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Abstract
Light extraction array, comprised of millions of discrete scattering dots randomly distributed on edge-lit light guide plates (LGPs), determines both the light efficiency and spatial uniformity of liquid crystal displays. However, it is hard to define by a specific mathematical expression. Here, we propose a novel analytic design for light extraction array based on geometrical optical principles. This design method consists of three successive procedures evolving from point- and line-source approximations to extended surface-source computation. Three procedures are demonstrated via both simulation and experiment, and the key factors influencing the performance of the light extraction array are also discussed. Our approach with high accuracy and reduced complexity will have broad prospect for illumination design.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid crystal displays (LCDs) are a market-dominating technology with optimal characteristics in terms of most key display features, including peak brightness, resolution density, and lifetime [1,2]. Less than 7% of the energy from the backlight module can pass through a typical LCD panel [3]. As the unique light source, the backlight module determines the optical performance, structure, and power consumption of the overall LCD system [4].
All edge-lit backlights that use LED light bars have essentially similar optical paths that require scattering-assisted extraction to regulate their output uniformity. One category is to artificially roughen the interface surface of the LED chip. These micro / nano structures significantly enhance the light extraction efficiency. The mechanism has been clarified by two-dimensional finite element simulation [5]. For experimental demonstration, femtosecond laser direct writing is an effective way to for light extraction efficiency enhancement [6]. Similar works can be found in Refs. [7–9]. Another category is the integration of light extractors on the LGP surface. Most light extractors are hemispherical dots located on the bottom surface of the LGP, although new extraction structures in various forms, shapes, and profiles are currently being developed [10,11]. The light-extraction efficiency is largely determined by the area and density of an extractor pattern, and backlight thickness reduction can be achieved [12–16]. Redistribution of the light-spreading angle is another function of light extraction array [17–20]. Overall, the light extraction array is one of the most critical part of an LCD backlit display, as it not only affects optical performance but also determines the system architecture.
The design of a light extraction array is a multi-parametric task that is impractical to manually tune, as, for instance, a common 264-mm (10.4-in) LGP can include 2,000,000 repeated light extraction structures [21]. One simplified approach involves arranging the extractors in fixed positions within regular rows and columns; however, this can cause light interference, i.e., the moiré phenomenon [22]. Randomizing the positioning of the light extractors with functional relationships is an effective method for avoiding moiré patterns [23,24]. After that, molecular dynamics (MD) methods were introduced into extractor pattern design to generate non-overlap random extractor patterns by treating individual dots as atoms. The MD approach was initially proposed by Idé et. al. [22], and was subsequently improved by the introduction of several algorithms that were more practical for optimization [25–27]. The maximum extractor density of a random distribution is estimated to be approximately 60% and that the density decreases with extractor size [28]; the resulting high computational complexity makes it difficult to utilize certain parameters of the extractor itself as variables during optimization. To address this problem, Lee et al. developed a dot pattern optimization algorithm by defining a pattern density function based on a regular dot arrangement [29,30]. Their solution enabled division of the LGP into several partitions with differing dot densities that could serve as individual design variables and applied a density-based approach that adopted a feedback scheme [31–33]. Other optimization approaches for extractor pattern include the use of genetic algorithms [34], neural-network models [35,36], fuzzy scheme strategies [37], and differential approaches [38]. In recent years, the design of light-extraction arrays has been refined continuously using methods that hybridize semi-empirical and optimization iterative approaches [39–43].
From the literature review above, existing design approaches for light extraction arrays can be divided into three categories involving semi-empirical mathematical formulae, random-distribution-generation algorithms, and iterative optimization schemes, respectively. Their approaches have a common limitation in that they require repeated amendment or several rounds of parameter tuning that relies heavily on prior experiences. To the best of our knowledge, it hasn’t been reported before to define a light extraction array based on LED sources by a specific mathematical expression. However, an analytic solution does enhance the design efficiency and avoid manual intervention. To address this issue, this paper presents an analytic design for light extraction array based on pure geometrical optical principles. Explicit physical expressions can be derived for a precise illuminance distribution on the bottom surface of the LGP based on three successive procedures evolving from point- and line-source approximations to extended surface-source computation. A mapping relationship between the calculated illuminance distribution and the prescribed uniform illumination is then established, from which the light extraction array can finally be defined using a difference equation and iterative calculation.
2. Design principle
2.1 Illuminance distribution based on extended LED sources
As the first-step approximation, the edge-lit LED light bar is initially simplified as a series of point LED sources with Lambertian radiation. As shown in Fig. 1, these point LEDs are located on the yoz-plane (corresponding to the light entrance surface of the LGP) at coordinates given by (0, y, z). The bottom surface of the LGP is located on the xoy-plane. The LEDs satisfy the Lambertian radiation condition Iθ = INcosθ, where θ is the angle between the emitting ray and the normal line of the source, Iθ represents the luminous intensity in the θ direction, and IN is the luminous intensity along the normal direction of the LED emitting surface (i.e., along the x-axis positive direction). Figure 1(a) shows a specific ray from a point-source S(0, yi, zi) that is normal to the point-to-plane surface N (i.e., the surface orthogonal to the incident direction). The normal and horizontal illuminances, En and Eh, respectively, at P(x, y, 0), the intersection point of the incident ray and surface N, can be calculated using the inverse-square law.
Fig. 1. (a) Two-dimensional (2D) cross-sectional plot and (b) three-dimensional (3D) plot of LGP and the edge-lit LEDs based on point source approximation.
Considering the incident ray is not located within the xoz-plane, as shown in Fig. 1(b), two angle parameters need to be defined, one is α, the angle between an incident ray and its projection onto the xoz-plane; the other is θi, the angle between IN and the projection of the emitting ray from the ith LED on the xoz-plane. By converting the angle parameters into coordinate parameters, the sum horizontal illuminance Eh from all point sources at point P can be obtained as
As the second-step approximation, the LED sources are extended from point sources to linear sources, as shown in Fig. 2(a). Assuming that each LED is a line light source parallel to the y-axis that can be divided into numerous tiny light-emitting units. The illuminance from each unit can be calculated using Eq. (1). A line LED of length L can be differentiated into individual light-emitting units of unit length dy, and the coordinates of the two ends of the line source are defined as A(0, yij, z) and B(0, yij, z). Iθ0 is the intensity in the direction perpendicular to AB and within the ABP-plane, Iθ0 = I00cos(α), and I00 represents the normal intensity of the LED sources. By integrating unit source dy, the illuminance distribution from the line-source approximation can be calculated as follows:
Fig. 2. Precise solution for illuminance distribution on the LGP bottom surface based on (a) line-source approximation and (b) extended surface-source derivation.
For the final procedure, the LED sources are treated as actual extended surface sources, which helps to precisely define the illuminance distribution on the LGP bottom surface. As shown in Fig. 2(b), each extended surface source is considered a combination of numerous line sources along the z-axis, which have major axes parallel to the LGP bottom surface. The illuminance from each line source can be calculated using Eq. (2). The ray paths involving direct illumination and total internal reflection are both taken into account. Finally, we obtain
2.2 Illuminance mapping establishment for solving the light extraction array
A mapping relationship between calculated illuminance distribution and prescribed uniform illumination can be established to precisely define the light extraction array. According to Eq. (3), the illuminance will decrease with the distance away from the sources. The energy absorption of the light extractors can be neglected relative to the sum of scattering energy. After scattering, the rays that cannot meet the total reflection condition will refract and emit from the LGP, while the remaining rays continue to propagate inside the LGP. As a result, the light energy is reduced as the distance from the light source increases, and the scattering-assisted extraction can be adjusted by specially designing the light extraction array with a varying size and arrangement.
As shown in Fig. 3, the bottom surface of the LGP can be divided into N sub-sections with identical size. A circular edge profile is considered for each light extractor given only in terms of its radius, r. To achieve a uniform output, the amount of light energy scattered from each section should be identical. By using a difference equation connecting each sub-section, the relationship between the illuminance and the radius distribution can be obtained:
Fig. 3. Partition of LGP bottom surface to establish mapping between calculated illuminance distribution light and prescribed uniform illumination.
3. Simulation results
To validate the proposed method, a 5.5-in backlight model using the parameters listed in Table 1 was built and simulated in optical software of TracePro. The parameters of the LED light sources are pre-defined. Three procedures of the derivation process are compared by simulation. Equations (1), (2), and (3) calculate the illuminance distribution on the LGP bottom surface based on three procedures of the derivation process, respectively. The corresponding radius distributions can be obtained by substituting Eqs. (1), (2), and (3), respectively, into Eq. (5). The radius distributions are calculated from three procedures of the derivation process in Matlab, and then written in RepTile file that can be imported into TracePro. During modelling, each coordinate system is consistent with the derivation process, with the LED light bars placed along the y-axis and the LGP bottom surface lying in the xoy-plane. r is the calculated radius corresponding to the coordinate position in the xoy-plane. The specific parameters of LGP and LED light bar are listed in Table 1. The property of light entrance side of the LGP is set as perfect transmitter, while the other three sides are diffuse white reflector. The LED source of model 4014 is commercially available, and features typical Lambertian light distribution. After the model was built and the RepTile file was imported, 500,000 rays were traced for simulation.
Table 1. Design parameters used to verify the three procedures in derivation process.
Figure 4 illustrates that the radius distribution gradually approaches an optimum through three successive procedures of the proposed method. The improvements can be found in three aspects. (1) The fill factor of the light extraction array gradually increases; (2) The radius change becomes much smoother; (3) The hot-spot phenomenon is gradually inhibited by the comb-like radius distribution near the light entrance side. The details are described as following. The radius distribution in Fig. 4(a) undergoes a significant change between the light entrance and the side furthest from the source, as the result of light propagation without sufficient scattering. The extractor radii at the entrance side have a comb-like distribution to avoid the illumination inhomogeneity [44]. Obvious changes can be seen in Fig. 4(b), in which the extractor size is increased significantly and the comb-like distribution is clearer at the entrance side. The overall radius change becomes much smoother, indicating that the extractor distribution has been gradually adjusted through the line source approximation. The radii are quite small at the side most distant from the sources, because the energy from total reflection within the LGP is not taken into account in the line-source approximation. Figure 4(c) shows the final radius distribution on the LGP bottom surface based on an actual extended LED light bar. The overall distribution of radii changes quite smoothly between the light entrance and the opposite side, with the corners showing peak values as a result of the low illuminance at those positions. The radii near the entrance side have an obvious comb-like distribution and avoid the hot-spot phenomenon.
Fig. 4. Radius distributions on LGP bottom surface calculated from (a) point-source approximation, (b) line-source approximation, and (c) extended surface-source computation. (d) Simulation model of LGP based on dot distribution in Fig. (c).
Figure 5 show the corresponding simulated illuminance distributions according to the radius distributions in Fig. 4. The upper figures in Fig. 5 show the illuminance distributions of the LGPs, and the corresponding illuminance curves at the red solid and gray dotted lines are drawn in the lower figures. In Fig. 5(a), the LGP entrance side has a lower average illuminance than the side most distant from the sources as a result of the significant radius change in Fig. 4(a). The uniformity of the pattern is improved somewhat when the line-source approximation is applied. Although the overall illuminance fluctuation in Fig. 5(b) is smaller than that in Fig. 5(a), an obvious center illuminance defect can still be observed. The final simulated illuminance distribution in Fig. 5(c) has the lowest degree of fluctuation in both the horizontal and vertical directions. The calculated output efficiency and uniformity of the designed LGP are 94 and 90.89%, respectively, results that validate the effectiveness and accuracy of the proposed method under simulation.
Fig. 5. Simulated illuminance distributions of 5.5-inch LGP and corresponding illuminance curves represented by red (horizontal) solid and gray (vertical) dotted lines based on extractor patterns from (a) point-source and (b) line-source approximation and (c) surface-source computation. White arrows represent light entrance direction.
From simulation results, it is obviously found that the light sources of the backlights significantly affect the effectiveness and accuracy of the light extraction array. Point- or line-source approximation can be considered to be an initial design start but not a final output, because the actual LEDs will be of comparable size to the LGP and the illumination target. The huge difference between the simulated point / line sources and the actual LED light bar causes the design deviation of the light extraction array from optimum. After the extended LED sources are considered, the final illuminance distribution can be precisely calculated using an actual optical model.
4. Experimental verification
4.1 Fabrication process
Several potential technologies were available to prepare the light extraction array, including screen printing, hot embossing, laser etching, etc. [45]. As extractor structures fabricated by hot embossing [46] and laser etching [47] have crater-like concave profiles with rough textures and rugged edges that did not meet our design, screen printing technology was applied to transfer the light extractors onto a bare LGP.
The detailed procedures for fabricating light extraction array are described as follows.
Step (I). The designed patterns were first prepared on a high-stability precision composite screen plate. Figure 6(a) shows the prepared films with point-, line-, and surface-source extractor patterns. Each pattern was then transferred onto a screen plate following UV exposure of the corresponding film.
Fig. 6. (a) Films and corresponding screen plate for extractor patterns. (b) Fixation and inspection of LGP and screen plate on printing equipment. (c) Pre-printing preparation and printing. (d) Cleaning and baking after printing.
Step (II). The bare LGPs, the screen plate, and the ink scraper were installed and fixed onto the screen printing equipment (ATMACE1014); as shown in Fig. 6(b), the LGP printing area and the pattern area had to be precisely aligned.
Step (III). After cleaning the LGP surface, printing ink (WPL-M09, PHILO) was dispersed evenly onto the screen plate (Fig. 6(c)). Then the printing process can effectively transfer the extraction array pattern onto the bare LGP surface.
Step (IV). Following printing, a finishing process including cleaning and baking was applied (Fig. 6(d)), with the LGPs left in an oven at 60°C for 35 min until the patterns were fully solidified.
Figure 7 shows the schematic of how the array pattern transfers to the LGP surface during screen printing. As shown in Fig. 7(a), the printing ink was first lightly scraped by the coating scraper from one side to the other to ensure that every mesh was filled with the printing ink. This process is called ink coating. Figure 7(b) shows the second procedure during printing process, called pattern transfer. The printing ink was vigorously scraped by the printing scraper, where the application of higher pressure caused the transfer of the printing ink from the mesh apertures to the LGP surface.
4.2 Measured results
Three 5.5-in backlight modules were assembled and compared, containing the extraction arrays from three procedures of the derivation process, respectively. The backlight components are shown in Fig. 8(a). The LED light bar and the corresponding integrated circuit modules are shown in Fig. 8(b). This LED light bar includes ten LED chips. The LED emitting size and the distance between adjacent LEDs are 4 mm × 1.4 mm and 8 mm, respectively. As shown in Fig. 8(c), the three LGPs have the same size and different light extraction array patterns obtained from the three procedures of the derivation process. Each light extraction array was observed and measured under an optical microscope (Olympus DP73). Figure 8(d) shows the captured picture. The measured radius ranges of the extractors were all within 111–531 µm, and the average center-to-center distance between adjacent dots was 1,093.43 µm.
Fig. 8. (a) Components of the backlight module. (b) LED light bar and the corresponding integrated circuit modules. (c) LGPs with printed point-, line-, and surface-source extractor patterns. (c) Light extraction dots observed under an optical microscope.
As shown in the upper row of images in Fig. 9, the experimental outputs of the three backlight modules have obviously different illumination effects. By comparison of Fig. 5(a) and Fig. 9(a), it can be found that the central area has a lower illuminance distribution relative to those at the light entrance and the side most distant from the sources. The experimental result is in good accordance with the simulation. The difference between the measured minimum (2,505 cd/m2) and maximum (10,900 cd/m2) brightnesses is quite large, primarily as the result of the significant change occurring over the point-source pattern shown in Fig. 4(a). In Fig. 9(b), the side most distant from the sources has a higher brightness than the central region as a result of the low fill factor. From a nine-point test, the uniformities of the point- and line-source patterned backlight modules were 22.98 and 60.55%, respectively. Following application of the surface-source pattern, however, the brightness uniformity of the backlight module reached 89.34% with no readily discernable brightness difference across the module (Fig. 9(c)). The measured minimum and maximum brightnesses over the nine tested points were 6,992 and 7,826 cd/m2, respectively. These experimental results validate the effectiveness and accuracy of the proposed method.
Fig. 9. Working states of the prepared backlight modules (upper row) and nine-point test results for evaluating uniformity (lower pictures). White arrows represent light entrance direction.
The backlight performance shows a great improvement from the measured results. It is noteworthy that the central brightness and the uniformity are both determined by the light extraction array. From the theoretical derivation, the radius distribution obtained by the point-source approximation has an obvious dependence on the distance to the light source. This causes insufficient light scattering and significant radius change shown in Fig. 4(a). That is why the central illuminance and uniformity are quite low from Fig. 9(a). During the following derivation, the radius distribution is further determined by a series of linear or surface light sources, respectively. As the light sources used for design gradually approach the actual ones, the radius distribution dependence can be significantly reduced, and the overall radius change becomes much smoother. This enables higher degree of freedom for large fill factor of the light extraction array and large single extractor size, resulting in the performance improvement that can be seen from Fig. 9(b) and 9(c).
5. Analysis and discussion
5.1 Performance adjustment by overprinting
Table 2 lists the performance obtained via simulation and experiment. It is seen that the experimental output efficiency was 8.19% lower than the efficiency, primarily resulting from the single extractor size. As is seen in Table 2, the minimum and maximum sizes of the printed extractors were smaller than the corresponding design values by 23 and 29 µm, respectively. In our research, screen printing technology was used for fabricating the light extraction array. The printing ink is homogeneously mixed with scattering particles. After fabrication, per unit size of the light extractor can be considered to provide equal light scattering ability. Therefore, a smaller light extractor will have a lower scattering ability and, therefore, will reduce the extraction efficiency of the backlight module.
Table 2. Comparison between simulation and experimental results.
Overprinting can be used to finely adjust the light extractor size. As shown in Figs. 10(a)–10(c), the measured radius was conspicuously enlarged with printing time. Following a normal printing, the diameter of the reference extractor was 358 µm. The diameter was increased to 389 and then 416 µm after one- and two-time additional overprintings, respectively. The variance in performance of the backlight modules with extractor size is shown in Fig. 10(d). The extractor size increasing by approximately 8.5% after each round of overprinting. A larger extractor size produces more light extraction, which in turn corresponds to a brightness increase. The measured central brightnesses after successive rounds of printing were 7,197, 7,534, and 7,689 cd/m2, respectively. By contrast, the uniformity is less sensitive to the extractor size. These results indicate that the overprinting could be an effective approach to adjust and improve the optical performance of the proposed method.
Fig. 10. Morphology of light extraction dots after (a) normal printing, (b) one-time overprinting, and (c) two-time overprintings. (d) Corresponding backlight module performance variation.
5.2 Influence of the spatial profile of light extractor on the performance
Generally, the performance of the backlight module depends on three factors of light extractors, including the shape, size, and arrangement. Here, to evaluate the influence on the performance, five different profile shapes were simulated and compared. The arrangements were kept the same during simulation and experiment. The cross-sectional areas can be defined by the radius of the circular profile, r, as listed in Table 3. Obviously, the inscribed profiles have smaller cross-sectional areas than circular profile, while the circumscribed ones are larger. Both simulation and experimental results in Table 3 show that the uniformity of inscribed type is better than circumscribed type. However, the relative efficiency of circumscribed type is higher than inscribed one. These results could provide guidance for optimizing the extractor shape without altering the distribution of initial extraction array.
Table 3. Influence of the profile shape of light extractor on the performance of backlight module.
5.3 Analysis of the diffuser film
Diffuser film is an important component to improve the visual uniformity of backlight module. Here, the parameters of the used diffuser films are provided, and how the diffuser films affect the uniformity is analyzed in detail. The specification of the used diffuser film is listed in Table 4. This diffuser film has a laminated structure consisting of an upper diffusion layer, a middle substrate, and a lower anti-blocking layer. As shown in the microscope picture in Fig. 11(a), the evenly distributed scattering particles in diffusion layer contribute largely to light distribution homogenization.
Fig. 11. (a) The laminated structure of the used diffuser film. (Inset: the microscope picture of the diffusion layer). Illumination output of the LGP, (b) without diffuser film; (c) with a single diffuser film; (d) with two diffuser films.
Table 4. The specification of the diffuser film used in our experiment.
As shown in Fig. 11(b)–11(d), the illumination outputs are experimentally compared among the backlight modules with no diffuser film, a single diffuser film, and two diffuser films. The light extraction dots can be observed directly and clearly without a diffuser film. These dots are used to extract light from the edge-lit LGP. However, the area without the extraction dots remains dark. As can be seen in Fig. 11(c)–11(d), the uniformity can be improved significantly with a single or two diffusion layers placed on top of the LGP. It is effective to combine the designed extraction array and additional diffuser films together for light distribution homogenization.
6. Conclusion
Light extraction array is the most critical part of an LCD display backlight. Different from other semi-empirical approaches, this paper proposes a novel analytic design method to precisely define the light extraction arrays based on pure geometrical optical principles. A series of mathematical expressions with explicit physical meaning were derived from three successive procedures evolving from point- and line-source approximation to extended surface-source computation. The three procedures were verified by simulation and experiment, respectively. Results show that the measured central brightness of the backlight was increased from 3,999 to 5,293 and finally to 7,240 cd/m2, and the uniformity was also improved from 22.98 to 89.34%. Other important issues were also discussed in detail, including the influence of the size and the profile shape of light extractors, and the diffuser film. Overall, the proposed method demonstrates outstanding advantages in terms of obtaining high design efficiency with the application of analytic formulae. By avoiding the use of an iterative optimization scheme, our approach reduces the computational complexity and, based on its use of an optical model using actual extended sources, it obtains a high degree of flexibility and accuracy.
This approach will have great potential and broad prospect for polarization related LGP and mini-LED backlights in future. Combined with a linearly polarized LED source, the light extraction array can be incorporated into a polarization-preserving LGP to increase the optical efficiency [48]. For mini-LED backlights, previous works have demonstrated their two-dimensional local dimming to boost the contrast ratio to 1,000,000:1 with an even thinner profile [4,49]. The difference between mini-LED backlights and edge-lit light extraction arrays is the location of the light sources. Since the outgoing light intensity distributions of the mini-LEDs and light extraction arrays are both Lambertian type, the light extraction array can be considered as the direct-lit sources with varying sizes and arrangement. However, the illuminance mapping needs to be re-established for solving the direct-lit light extraction array, and the iteratively reduced illuminance partition should be replaced by uniform partition. In conclusion, this approach will have potential for advanced illumination design.
Funding
National Key Research and Development Plan (2017YFB0404604); Fujian Science and Technology Key Project (2018H6011, 2018J01802).
Acknowledgments
The authors would like to extend their sincere gratitude to the colleagues of Lv Xin Optical (Shenzhen) Co., Ltd. and Top Victory Electronics (Fujian) Co., Ltd. for their assistance on this thesis.
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