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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26972–26982
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A slim apparatus of transferring discrete LEDs’ light into an ultra-collimated planar light source

Tun-Chien Teng, Wen-Shing Sun, Li-Wei Tseng, and Wei-Chung Chang  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26972-26982 (2013)
http://dx.doi.org/10.1364/OE.21.026972


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Abstract

In this paper, we proposed a novel apparatus, which has very slim volume and can transfer light emitted from discrete LEDs into a uniform and ultra-collimated planar light source (UCPLS). This apparatus adopts the two-layer folded frame and two-stage CPC design so that thickness of the entire apparatus can be minimized; especially the feeder in the two-stage CPC design can greatly reduce the thickness of the CPC and make the light passing through the second-stage CPC become much more collimated. In addition, by side-by-side arrangement, a large-sized UCPLS can also be obtained. In our embodiment with an emitting area of the upper LGP of 280 mmX80 mm and a LED with optical flux of 8 lumens used as the light source, the performance according to the related simulation results shows as follows: angular FWHM of the resultant light emitted from the apparatus in the vertical and horizontal is 4.87 degrees and 24 degrees, respectively; spatial uniformity and total energy efficiency reach 84% and 69%, respectively; the average head-on luminance reaches up 5600 nit, yet this apparatus consumes just 60 mW. Furthermore, the results also demonstrate this design has potential to be applied to the product of 23 inches above while thickness of the entire apparatus is only 2.2 mm.

© 2013 Optical Society of America

1. Introduction

According to the above-mentioned literature about LGP designs for the HCPLS, we can summarize as follows. First, the angular distribution ranges from 10 to 38 degrees. Second, most of the designs have complicated and sophisticated microstructures on the LGP such as sub-wavelength gratings or segmented prisms; some need different material to match refractive index; others need thicker or wider volume to accommodate the specific surface profile or an extra pre-collimation component. So, it is very difficult for them to be applied to a large-sized product. Therefore, we propose a novel design for a slim planar apparatus for the UCPLS in this paper, which can transfer the light from the discrete LED into uniform planar light source with ultra-collimated emitting light of 5 degrees (FWHM) below. Furthermore, this apparatus does not need a complicated process to form sophisticated microstructures on the LGP such that it is easy to be applied to large-sized product while keeping relative slim volume.

2. Design concept and principle model

In order to avoid the need for sophisticated microstructures formed on the LGP, we adopt the method similar to the above-mentioned fourth kind, firstly utilizing the compound parabolic concentrator (CPC) to pre-collimate the light emitted from a LED and then obtaining ultra collimated light emitted from the LGP by well-designed but relatively easily-manufactured microstructures on the LGP. The merit of our method is that the microstructures on the LGP can be simplified as the V-groove which can be processed by precise mechanical tooling. However, the drawback is that the CPC occupies extra space such that the apparatus becomes bulky. Therefore, we must mitigate this drawback as possible to keep the apparatus slim. How to mitigate this drawback will be detailed later.

The relationship between the angular range of the light entering the inlet of the CPC and that of the light emitted from the outlet of the CPC can be expressed as follows:

A1A2=n2sinθ2n1sinθ1,
(1)
A1A2=(n2sinθ2)2(n1sinθ1)2.
(2)

Equation (1) is applied to 2D cases, and Eq. (2) is for 3D cases, where A1 and A2 are the area of the inlet and outlet of the CPC; n1 and n2 are the refractive index of the material in which the CPC inlet and outlet are immersed respectively. From the equations, we know the collimation effect of the CPC depends on the ratio of its outlet area to inlet area; the higher the ratio is, the more collimated the emitting light is. However, for a higher ratio, dimensions of the CPC also become larger. Further, we also elongate a CPC but keep its ratio in order to improve both spatial and angular uniformity of the emitting light. They both need extra peripheral space, which make the apparatus bulky. Therefore, the slim planar apparatus proposed in this study adopts a two-layer folded frame; the upper and lower layers accommodate the LGP (called ‘upper LGP’ hereafter) and CPC, respectively. So, this frame provides sufficient space for the length and width of the CPC, but the space for thickness of the CPC is still limited. Consequently, thickness of the CPC is the bottleneck for the design. According to Eq. (1), we must maintain the higher ratio of outlet thickness of CPC to inlet thickness in order to let emitting light be more collimated in the vertical direction. With the limit on thickness of the slim apparatus, we can only reduce inlet thickness of the CPC. However, inlet thickness of the CPC also has a minimum limit because it must match the thickness of a LED that can provide enough luminous flux. In order to overcome this conflict, we proposed a new design ‘Distributed sub-layer feeding CPC (DSLF CPC)’ to resolve the problem. The design concept is to couple the light emitted from a LED of certain thickness dispersedly into the duplicate CPCs that parallel each other. We use a ‘feeder’ facing the emitting surface of the LED, which splits into several sub-layers to guide the emitting light to spread horizontally and then into each of the CPCs, as shown in Fig. 1
Fig. 1 Illustration of the feeder used in DSLF CPC design: (a) perspective view; (b) front view (not drawn to scale).
. In the example of Fig. 1, the feeder splits into four sub-layers alternately spreading in the horizontal, and each sub-layer connects a CPC. Thus, the inlet thickness of the CPC can reduce into one fourth of the thickness of the LED, and the ratio of the outlet thickness to inlet thickness can increase up to four times at the same outlet thickness. Because we want the CPC to collimate the light both in the horizontal and vertical, the CPC is booleaned by two 2D CPCs, one for vertical collimation and the other for horizontal collimation. The cross-section of the resultant CPC is rectangular. In order to easily fix the CPC, the bottom and top surfaces of the CPC are designed to be planar and parabolic, respectively. Furthermore, we use the CPC made of PMMA to transfer light by TIR to avoid absorption loss.

Next, we note that energy loss occurs during the process that the light emitted from LEDs horizontally spreads to be coupled into CPCs by the feeder. Generally, the light suffers less loss during the process when the light is more collimated in the horizontal. Therefore, we adopt the two-stage CPC design to address this issue. We use the first-stage CPC to preliminarily collimate the light emitted from the LED in the horizontal and then let the light enter the feeder, as shown in Fig. 2
Fig. 2 Illustration of the component layout in the lower layer of the apparatus.
. Because the channel in the feeder has 45-degree corner facet for the purpose of keeping feeder volume compact, the entering light cannot propagate by TIR all the way in the feeder when it is not collimated enough. So, the corner facets should be coated with reflecting layer. Of course, it will suffer some energy loss due to absorption, but it is acceptable. The light from the LED is preliminarily collimated by the first-stage-CPC, then coupled into the second-stage CPC (i.e. DSLF CPC) by the feeder, and finally becomes highly collimated light through the second-stage CPC.

Since the light exiting from the second-stage CPC is highly collimated, it is difficult to mix with the light of adjacent CPCs to integrate a uniform linear light source for the upper LGP sequent use. In order to overcome this issue, we set up a light-mixing plate behind the end of the second-stage CPC to improve horizontal spatial uniformity of light entering the upper LGP. The light-mixing plate is made of PMMA and has an array of lenticular micro-structures on its front end (as shown in the upper right inset of Fig. 2), which can horizontally spread the light emitted from the second-stage CPC to benefit light-mixing. The profile of the lenticular micro-structure affects diffusion and mix of the emitting light. For high-sag profile, effect of light-mixing is better, but collimation in the horizontal becomes worse; on the contrary, effect of light-mixing is poor. Therefore, how to make proper trade-off for the profile design is very important.

Next, we arrange a coupling prism to guide the light exiting from the light-mixing plate into the upper LGP. Such design can greatly reduce peripheral volume of the apparatus because the peripheral volume just needs to accommodate a coupling prism instead of a CPC. The coupling prism is an elongated pillar substantially with cross-section of an isosceles right triangle as shown in Fig. 3
Fig. 3 Cross-section of the coupling prism.
, which is made of PMMA. The light from the light-mixing plate enters the lower left facet of the coupling prism, then reflects on the two left slope facets, and finally exits from the upper left facet. If the light entering the coupling prism is sufficiently collimated in the vertical, the light can be almost fully coupled into the upper layer by TIR on the two right slope facets. On the contrary, some stray light will appear, and coupling efficiency decreases. In order to improve coupling efficiency, we cut the vertex corner of the coupling prism and coat reflective layer on the two right slope facets. Further, the coupling prism has a reflective protrusion on its center to keep the stray light of the lower layer from entering the upper layer.

Next, the light exiting from the light-mixing plate is guided into the upper LGP through the coupling prism. The object of the upper LGP is to transfer the linear light source from the coupling prism into a uniform and ultra-collimated planar light source (UCPLS) by its micro-structures with various distribution densities. Since the light entering the upper LGP is highly collimated, we just need to design the proper micro-structure such as V-groove, to deflect the light into the normal. In this study, the upper LGP has micro-structures of V-groove protruding from its bottom surface, and slope facet of the micro-structure has 43~44 degrees with the horizontal. If the light already uniformly distributes in the horizontal before entering the upper LGP, the V-groove micro-structure can elongate transversely (horizontally) across the entire upper LGP and thus variously distributes just along the longitudinal (vertical) direction; it is easier to fabricate such a mold by machining process. If the light distribution in the horizontal is not sufficiently uniform, we need the micro-structure of a segmented V-groove to modulate both horizontal and vertical distribution densities to obtain a uniform UCPLS. Such a mold with micro-structures of the segmented V-groove thereon cannot be fabricated by mechanical process, but needs photoresist process, which increases the cost. Further, slope of the V-groove micro-structure must be highly precise, but photoresist process cannot guarantee precision. In order to extract most of the light entering the upper LGP, we adopt a wedge upper LGP. Although energy utility is not much different between the flat and wedge LGP when the LGP has high ratio of its length to thickness, part of the such collimated light entering the flat upper LGP directly passes through the LGP without touching the V-groove micro-structure and cannot be extracted. The entire apparatus assembling the above-mentioned components is schematically illustrated in Fig. 4
Fig. 4 Schematic illustration of the entire apparatus: (a) perspective view; (b) front view (not drawn to scale).
.

3. Simulation results and discussion

Next, we adopt a coupling prism to guide the light exiting the light-mixing plate into the upper LGP in the upper layer of the apparatus. In our simulation model, the total thickness of the coupling prism is 2.2 mm; the thickness of its central protrusion is 0.2 mm; the width of the coupling prism is 80 mm. In order to enhance coupling efficiency, the two facets adjacent to the right angle are coated with reflectivity of 0.98. In simulation analysis, we find the coupling prism has very little impact on spatial and angular distribution of light except little part of the light is absorbed; the coupling efficiency of this component is about 0.93. Here, the upper LGP is a wedge LGP with taper angle of 0.12 degree, length of 280 mm, width of 80 mm, and thickness of the front end of 1 mm. Further, the upper LGP has V-groove micro-structures on its bottom surface to extract light out. The cross-section profile of the V-groove micro-structure is an isosceles angle with width of 25 um and vertex angle of 92 degrees. Also, we put a specular type of reflector with reflectivity of 0.98 (e.g. enhanced specular reflector, ESR, 3M Corp.) underneath the upper LGP. The simulation results of angular distributions and illuminance of the light resultant emitted from the upper LGP are shown in Figs. 6(a)
Fig. 6 Energy distribution of the light emitted from the upper LGP: (a) angular distribution; (b) spatial distribution.
and 6(b), respectively. In Fig. 6(a), we can find the resultant emitting light is ultra-collimated with average FWHM of 4.87 degrees in the vertical and substantially has the same trend in angular distribution from near to far region of the upper LGP. If we further optimize slope of the facet of the V-groove micro-structures regarding their respective positions, the resultant emitting light might be further collimated and have higher peak intensity. As for horizontal angular distribution of the resultant emitting light, it has FWHM of 24 degrees the same as Fig. 5(b) because the transverse-extension V-groove does not affect the horizontal angular distribution. In Fig. 6(b), we can find the illuminance varies within ± 9% longitudinally across the upper LGP. The result shows spatial uniformity of the resultant emitting light is 84% and acceptable. In addition, the average head-on luminance of the resultant emitting light is about 5600 nit.

Next, we analyze energy efficiency for each component of the apparatus. For non-image optics, energy efficiency is a very important factor. Especially for the era concerning energy-saving, the apparatus only with ultra-collimated emitting light is not enough, and it also must have higher energy efficiency. We list energy efficiency (simulation) of each component in Table 3

Table 3. Energy efficiency for the components of the apparatus.

table-icon
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. In Table 3, we can find energy loss mostly occurs in the first-stage CPC and feeder, about 20% loss, mainly due to absorption on the reflective layer. If the feeder has a smooth curved channel to guide light separately into the second-stage CPC, the feeder does not need reflective coating such that energy loss can greatly reduce [24

24. J. Chaves, W. Falicoff, O. Dross, J. C. Miñano, P. Benitez, and W. A. Parkyn, “Combination of light sources and light distribution using manifold optics,” Proc. SPIE 6338, 63380M (2006).

]. However, such a design needs more space and is not as compact as the feeder proposed in this paper. The secondary energy loss occurs in the coupling prism, about 5% more, mainly due to absorption on the reflective layer. The third energy loss occurs in the 2nd-stage CPC, about 5% less, mainly due to Fresnel loss and bulk absorption of PMMA. The energy efficiency of the entire apparatus is about 69%; this value is not high but is acceptable, especially for such a UCPLS. If we can implement anti-reflective coating on some facets of the components or even glue some components together to reduce Fresnel loss, energy efficiency of the entire apparatus can further improve.

Finally, we discuss feasibility of this apparatus design. Indeed, the precise molds required for feeder are not easily fabricated. Especially for the feeder, tolerance of the mold must be tight; otherwise energy loss in the feeder will increase. The feeder might be divided into several sub-layers that can be inject-molded separately, and then the sub-layers are combined into a feeder. As for the CPC, the solid CPC has been used for solar collector or concentration, which can be fabricated by inject-molding. Although the CPC used in this apparatus is on the scale of millimeters, because the CPC used in the apparatus are surrounded by three paraboloidal surfaces and one planar surface, fabricating the mold for such a CPC is relative simple as compared with the mold for the freeform lens. Of course, if the mold is not precise or smooth enough, energy efficiency of the CPC will reduce. Although adopting the CPC increases cost and makes fabrication complex, the upper LGP can be fabricated more easily because the complicated micro-structures on the LGP are no longer required. As compared with the very complicated LGP proposed in the literature, our design is worth adopting, especially considering its outstanding performance and potential for large-sized application. By the way, we also need to arrange some pads in vacancy of the lower layer of the apparatus to support the reflector sheet and upper LGP; the pads are not shown in Fig. 4.

4. Conclusion

Acknowledgments

References and links

1.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, K. Aiki, and M. Ogawa, “A full color eyewear display using holographic planar waveguides,” SID Symp. Dig. Tech. Pap. 39, 89–92 (2008).

2.

A. Cameron, “Optical waveguide technology and its application in head mounted displays,” Proc. SPIE 8383, 83830E (2012). [CrossRef]

3.

T. Levola, “Color distribution in exit pupil expanders,” US patent 8254031 (2012).

4.

A. Travis, N. MacCrann, N. Emerton, J. Kollin, A. Georgiou, J. Lanier, and S. Bathiche, “Virtual image display as a backlight for 3D,” Opt. Express 21(15), 17730–17735 (2013). [CrossRef] [PubMed]

5.

K. W. Chien, H. P. D. Shieh, and H. Cornelissen, “Polarized backlight based on selective total internal reflection at microgrooves,” Appl. Opt. 43(24), 4672–4676 (2004). [CrossRef] [PubMed]

6.

M. Xu, H. P. Urbach, and D. K. G. de Boer, “Simulations of birefringent gratings as polarizing color separator in backlight for flat-panel displays,” Opt. Express 15(9), 5789–5800 (2007). [CrossRef] [PubMed]

7.

Y. C. Kim, H. D. Im, M. G. Lee, and H. Y. Choi, “Directivity enhanced BLU for edge-type local dimming,” SID Symp. Dig. Tech. Pap. 42, 662–664 (2011).

8.

P. C. Chen, H. H. Lin, C. H. Chen, C. H. Lee, and M. H. Lu, “Color separation system with angularly positioned light source module for pixelized backlighting,” Opt. Express 18(2), 645–655 (2010). [CrossRef] [PubMed]

9.

K. Nakamura, T. Fuchida, K. Yamagata, A. Nishimura, T. Takita, and H. Takemoto, “Optical design of front diffuser for collimated backlight and front diffusing system,” IDW 11, 475–478 (2011).

10.

K. W. Chien and H. P. D. Shieh, “Time-multiplexed three-dimensional displays based on directional backlights with fast-switching liquid-crystal displays,” Appl. Opt. 45(13), 3106–3110 (2006). [CrossRef] [PubMed]

11.

LGD, “Stereoscopic display device using electrically-driven liquid crystal lens,” US patent 7855756 (2010).

12.

L. Pyayt, G. K. Starkweather, and M. J. Sinclair, “One telescope per pixel,” OSA CLEO (2010).

13.

W. Mphepö, Y. P. Huang, P. Rudquist, and H. P. D. Shieh, “Digital micro hinge (DMH) based display pixels,” J. Disp. Technol. 6(4), 142–149 (2010). [CrossRef]

14.

H. C. Cheng, J. Yan, T. Ishinabe, N. Sugiura, C. Y. Liu, T. H. Huang, C. Y. Tsai, C. H. Lin, and S. T. Wu, “Blue-phase liquid crystal displays with vertical field switching,” J. Disp. Technol. 8(2), 98–103 (2012). [CrossRef]

15.

J. H. Lee, H. S. Lee, B. K. Lee, W. S. Choi, H. Y. Choi, and J. B. Yoon, “Simple liquid crystal display backlight unit comprising only a single-sheet micropatterned polydimethylsiloxane (PDMS) light-guide plate,” Opt. Lett. 32(18), 2665–2667 (2007). [CrossRef] [PubMed]

16.

S. Aoyama, A. Funamoto, and K. Imanaka, “Hybrid normal-reverse prism coupler for light-emitting diode backlight systems,” Appl. Opt. 45(28), 7273–7278 (2006). [CrossRef] [PubMed]

17.

S. R. Park, O. J. Kwon, D. Shin, S. H. Song, H. S. Lee, and H. Y. Choi, “Grating micro-dot patterned light guide plates for LED backlights,” Opt. Express 15(6), 2888–2899 (2007). [CrossRef] [PubMed]

18.

Nanogate Advanced Materials, “Illuminating device,” US patent 7682062 (2010).

19.

W. H. Yang, H. H. Lin, C. J. Hsu, and Y. N. Pao, “LED coupler lens array for one dimensional collimating backlight,” IDW 11, 1399–1400 (2011).

20.

D. Grabovičkić, P. Benítez, J. C. Miñano, and J. Chaves, “LED backlight designs with the flow-line method,” Opt. Express 20(S1), A62–A68 (2012). [CrossRef] [PubMed]

21.

A. Travis, T. Large, N. Emerton, and S. Bathiche, “Collimated light from a waveguide for a display backlight,” Opt. Express 17(22), 19714–19719 (2009). [CrossRef] [PubMed]

22.

I. B. M. Corporation, “Light guide apparatus, a backlight apparatus and a liquid crystal display apparatus,” US patent 6667782Bl (2003).

23.

J. W. Pan and C. W. Fan, “High luminance hybrid light guide plate for backlight module application,” Opt. Express 19(21), 20079–20087 (2011). [CrossRef] [PubMed]

24.

J. Chaves, W. Falicoff, O. Dross, J. C. Miñano, P. Benitez, and W. A. Parkyn, “Combination of light sources and light distribution using manifold optics,” Proc. SPIE 6338, 63380M (2006).

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.3670) Optical devices : Light-emitting diodes
(220.2945) Optical design and fabrication : Illumination design
(080.4298) Geometric optics : Nonimaging optics

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: September 17, 2013
Revised Manuscript: October 19, 2013
Manuscript Accepted: October 22, 2013
Published: October 31, 2013

Citation
Tun-Chien Teng, Wen-Shing Sun, Li-Wei Tseng, and Wei-Chung Chang, "A slim apparatus of transferring discrete LEDs’ light into an ultra-collimated planar light source," Opt. Express 21, 26972-26982 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26972


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References

  1. H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, K. Aiki, and M. Ogawa, “A full color eyewear display using holographic planar waveguides,” SID Symp. Dig. Tech. Pap.39, 89–92 (2008).
  2. A. Cameron, “Optical waveguide technology and its application in head mounted displays,” Proc. SPIE8383, 83830E (2012). [CrossRef]
  3. T. Levola, “Color distribution in exit pupil expanders,” US patent 8254031 (2012).
  4. A. Travis, N. MacCrann, N. Emerton, J. Kollin, A. Georgiou, J. Lanier, and S. Bathiche, “Virtual image display as a backlight for 3D,” Opt. Express21(15), 17730–17735 (2013). [CrossRef] [PubMed]
  5. K. W. Chien, H. P. D. Shieh, and H. Cornelissen, “Polarized backlight based on selective total internal reflection at microgrooves,” Appl. Opt.43(24), 4672–4676 (2004). [CrossRef] [PubMed]
  6. M. Xu, H. P. Urbach, and D. K. G. de Boer, “Simulations of birefringent gratings as polarizing color separator in backlight for flat-panel displays,” Opt. Express15(9), 5789–5800 (2007). [CrossRef] [PubMed]
  7. Y. C. Kim, H. D. Im, M. G. Lee, and H. Y. Choi, “Directivity enhanced BLU for edge-type local dimming,” SID Symp. Dig. Tech. Pap.42, 662–664 (2011).
  8. P. C. Chen, H. H. Lin, C. H. Chen, C. H. Lee, and M. H. Lu, “Color separation system with angularly positioned light source module for pixelized backlighting,” Opt. Express18(2), 645–655 (2010). [CrossRef] [PubMed]
  9. K. Nakamura, T. Fuchida, K. Yamagata, A. Nishimura, T. Takita, and H. Takemoto, “Optical design of front diffuser for collimated backlight and front diffusing system,” IDW11, 475–478 (2011).
  10. K. W. Chien and H. P. D. Shieh, “Time-multiplexed three-dimensional displays based on directional backlights with fast-switching liquid-crystal displays,” Appl. Opt.45(13), 3106–3110 (2006). [CrossRef] [PubMed]
  11. LGD, “Stereoscopic display device using electrically-driven liquid crystal lens,” US patent 7855756 (2010).
  12. L. Pyayt, G. K. Starkweather, and M. J. Sinclair, “One telescope per pixel,” OSA CLEO (2010).
  13. W. Mphepö, Y. P. Huang, P. Rudquist, and H. P. D. Shieh, “Digital micro hinge (DMH) based display pixels,” J. Disp. Technol.6(4), 142–149 (2010). [CrossRef]
  14. H. C. Cheng, J. Yan, T. Ishinabe, N. Sugiura, C. Y. Liu, T. H. Huang, C. Y. Tsai, C. H. Lin, and S. T. Wu, “Blue-phase liquid crystal displays with vertical field switching,” J. Disp. Technol.8(2), 98–103 (2012). [CrossRef]
  15. J. H. Lee, H. S. Lee, B. K. Lee, W. S. Choi, H. Y. Choi, and J. B. Yoon, “Simple liquid crystal display backlight unit comprising only a single-sheet micropatterned polydimethylsiloxane (PDMS) light-guide plate,” Opt. Lett.32(18), 2665–2667 (2007). [CrossRef] [PubMed]
  16. S. Aoyama, A. Funamoto, and K. Imanaka, “Hybrid normal-reverse prism coupler for light-emitting diode backlight systems,” Appl. Opt.45(28), 7273–7278 (2006). [CrossRef] [PubMed]
  17. S. R. Park, O. J. Kwon, D. Shin, S. H. Song, H. S. Lee, and H. Y. Choi, “Grating micro-dot patterned light guide plates for LED backlights,” Opt. Express15(6), 2888–2899 (2007). [CrossRef] [PubMed]
  18. Nanogate Advanced Materials, “Illuminating device,” US patent 7682062 (2010).
  19. W. H. Yang, H. H. Lin, C. J. Hsu, and Y. N. Pao, “LED coupler lens array for one dimensional collimating backlight,” IDW11, 1399–1400 (2011).
  20. D. Grabovičkić, P. Benítez, J. C. Miñano, and J. Chaves, “LED backlight designs with the flow-line method,” Opt. Express20(S1), A62–A68 (2012). [CrossRef] [PubMed]
  21. A. Travis, T. Large, N. Emerton, and S. Bathiche, “Collimated light from a waveguide for a display backlight,” Opt. Express17(22), 19714–19719 (2009). [CrossRef] [PubMed]
  22. I. B. M. Corporation, “Light guide apparatus, a backlight apparatus and a liquid crystal display apparatus,” US patent 6667782Bl (2003).
  23. J. W. Pan and C. W. Fan, “High luminance hybrid light guide plate for backlight module application,” Opt. Express19(21), 20079–20087 (2011). [CrossRef] [PubMed]
  24. J. Chaves, W. Falicoff, O. Dross, J. C. Miñano, P. Benitez, and W. A. Parkyn, “Combination of light sources and light distribution using manifold optics,” Proc. SPIE6338, 63380M (2006).

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