active barrier dynamic backlight slit system with a naked eyes multi-view stereo display. With 240Hz display and tunable frequency LED backlight slits, only a pair of page-flipped left and right eye images was necessary to produce a multi-view effect. Furthermore, full resolution was maintained for the images of each eye. The loading of the transmission bandwidth was controllable, and the binocular parallax and motion parallax is as good as the usually full resolution multi-view autostereo display.

A lenticular-based 3D display directs the light of neighboring sub-pixels into different directions by means of small lenses placed immediately in front of the sub-pixels. In this manner different pictures can be transmitted into different directions. Usually a multitude of directions is chosen, e.g. 4 different views. Two of these views can be seen by the left and right eye respectively, and as such create a stereoscopic (3D) image. Figure 2
Fig. 2 The structure of the proposed multi-view 3D display.
shows the structure of the proposed multi-view 3D display. Only one eye individually receives the image at one corresponding viewing zone at its displaying time period, such as 1/240 second. As a result, the 3D image can be created for the viewer by naked eyes. Lenticular plate has four groups 1-4 of light sources corresponding to four viewing zones 1-4. Each view is 60Hz. The uni-direction diffusion lens plate can condense the light individually belonging to each the lenticular lens at transverse direction.

The dynamic light slit source is divided into four groups, which are turned on sequentially, and then a displaying rate of 60 Hz for displaying 3D image still maintain. The time sequence for turning on the four groups of the light source is illustrated for four viewing zones. When the group 1 of the light source is turned on, represented by white region, the other groups 2-4 are turned off. At this moment, only the viewing zone (view 4) corresponding to one eye can be viewed. When the group 2 is turned on and groups 1, 3-4 are turned off, only the viewing zone (view 3) can be viewed at another eye. The display panel correspondingly displays the images with a period of 1/240 second four different viewing zones. Likewise, the group 2, group 3, and group 4 are sequentially turned on for viewing zones 3, 2 and 1. Four viewing zones can be created.

This paper addresses the specific technological challenges of autostereoscopic 3D displays and presents a novel system that integrates a time-multiplex autostereoscopic display based on active directional backlight (active dynamic backlight) with an autostereoscopic display. Our successfully designed prototype utilized a FPGA system to synchronize between a display panel and backlight slit panel. With 240Hz display and dynamic backlight panel, only two pairs of page-flipped left and right eye images were necessary to produce a multi-view effect. Furthermore, full resolution was maintained for the images of each eye. The loading of the transmission bandwidth was controllable, and the binocular parallax and motion parallax is as good as the usually lower resolution multi-view autostereo display. Device configuration of the dynamic light is shown in Fig. 3
Fig. 3 Configuration of the proposed autostereoscopic display.
and Fig. 4
Fig. 4 The switching mechanism of the dynamic light.
. The maximum speed of switching of the dynamic light slit is 1/240 sec, the backlight modular provides backlight control signals which are dependent on the position of an associated part of the panel. The system is provided for controlling synchronization timing between backlighting and pixel refresh, in dependence of a location of a section within the display panel. The backlight unit is separated into four viewable groups. Let’s take 4 viewer backlight groups as the example as in Fig. 4. The illumination period is one quarter of the full backlight duty time. Frame sequential (page flip, temporal multiplexed) process, the process is referred to as alternate frame sequencing.

3. Experiments

Lenticular lens displays are tunable in a manner similar to parallax barrier displays. There are four basic parameters in a uniform lenticular lens sheet: lens width, lens radius, backing sheet thickness, and lens orientation. Adjusting the lens width controls the number of views the display can support; roughly the number of subpixels in a row under a single lenticule controls the maximal number of views before a repeat. Unlike a parallax barrier, increasing the number of views does not drastically reduce overall brightness; instead of allowing a subpixel to emanate light in all directions, a lenticule focuses the outgoing light into a subset of directions. Our current prototype system uses a lenticular lens multiview technique with a time-multiplex autostereoscopic display based on active directional backlight (active dynamic backlight).

To describe observed images in the lenticular display system, we need to model the system in detail. Let us assume that a viewer’s eye sees the 2nd lenticular as in Fig. 5
Fig. 5 Optical system of lenticular display.
. Here, d denotes the distance from a lenticule to the eye, and LH denotes the horizontal displacement from the eye to the observed lenticular center. (R + 2R) and p are the focal length and pitch of lenticules, respectively, and LD is the horizontal displacement from the observed lenticular center to the observed position on the LCD pixel array. If we know the values of (R + 2R), and p, LD can be calculated as follows. Using the Snell’s law [15

15. D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (John Wiley and Sons, 2001).

], the equation of crosstalk ratio is illustrated in Eqs. (1)(3), which shows the distance from a lenticule to the eye and from the observed lenticular center to the observed position on the LCD.
L:65=2R:(d+R)P:4L=(d+R):(d+3R)
(1)
L denotes the width of the LED light emitted area, P is pitch of lenticules, R is a radius of lenticules, at sinθi=nrsinθr, where nr is the refractive index of lenticules. And from Fig. 5,
sinθi=LHd2+LH2    ,and   sinθγ=LD(R+2R)2+LD2
(2)
Using Eqs. (2), we can represent LD as

LD=(R+2R)LHnr2(d2+LH2)LH2
(3)

It is desirable to design lenticules so that the width of the region observed through a lenticule at a certain viewing zone may be equal to or smaller than that of one sub-pixel in the LCD pixel array. Here, the ray passing through the lenticular center can predict center of the region observed from a certain viewing zone.

Above Eqs. (1)(3), the light is emitted from fixed LED light bars which are located at the bottom of the figure. While the refractive index(nr) equal to 1. The incident light(angle) and refractive light(angle) should be switched each other. Ex.θi, <-> θr.

In Retroreflective displays type, retroreflective displays consist of two parts: a front screen projector and a retroreflective projection screen. While the projector can be a standard projector, this type of screen behaves significantly different from a normal projection screen. A standard front screen projection screen diffuses incoming light in all directions; this diffusion reduces glare and permits the image to be viewed from any reasonable direction. An ideal retroreflective screen reflects incoming light back along the same direction it came; in ray tracing terms, the angle of incidence,θi, is equal to the angle of reflectance, θr.

According to the time sequence for turning the groups of the light source, multiple viewing zones at multiple directions are created. To meet the requirements of different one-eye images, we propose that the real-time active barrier dynamic backlight slit system on stereo-display. To confirm our design workable, we did the optical simulation using ASAP software. The detector is set at the convergent point, and the intensity profiles of the four views are shown in Fig. 6
Fig. 6 The optical simulation using ASAP software.
. The intensity profiles are evolving every 1/240 sec, and the separation of peaks is about 60 mm, quite close to the design value, 65 mm. The small inaccuracy resulted from the absorption of black matrix, and it makes the dead zone explicit. Setting the pixel size larger, or the black matrix smaller would improve the results. On the other hand, the center-viewing group has the least crosstalk, (View 1(A peak)、View 2(B peak)、View 3(C peak)、View 4(D peak)) and side lobe groups have larger crosstalk, especially when viewing groups departs from center very much. The increase of crosstalk arises from the abbreviation when light is not close to the optical axis. Thus, the profiles of the four views confirm our design workable.

4. Results and discussion

The photographs of displayed images used the luminance meter (Konica Minolta CS-200) as shown in Fig. 7
Fig. 7 Four views backlight.
. The distance from the optical sensor to the center of LED backlight panel is in 60 cm, which is the normal range of distance for watching a 3D computer monitor. Measurements of angle are done from observation point −50 degree to observation point + 50 degree; view 2 is the central view. The illuminance meter has an analog output to the oscilloscope and the illuminance signal can be recorded and processed by a computer.

Yellow stripe pattern is created by phosphor of yellow color. White LEDs are blue LED chips covered with a phosphor that absorbs some of the blue light and fluoresces with a broad spectral output ranging from mid-green to mid-red. So, the backlight modular was taken on yellow stripe.

The configuration of uni-direction diffusion lens plate is shown in Fig. 8(b)
Fig. 8 (a)Schematic overview shows the crosstalk between different views. The light intensity of a pixel in a view roughly has the shape of a gaussian. (b) The light intensity of the configuration with uni-direction diffusion lens plate.
. The panel of 240Hz displays the corresponding images of the four viewing zones by the same time sequence according to temporal multiplexed mechanism. The uni-direction diffusion lens plate can condense the light individually belonging to each the lenticular lens at transverse direction. The lenticular lenses of the lens array receive the light and deflect the light into each viewing zone in a time sequence, respectively.

According to the time sequence for turning the groups of the light source, multiple viewing zones at multiple directions are created. To meet the requirements of different one-eye images, we propose that the real-time active barrier dynamic backlight slit system on stereo-display. The center viewing group has the least crosstalk, and side lobe groups have larger crosstalk, especially when viewing groups departs from center very much. The crosstalk under different observation scanning angles is showed from data in Fig. 8(b), including the cases of 4-views field scanning. The crosstalk of view 1 is about 5% respectively; the results are better than slanted lenticuler lens type.

There is a comparison for simulation and experimental evaluation viewing zone area of the system. The horizontal axis and the vertical axis matched for comparing the ASAP simulation (Fig. 6) and the experimental results (Fig. 8(b)).The viewable zone area from first viewing zone to be contiguous to second viewing zone is 90 mm, and for 4 viewing zone of viewable area is 360 mm(The separation of viewing zones is about 90 mm, and overall width of viewing group is 360 mm).

In the simulation, the lenticular and backlight are aligned perfectly. However, in the experimental, the alignment is a little shifted, which causes that the peaks A’,B’,C’, and D’ are shifted by 100 mm. The simulation and experimental results are consistence.

In the 3D displays, crosstalk is always an issue. The light intensity distribution of each view of active barrier dynamic backlight are shown in Fig. 8, and the equation of crosstalk ratio is illustrated in Eq. (4), which shows the effect between the (n)th and (n + 1)th view.
CrosstalkRatio=LightIntensityview(n)LightIntensityview(n)+LightIntensityview(n+1)×100[%]
(4)
As shown in Fig. 8(a), the most significant contribution for certain observation point comes from the respective central view and its two closest neighbors. For example, for observation point degree 22, we measure the contribution of View 2 (central for this observation point), and its two neighboring views, View 1 and View 3. The crosstalk of the configuration with uni-direction diffusion lens plate under different observation scanning angles is showed from data in Fig. 8(b), including the cases of 4-views field scanning. The crosstalk of view 2 is about 5% respectively, the results are better than slanted lenticuler lens type. Due to the display showing 4 or 5 views simultaneously, each view contains only 1/4 or 1/5 of the standard resolution of the display panel. We have proposed a new optical system for time-multiplex autostereoscopic display to solve problems that are intrinsic and extrinsic to lenticular display system technology. From the results, the 3D display with dynamic backlight has less crosstalk than the conventional one. Therefore, the image quality can be improved due to lower crosstalk.

The lenticular lenses of the lens array receive the light and deflect the light into each viewing zone in a time sequence, respectively. Lenticular lenses are plastic lenses consisting of an array of optical elements (lenticules). When viewed from different angles, different areas under the lens are magnified. The display panel displays the corresponding images of the four viewing zones by the same time sequence according to temporal multiplexed mechanism. Further descriptions about the 3D image display mechanism will be provided later in Fig. 9
Fig. 9 Photographs of the images: (a) −3° image content, (b) 5° image content, (c) 13° image content, (d) 21° image content.
. The photo shows high density active barrier dynamic LED backlight, the slit pitch is 700um, and the LED chip size is 10 × 23mil for 7 inch full resolution multi-view autostereoscopic display.

Figure 9 shows the photographs of images captured from various viewing angles. This study demonstrated a time-multiplex autostereoscopic display based on active directional backlight (active dynamic backlight) of a synchro-signal LED scanning system that can correspondingly send different pairs of stereo images based on the viewer’s position. The backlight group provides a light source to the display panel, the backlight modular is synchronously turned on and off according to the right eye synchronizing vertical signal and is also synchronously turned on and off according to the left eye synchronizing vertical signal. Additionally, a 4-view autostereoscopic display was implemented with full resolution in the display panel, achieving high 3D image quality in the preliminary configuration.

The lenticular lens array and the active barrier form as a backlight source. According to the time sequence for turning the groups of the light source, multiple viewing zones at multiple directions are created. The lights belonging to different viewing zones can enter the left eye (L) and the right eye (R) at different time period. Since the directions of light for the viewing zones are different, the two eyes do not interfere. Only one eye individually receives the image at one corresponding viewing zone at its displaying time period, such as 1/240 second. As a result, the 3D image can be created for the viewer by naked eyes.

5. Conclusions

In this research, we have successfully designed and fabricated the optical system, high density active barrier dynamic LED backlight, the slit pitch is 700um, and the LED chip size is 10 × 23mil for full resolution multi-view autostereoscopic display. From the measurement results, the dynamic LED backlight optical system can yield ideal parabolic curvature and the crosstalk is lower than 5%. Besides, the lenticular lenses of the lens array optical system was successfully received the light and deflected the light into each viewing zone in a time sequence, which could be one of the candidates for future full resolution time-multiplexed 3D applications.

References and links

1.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. von Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007). [CrossRef]

2.

P. Surman, I. Sexton, R. Bates, W. K. Lee, K. Hopf, and T. Koukoulas, “Latest developments in a multi-user 3D display,” Proc. SPIE 6016, 231–238 (2005).

3.

R. Braspenning, E. Brouwer, and G. de Haan, “Visual quality assessment of lenticular based 3D-displays,” in Proceedings of 13 European Signal Processing Conference, EUSIPCO, Turkey, 1–4 (2006).

4.

X3D–23” Users’ Manual, NewSight GmbH, Firmensitz Carl-Pulfrich-Str., 1 07745 Jena (2006).

5.

H.-K. Hong, S.-M. Jung, B.-J. Lee, and H.-H. Shin, “Electric-field-driven LC lens for 3-D/2-D autostereoscopic display,” J. Soc. Inf. Disp. 17(5), 399–406 (2009). [CrossRef]

6.

G. J. Woodgate and J. Harrold, “Efficiency analysis for multiview spatially multiplexed autostereoscopic 2D/3D display,” J. Soc. Inf. Disp. 15(11), 873–881 (2007). [CrossRef]

7.

O. H. Willemsen, S. T. de Zwart, M. G. H. Hiddink, D. K. G. de Boer, and M. P. C. M. Krijin, “Multi-view 3D Displays,” in Proceedings of Society for Information Display 2007 (Society for Information Display, 2007), pp. 1154–1157.

8.

O. H. Willemsen, S. T. De Zwart, M. G. H. Hiddink, and O. Willemsen, “2D/3D switching displays,” J. Soc. Inf. Disp. 14(8), 715–722 (2006). [CrossRef]

9.

C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997). [CrossRef]

10.

J.-Y. Son and B. Javidi, “Three-dimensional image methods based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005). [CrossRef]

11.

C. van Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999). [CrossRef]

12.

D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light-guide plates for liquid crystal display backlight,” J. Opt. A, Pure Appl. Opt. 7(3), 111–117 (2005). [CrossRef]

13.

C.-Y. Chen, T.-T. Yang, and W.-S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16(20), 15495–15505 (2008). [CrossRef] [PubMed]

14.

B. Kim, J. Kim, W.-S. Ohm, and S. Kang, “Eliminating hotspots in a multi-chip LED array direct backlight system with optimal patterned reflectors for uniform illuminanceand minimal system thickness,” Opt. Express 18(8), 8595–8604 (2010). [CrossRef] [PubMed]

15.

D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (John Wiley and Sons, 2001).

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.0230) Optical devices : Optical devices
(220.2945) Optical design and fabrication : Illumination design

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: January 28, 2011
Revised Manuscript: April 14, 2011
Manuscript Accepted: May 3, 2011
Published: May 23, 2011

Citation
Jian-Chiun Liou and Fu-Hao Chen, "Design and fabrication of optical system for time-multiplex autostereoscopic display," Opt. Express 19, 11007-11017 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11007


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References

  1. P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. von Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007). [CrossRef]
  2. P. Surman, I. Sexton, R. Bates, W. K. Lee, K. Hopf, and T. Koukoulas, “Latest developments in a multi-user 3D display,” Proc. SPIE 6016, 231–238 (2005).
  3. R. Braspenning, E. Brouwer, and G. de Haan, “Visual quality assessment of lenticular based 3D-displays,” in Proceedings of 13 European Signal Processing Conference, EUSIPCO, Turkey, 1–4 (2006).
  4. X3D–23” Users’ Manual, NewSight GmbH, Firmensitz Carl-Pulfrich-Str., 1 07745 Jena (2006).
  5. H.-K. Hong, S.-M. Jung, B.-J. Lee, and H.-H. Shin, “Electric-field-driven LC lens for 3-D/2-D autostereoscopic display,” J. Soc. Inf. Disp. 17(5), 399–406 (2009). [CrossRef]
  6. G. J. Woodgate and J. Harrold, “Efficiency analysis for multiview spatially multiplexed autostereoscopic 2D/3D display,” J. Soc. Inf. Disp. 15(11), 873–881 (2007). [CrossRef]
  7. O. H. Willemsen, S. T. de Zwart, M. G. H. Hiddink, D. K. G. de Boer, and M. P. C. M. Krijin, “Multi-view 3D Displays,” in Proceedings of Society for Information Display 2007 (Society for Information Display, 2007), pp. 1154–1157.
  8. O. H. Willemsen, S. T. De Zwart, M. G. H. Hiddink, and O. Willemsen, “2D/3D switching displays,” J. Soc. Inf. Disp. 14(8), 715–722 (2006). [CrossRef]
  9. C. van Berkel and J. A. Clarke, “Characterization and optimization of 3D-LCD module design,” Proc. SPIE 3012, 179–186 (1997). [CrossRef]
  10. J.-Y. Son and B. Javidi, “Three-dimensional image methods based on multiview images,” J. Disp. Technol. 1(1), 125–140 (2005). [CrossRef]
  11. C. van Berkel, “Image preparation for 3D-LCD,” Proc. SPIE 3639, 84–91 (1999). [CrossRef]
  12. D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light-guide plates for liquid crystal display backlight,” J. Opt. A, Pure Appl. Opt. 7(3), 111–117 (2005). [CrossRef]
  13. C.-Y. Chen, T.-T. Yang, and W.-S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16(20), 15495–15505 (2008). [CrossRef] [PubMed]
  14. B. Kim, J. Kim, W.-S. Ohm, and S. Kang, “Eliminating hotspots in a multi-chip LED array direct backlight system with optimal patterned reflectors for uniform illuminanceand minimal system thickness,” Opt. Express 18(8), 8595–8604 (2010). [CrossRef] [PubMed]
  15. D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (John Wiley and Sons, 2001).

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