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Angularly positioned LED-based spatial-temporal color separation system

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Abstract

This study proposes a two-field driving scheme for field sequential color liquid crystal displays (LCDs) without color filters. The proposed scheme is based on angularly positioned color LEDs. In each field, the angular rays of two colors are collimated by a collimation lens, redirected by a light guide, and converged by a cylindrical-lens array to map into corresponding sub-pixel positions to efficiently display color images. The three main advantages of this approach are the elimination of dye color filters, high feasibility using conventional ultra-precision machining processes, and a larger color gamut.

©2012 Optical Society of America

1. Introduction

A color display synthesizes a color image from the primary colors of a light source. Color synthesis can generally be divided into two types. The first approach is the direct optical superposition of three primary color images, which is commonly used in projection display systems. The second approach is the spatial additive color synthesis using dye color filters. This approach is suitable for direct-view color displays, such as color liquid crystal display (LCDs). Although dye color filters have been applied successfully in most LCD panels, this method has one significant limitation: visible colors are generated at the cost of the absorption of the undesired spectra. Therefore, researchers have proposed several approaches using hologram elements [15] to increase light efficiency by discarding the absorption-type color filter. Dammann [2] used an interleaved structured grating that diffracts three primary colors (RGB) into a microlens array to spatially separate colors. Caputo [4] designed a subwavelength grating with a period of 320 nm to diffract light coming from the opposite directions of a light guide into a microlens array to generate a symmetric color pattern. These methods require a precise, short-period grating profile that must be fabricated with e-beam or interferometry, making it unsuitable for mass production. A well-known alternative is to use a field sequential color (FSC) illumination LCD, which attempts to increase power efficiency by 300%. Although FSC looks promising, it must drive each pixel at a high rate exceeding 180 Hz to avoid annoying color-break-up artifacts [6].

To overcome these problems, we earlier proposed a structure for a color LCD module (Fig. 1 ) that separates the white spectrum into five color components by angularly positioning an array of point LED sources [7]. This method requires an ultra-precision process to fabricate a pentagon prism array near the focal point of the cylindrical lens for redirecting each color to perpendicularly leave the surface of the LCD. This approach also suffers from low resolution and complex signal processing of five color components (red-green-blue-green-red (RGBGR)). This study proposes an angularly positioned LED based spatial-temporal color separation system (ALED-ST) to improve on this earlier design. The ALED-ST uses color LEDs and a two-field driving scheme to produce RBR/GBG color lines, instead of R-G-B-G-R color lines, on the LCD panel. Each full pixel is equal to the width of each lens of the cylindrical-lens array (i.e., two instead of five sub-pixels wide). The proposed method is more promising than the color-filterless FSC LCD because it reduces the field number and alleviates the demand for fast-response LC modes in FSC LCDs.

 figure: Fig. 1

Fig. 1 A color separation backlight side-lit by an array of R-G-B-G-R LEDs.

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2. Backlight system and design

Before describing the proposed configuration, this section presents a review of the potential designs of RGB LED-based spatial color separation backlights and their limitations. These backlights include the following components: a RGB LED collimation module to provide angularly separated color light, a light guide to redirect the color light, and a cylindrical-lens array to generate spatial color light at the corresponding sub-pixels.

The starting geometry of the light source arrangement has been schematically represented in Fig. 2(a) . After being collimated by a collimation lens, the angular direction of blue rays, but not red and green rays, is parallel with the edge of the light guide in the Z-axis. This type of arrangement has the following disadvantages. For the red and the green rays, either side of the center will leave a shadow that induces non-uniform illuminance after these rays pass through the cylindrical-lens array. On the other hand, green and red rays angularly mix together in the reflection area, inducing yellow rays (not pure green or red rays) after passing through the cylindrical-lens array. To solve this color mixing problem, a second configuration [7] was designed by angularly positioning a sequence of R-G-B-G-R LEDs. As Fig. 2(b) shows, when the rays of the same color are reflected from the edge of the light guide, they overlap with the symmetrical, same color rays. In this case, the same color rays inside the light guide do not angularly mix with other color rays. However, this configuration has several limitations, such as the requirement of a pentagon prism array and complex signal processing, as discussed in the introduction section.

 figure: Fig. 2

Fig. 2 (a) An arrangement of R-G-B LEDs and a collimation lens performs the angular color-separation, but induces asymmetrical illumination (such as the red rays shown) in the light guide and color mixing after passing through the cylindrical-lens array; (b) An arrangement of R-G-B-G-R LEDs and a collimation lens generates the symmetric angular color-separation in the light guide without color mixing after passing through the cylindrical-lens array.

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The third configuration was also designed by angularly positioning a sequence of RG-B-GR LEDs (Fig. 3 ). Unlike the second design, this configuration does not require a pentagon prism array, but requires two dye color filters. The red and the green LEDs are arranged in the same position. Color-mixing between R and G in the light guide generates a yellow-blue-yellow angular color distribution. After the light passes through the cylindrical-lens array, two dye color filter layers (R and G types) transmit the desired bandwidth and filter out the undesired spectra to generate R and G color lines, respectively. Compared with a conventional color LCD, which use three color filter layers (R, G and B types), this method doubles the optical efficiency.

 figure: Fig. 3

Fig. 3 An arrangement of RG-B-RG LEDs to a collimation lens yields the angular color-separation. After passing through the cylindrical-lens array, two conventional color filter layers filter the mixing colors to produce three primary colors: R, B, and G.

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Although this configuration looks promising, optical efficiency can be further improved to 3X by introducing the two-field driving scheme. The two-field driving scheme lacks the third temporal degree of freedom in displaying the third primary information. This problem can be solved by incorporating spatial color filters [8,9] or a spatially modulated color backlight [10]. The former approach requires special dye materials, whereas the latter requires a complex two-field algorithm to control the light spreading function of the backlighting.

The proposed ALED-ST takes advantage of angularly positioning a sequence of color LEDs and the two-field driving scheme. The ALED-ST requires no special materials or complex two-field algorithms to control the light spreading function. By displaying two field colors time sequentially, the ALED-ST can form a full color image for the human visual system. In this design, the red, green, and blue lights are assigned as the first, second, and third primary colors, respectively. Blue colors existing in both fields can typically reduce visual deviation of images reproduced by the two-field method because the human visual system is less sensitive to blue information [10]. Therefore, red and blue LEDs are lit simultaneously in the first field to create a magenta-like color (Fig. 4(a) ). In the second field, green and the blue LEDs are lit simultaneously to create a cyan-like color (Fig. 4(b)).

 figure: Fig. 4

Fig. 4 The configuration of ALED-ST in (a) field 1 and (b) field 2.

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However, the two-field driving scheme is also a drawback of the ALED-ST. The ALED-ST could be thicker. To drive two fields, the red chip and the blue chip must be packaged at different heights in the same LED, which may increase the thickness by 1.5 mm compared to the second configuration [7]. Conversely, the ALED-ST only requires two electronic sub-systems to drive two sub-pixels, whereas the second configuration requires five electronic sub-systems to drive five sub-pixels. Therefore, the extra thickness may be reduced by considering the volume reduction of the electric system.

The structure of an ALED-ST system includes three main modules: (1) the light source collimation module, (2) the light guide with v-grooves, and (3) the cylindrical-lens and the prism array. In the design stage, the ray-tracing tool ZEMAX [11] was first used to determine the initial profiles of the collimation lens. All ZEMAX parameters were then substituted into ASAPTM [12] to analyze the system’s overall performance. The ALED-ST can be viewed as a relay system that relays the color rays from LED chips to the sub-pixels of the liquid crystal layer.

In the collimation module (Fig. 5(a) ), the first-order relationship between the focal length (F) of the collimation lens, the off-axis distance (H) of a LED position, and the propagation direction of the generated collimated rays (θ) can be estimated by

H~F×tan(θ)
In this design, the blue LED is situated at the focal point of collimation lens. The green and the red LEDs are arranged in the same angular position ( = θ), but at different heights. Because a LED exhibits Lambertian radiation, this design requires a reflective cup for converging outer light from each LED, as in our previous design [7]. After the rays pass through the collimation lens with a focal length being 57 mm, the ray distributions are 0° ± 2° for the blue rays and 10° ± 2.7° for the green and the red rays, as calculated by ASAP TM (Fig. 5(b)).

 figure: Fig. 5

Fig. 5 (a) With color LEDs being set on the focal plane of a collimation lens, the color rays are collimated; (b) The corresponding propagation picture drawn by ASAPTM.

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The main function of the light guide is to provide a uniform light distribution and redirect the rays from the collimation module to the liquid crystal panel. To maintain the collimation along the Z-axis (Fig. 4), V-grooves with an apex angle of 80° and a reflector were designed at the bottom of light guide. A uniformity of 70.5% and a coupling efficiency of 75% were achieved by controlling the distribution of depth and period in simulation using ASAPTM (Fig. 6(a) ). Similar to a conventional light guide, this light guide induces “hot” and “cold” spots (Fig. 6(b)), and requires a front diffuser in the following light path.

 figure: Fig. 6

Fig. 6 (a) Schematic V-grooves and reflector of the light guide; (b) The uniformity of the output rays from light guide.

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The cylindrical lens converges each color to pass through the corresponding subpixel, whereas the prism array redirects each color to perpendicularly leave the surface of the LCD. As Fig. 7(a) shows, the parameters of the cylindrical-lens array are related to the angular components φ and the full-pixel size D, which is also the width of each cylindrical lens. The thicknesses of the cylindrical-lens film, the glue layer, the polarizer, and the bottom glass of LC panel are t1, t2, t3, and t4, respectively, and their deflective angles are φ1, φ2, φ3, and φ4, respectively. If we assume that the refractive indices of these films are the same (n), φ1, φ2, φ3, and φ4 can be simply represented by a constant φ. The first-order relationship between the film thicknesses and the sub-pixel width (p) can be described by

 figure: Fig. 7

Fig. 7 (a) Geometry of the cylindrical-lens array with respect to the pixels; (b) Simulated optical diagram of the cylindrical lens array. LC layer are set around the focal plane with less color crosstalk; (c) and (d) are the footprint diagrams for field 1 and field 2, respectively.

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p=D2=(t1+t2+t3+t4)×tanϕ

The focal length (f) of the cylindrical lens is a function of the refractive index and the thickness of each film, and is computed by

f=t1n1+t2n2+t3n3+t4n4=(t1+t2+t3+t4)n
The focal length further determines the curvature radius (R) of the cylindrical lens. After passing through the LC layer, each color component has different directions, causing a color shift. The spread of each color is narrow, and is usually less than ± 10∘after passing through the cylindrical lens. According to Yamada [13], the directions of each color can be redirected by a prism array and each color emerges normally from the top glass. Because the divergence of each color is still small, a highly efficient front diffuser, such as a wave film with a sinusoidal profile, can be attached on the top glass to increase the intensity distribution from ± 9.8∘to ± 35∘ (Fig. 7(a)). This study mainly presents a cylindrical-lens array to demonstrate the concept of spatial-temporal color separation with angularly positioned LEDs under limited resources. The target display has a sub-pixel size of 300 μm. For the two-field scheme, a full pixel is 600 μm wide. Based on simulation data, a radius of curvature 688 μm and a resin with a refractive index of 1.495 were chosen for the cylindrical-lens array. The LC layer was set around the focal plane of the cylindrical-lens array, where there is less color crosstalk between the two colors (Fig. 7(b)). Figures 7(c) and 7(d) show the footprint diagrams of field 1 and field 2, respectively. These two diagrams are not exactly the same because the R, G, and B LEDs are not set at the same height at the end of the reflector cups. Table 1 lists the efficiency performance of the most popular color separation technologies applied for backlighting. Compared with other color separation technologies, the ALED-ST not only achieves high efficiency, but can also be fabricated with conventional ultra-precision technology. Nevertheless, the ALED-ST also has some issues, as described in Section 3. Table 1 also lists the drawbacks associated with each approach.

Tables Icon

Table 1. Comparison of ALED-ST Performance with Current Color-separation Technologies

3. Experimental results and discussions

An ALED-ST prototype was manufactured for a 3.2-inch backlight. The collimation lens in the collimation module was made of poly-methyl-methacrylate (PMMA) and fabricated by infrared (IR) laser machining. To achieve high collimation, the side-wall of the collimation lens was further polished by a V-cut precision machine. The reflective cup was also cut from a PMMA sheet. After manually polishing the side-wall, a reflective aluminum alloy reflective film was attached to enhance reflection. To reduce optical energy loss, the collimation lens and the reflective cup were sandwiched between two silver reflectors, each of which had a reflectivity of 99.1%. Because the green and red LEDs were set in the same angular position but at different heights, three 3-in-1 RGB LEDs (Fig. 8(a) ) were used in the collimation module. This RGB LED created a D65 (i.e., a color temperature of 6500k) white-balanced luminous flux of 23 lm. Measurements from an integrating sphere showed that over 22% (approximately 5.1 lm) of efficiency loss occurred during collimation. The measured ray distributions were 0° ± 1.8° for the blue rays and 10° ± 2.5° for the green and the red rays, which matched design values well.

 figure: Fig. 8

Fig. 8 (a) Photograph of a 3-in-1 RGB LED; (b) A diamond cutter with the designed profile was used to cut the mold on a roller; (c) The cross-sectional profile of a cylindrical lens under the microscope; (d) SEM image of the cross-sectional profile of a wave film.

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The light guide consisted of a V-grooved PMMA plate and a bottom silver reflector. The V-grooves at the bottom side were also formed by a V-cut precision machine. Measurements of optical coupling efficiency showed that over 32% of efficiency loss occurred during the redirection of the side-incident beam to the surface of the light guide. The efficiency loss could be further reduced by reducing the surface roughness of V-grooves and adopting a better structure design.

The cylindrical-lens array was imprinted on an 188 μm thick polyethylene terephthalate (PET) film using the roll-to-roll UV–cured imprinting process. The fabrication steps were as the follows. First, a diamond cutter with the designed profile was used to form a micro-structure on a copper roller (Fig. 8(b)). Second, ultraviolet (UV) resin was dropped onto the PET film, imprinted by the roller, hardened by UV light, and demolded from the roller. Figure 8(c) shows the surface profile obtained by a microscope. The measured pitch of each lens was 600 μm, which matched our design specification. The fabrication of a wave film with a sinusoidal profile (Fig. 8(d)) is also similar to that of a cylindrical-lens array.

A Topcon SR-UL1R spectroradiometer (Fig. 9(a) ) was used to measure the luminance and color gamut of the ALED-ST prototype. In measurement, the light guide was illuminated by one side-lit collimation LED modules (Fig. 9(b)). Measurements showed that the proposed ALED-ST had an average peak luminance of 40.5 cd/m2 under a measurement aperture of 2∘ and a 91% NTSC color gamut. Figures 9(c) and 9(d) show the RBR and GBG periodical line patterns for each field. The un-illuminated space between each line is clearly visible, which shows two merits of this system compared to other color separation methods. First, most of the energy of the separated colors can pass through the liquid crystal layer without hitting the black matrix area in the thin film transistor liquid crystal display (TFT-LCD). Second, the primary colors can be clearly distinguished and the overlap is significantly reduced.

 figure: Fig. 9

Fig. 9 (a) The optical measurement setup for measuring the performance of the ALED-ST system; (b) Top view of the system with red and green LEDs lit simultaneously; One periodic line pattern captured by a CCD camera. (c) The R-B-R (left image) and (d) G-B-G (right image) for field 1 and field 2, respectively.

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Although the ALED-ST looks promising, it must overcome several constraints before commercialization. The first constraint is that the collimation module is large and inefficient. For example, the prototype uses a large collimation module (over 7 cm in length) to generate beams. If this collimation module is set on the two-sides of the light guide, it obviously reduces the display area. An alternative is to set the collimation module under a light guide at the cost of increasing the thickness of the whole panel. Conversely, measurements show that over 22% of efficiency loss occurs during collimation. Therefore, it is necessary to develop a more efficient and smaller collimation module. The second constraint relates to the light source. To display color time sequentially, the light source of the ALED-ST must be R-G-B LEDs, which have less discoloration and generate a wider color gamut compared with a blue LED with yellow phosphor. The RGB LED has a 105%-120% NTSC color gamut, whereas a blue LED with yellow phosphor has a 40%-70% NTSC color gamut. However, the optical efficiency (usually 30-45 lm/watt) of a R-G-B LEDs is approximately 50% of a blue LED with yellow phosphor (usually 80-90 lm/watt). The overall improvement of the ALED-ST in optical efficiency is therefore reduced from 3X to 1.5X unless the gap in source technology is closed. The third constraint is the front diffuser, which increases beam divergence at the cost of inducing light loss and haze. Measurements show that for a wave film with a sinusoidal profile, the IFWHM (full width of intensity at half maximum) of a beam from the cylindrical-lens array can be increased from ± 10° to ± 36°, which meets the requirements of a commercial LCD. However, the energy loss is as high as 10%. The fourth constraint is the requirement of precise alignment between the cylindrical lens, the prism array, and the sub-pixels of the LC layer. The glass containing the LC layer is hard, whereas the cylindrical-lens film or the prism film is plastic. Thus, it is not easy to precisely align the sub-pixels of the LC layer with the structures of films during attachment, especially for large LCDs or high-resolution applications. In many cases, it is necessary to attach the plastic film to a hard substrate glass to facilitate alignment. After bonding the film to the glass, the plastic film is then detached from the substrate glass.

Considering these constraints, the achievable optical efficiency improvement of an ALED-ST may vary from 2X to 3X. For example, when comparing an ALED-ST with a similar size panel but absorptive color filters, the overall efficiency of each configuration without considering other common components can be roughly estimated as follows.

The overall efficiency (47.8%) of the proposed ALED-ST is the multiplication of the efficiency of collimation module (78%), the coupling efficiencies of a light guide (68%), and a front diffuser (90%). Therefore, under the illumination of white light from a R-G-B LED with an average luminous flux of 12 lm, the estimated output luminous flux from the ALED-ST is 5.74 lm. For a similarly sized panel using absorptive color filters, the overall efficiency (18.48%) is the multiplication of the coupling efficiency of a light guide (70%), the filtering efficiency of in-pixel dye color filters (33%), and the limited aperture ratio in the crystal layer (80%). Therefore, under the illumination of white light from a R-G-B LED with a luminous flux of 12 lm, the estimated output luminous flux from the conventional panel is 2.22 lm. The estimated efficiency improvement of an ALED-ST is therefore 2.58X.

Finally, it is important to consider the achievable luminance. For a 40-inch side-lit LCD TV, the peak device luminance must typically be as high as 400 cd/m2, which requires two hundred RGB LEDs on each side of the light guide. If the LEDs are designed along the long sides (approximately 88 cm), the spacing between each LED is 0.44 cm. In the ALED-ST prototype, the width of each collimation module is 4.6 cm. We therefore need to shrink the collimation module by approximately 10X. In practice, this problem can be solved by simultaneously selecting high power RGB LEDs and bonding more RGB chips along the height direction at the end of each reflector cup. For example, if the bonding spacing is 1 mm and the newly selected RGB LED is 1.3X output, the required height of bonding pad is 8 mm. However, this temporal solution increases the panel thickness. As mentioned previously, the permanent solution is to develop a smaller, more efficient collimation module.

4. Conclusion

This study presents the design and fabrication of a prototype of ALED-ST consisting of RG-B-RG LED modules driven by a two-field scheme as a color separation system. Color rays from RG-B-RG LEDs are collimated to produce angular-color components (RBR and GBG for field 1 and field 2, respectively) in the light guide. The position-color components RBR/GBG are then generated after these angular-color components pass through a cylindrical-lens array. The proposed ALED-ST has the potential to replace the absorbing-type color filters (e.g., dye-gelatin and dielectric film) for LCD applications, because the maximum theoretical power efficiency is three times that of a conventional dye color filter. The measured color-gamut of an ALED-ST prototype is as high as NTSC 91%. In addition, most key components of the system, including the collimation lens, the V-grooved light guide, the cylindrical-lens array, and the front diffuser, are feasible to fabricate using conventional ultra-precision machining methods, which are low-cost mass production technologies.

Acknowledgments

This study was supported by the National Science Council of Taiwan, R.O.C. under grant numbers NSC 100-2221-E-035-058-MY2 and NSC 100-2622-E-035 −014 -CC3.

References and links

1. T. V. Gunn and W. Haistead, “Diffractive color separation fabrication,” Proc. SPIE 3363, 198–208 (1998). [CrossRef]  

2. H. Dammann, “Color separation gratings,” Appl. Opt. 17(15), 2273–2279 (1978). [CrossRef]   [PubMed]  

3. H.-H. Lin, C.-H. Lee, and M.-H. Lu, “Dye-less color filter fabricated by roll-to-roll imprinting for liquid crystal display applications,” Opt. Express 17(15), 12397–12406 (2009). [CrossRef]   [PubMed]  

4. R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, and H. J. Cornelissen, “Short period holographic structures for backlight display applications,” Opt. Express 15(17), 10540–10552 (2007). [CrossRef]   [PubMed]  

5. C. Joubert, B. Loiseaux, A. Delboulbé, and J. P. Huignad, “Phase volume holographic optical components for high-brightness single-LCD projectors,” Appl. Opt. 36(20), 4761–4771 (1997). [CrossRef]   [PubMed]  

6. S. G. Kang, J-S. Lee, H-H. Hwang, and C-S. Cho, “A design optimization of the OCB-Mode for the application of field-sequential color microdisplays,” SID 01 Digest, 855−857 (2001).

7. 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]  

8. R. L. D. Silverstein, “STColor: hybrid spatial-temporal color synthesis for enhanced display image quality,” SID 05 Digest, 1112–1115 (2005).

9. M. J. J. Jak, G. J. Hekstra, J. J. L. Hoppenbrouwers, F. J. Vossen, N. Raman, and O. Belik, “Spectrum sequential liquid crystal display,” SID 05 Digest, 1120–1123 (2005).

10. Y.-K. Cheng, Y.-P. Huang, Y.-R. Cheng, and H.-P. D. Shieh, “Two-field Scheme: spatiotemporal modulation for field sequential color LCDs,” J. Disp. Technol. 5(10), 385–390 (2009). [CrossRef]  

11. ZEMAX, Radiant ZEMAX, Inc., http://www.radiantzemax.com/en/design/.

12. Advanced System Analysis Program, (ASAP TM), Breault Research Organization, Inc., http://www.breault.com/index.php.

13. F. Yamada, S. Ono and Y. Taira, “Dual layered very thin flat surface micro prism array directly molded in an LCD cell,” Euro display 2002, 339–342 (2002).

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Figures (9)

Fig. 1
Fig. 1 A color separation backlight side-lit by an array of R-G-B-G-R LEDs.
Fig. 2
Fig. 2 (a) An arrangement of R-G-B LEDs and a collimation lens performs the angular color-separation, but induces asymmetrical illumination (such as the red rays shown) in the light guide and color mixing after passing through the cylindrical-lens array; (b) An arrangement of R-G-B-G-R LEDs and a collimation lens generates the symmetric angular color-separation in the light guide without color mixing after passing through the cylindrical-lens array.
Fig. 3
Fig. 3 An arrangement of RG-B-RG LEDs to a collimation lens yields the angular color-separation. After passing through the cylindrical-lens array, two conventional color filter layers filter the mixing colors to produce three primary colors: R, B, and G.
Fig. 4
Fig. 4 The configuration of ALED-ST in (a) field 1 and (b) field 2.
Fig. 5
Fig. 5 (a) With color LEDs being set on the focal plane of a collimation lens, the color rays are collimated; (b) The corresponding propagation picture drawn by ASAPTM.
Fig. 6
Fig. 6 (a) Schematic V-grooves and reflector of the light guide; (b) The uniformity of the output rays from light guide.
Fig. 7
Fig. 7 (a) Geometry of the cylindrical-lens array with respect to the pixels; (b) Simulated optical diagram of the cylindrical lens array. LC layer are set around the focal plane with less color crosstalk; (c) and (d) are the footprint diagrams for field 1 and field 2, respectively.
Fig. 8
Fig. 8 (a) Photograph of a 3-in-1 RGB LED; (b) A diamond cutter with the designed profile was used to cut the mold on a roller; (c) The cross-sectional profile of a cylindrical lens under the microscope; (d) SEM image of the cross-sectional profile of a wave film.
Fig. 9
Fig. 9 (a) The optical measurement setup for measuring the performance of the ALED-ST system; (b) Top view of the system with red and green LEDs lit simultaneously; One periodic line pattern captured by a CCD camera. (c) The R-B-R (left image) and (d) G-B-G (right image) for field 1 and field 2, respectively.

Tables (1)

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Table 1 Comparison of ALED-ST Performance with Current Color-separation Technologies

Equations (3)

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H~F×tan(θ)
p= D 2 =( t 1 + t 2 + t 3 + t 4 )×tanϕ
f= t 1 n 1 + t 2 n 2 + t 3 n 3 + t 4 n 4 =( t 1 + t 2 + t 3 + t 4 )n
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