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In this paper, a method is proposed for highly precisely simulating the optical behavior of a light guide plate, which has microstructures of rough texture and rugged edges thereon. By adopting the ‘equivalent medium-immersed measurement’ to establish precise optical characteristic of the light guide plate, the simulated results of luminance distribution are much accordant with experimental measurement. This method will be useful in luminance uniformity evaluation and hot-spot check in advance, and it will greatly contribute to save time and cost of product development.
©2010 Optical Society of America
1. Introduction
The flat panel display (FPD) is a rapidly expanding industry. Many related technologies compete with another for the large and booming market. So far, a thin-film-transistor liquid crystal display (TFT-LCD) dominates the display market for applications in all different sizes. The modules of TFT-LCD include two mainly parts: a TFT liquid crystal panel (LC panel) and a backlit unit (BLU). BLU is used to provide a uniform flat lighting from the backside of the LC panel. In terms of cost, the BLU is the second most expensive component, and it also greatly affects the optical quality of the TFT-LCD. The types of BLU includes direct-lit and edge-lit according to the arrangement of the light source. In general, direct-lit BLU is easy to provide sufficient luminance, so it is suitable for TV application especially. On the other hand, edge-lit BLU can provide a thinner and weightless solution, especially for mobile applications such as cell phone, Digital Still Camera (DSC), and notebook (NB) etc. In the past, cold cathode fluorescent lamp (CCFL) was a mainly light-source component, but now LED rapidly replaces CCFL. As optical efficiency of LED much improves, edge-lit BLU is gradually used in larger-size application such as TV.
Figure 1 illustrates a typical edge-lit BLU. The light guide plate (LGP) made of Polymethyl methacrylate (PMMA) is a very important optical element in edge-lit BLU and its function is to propagate lights from LED by total internal reflection (TIR) and distribute light-emitting uniformly across the emitting surface of LGP [1–6]. There are many microstructures on the top, bottom or both the surfaces to frustrate TIR to let light emerge from the LGP inside. To form the different types of microstructures on LGP surface, several different technologies are available including screen-printing, inkjet-printing, hot embossing, and inject molding [7–11]. Since inject molding is capable of producing a well-distributed pattern in one pass, the microstructures on the LGP generally are formed by this method, especially for NB application. For inject molding, the well-designed microstructure pattern are formed on a stamper or mold in advance. The types of microstructures usually include microlens, dots, powder-blasting texture and V-cutting groove. In order to get uniform luminance across the emitting surface of LGP, the density of microstructures should distribute and vary properly. As LED is used for light source, microstructures of the dot-pattern and microlens are preferred because it is easy to fine-tune luminance uniformity. Those microstructures are formed on a stamper by chemical etching or laser etching [12,13]. In general, chemical etching forms hemisphere-like microstructures with a shallow depth, and the texture of them is substantially smooth. On the contrary, laser etching forms crater-like microstructures with rough texture and rugged edges. The profile of the crater-like microstructure is shown as Fig. 2 . In this case, the diameter of the crater-like microstructures is about 48 um; the convex portion of the microstructure is about 4 um outward from the bottom surface of the LGP, and the concave portion of the microstructure is about 3 um sunk into the bottom surface.
Since uniform luminance is a crucial task, some ray-tracing optical simulation tools are used to aid designing density distribution of microstructures (simply called ‘pattern density’) and some related design algorithms are also proposed [14–16]. When the software is used, there are two mainly parts to be focused: the first is to check whether luminance is uniform from the region near LED to the furthest of the LGP; the second is to check if hot-spot exists in the region of the LGP near LED. So-called ‘hot-spot’ is meant to the region of emitting surface of the LGP near LED with ultra-brightness compared with its neighborhood, shown as in Fig. 3 . The hot-spot appears because LED is a kind of a discrete light source instead of a linear light source like CCFL. The hot-spot becomes more obviously as the number of LED is greatly reduced recently due to cost, so it is more important for LGP design to implement precise optical simulation to check if hot-spot exists in advance. In general, it is easier to precisely simulate optical behavior of microstructures with smooth texture and regular profile by ray-tracing software, but it is very difficult for microstructures with rough texture and rugged edges, especially for precise simulating hot-spot phenomena. It should be noted that correct and precise predicting optical behavior of microstructures is essential for simulation and design of the LGP and it highly contributes to save time and cost of product development. However, due to environment issue and time cost of product development, laser etching is going to replace chemical etching for forming microstructure patterns on a stamper. Therefore, how to implement precise simulation for the LGP inject-molded by such a stamper is a crucial task. In this study, a method is proposed for highly precise simulating the optical behavior of such a LGP, and both optical simulation and experiment results are demonstrated.
2. Principles of the model
Since the optical properties of microstructures of rough texture and rugged edges is very difficult to be defined accurately only based on geometry, in this study we measure bi-directional scattering distribution function (BSDF) instead of geometry of microstructures for optical simulation. BSDF is defined as follows:
where Ψ is optical flux density of scattering light; r is the distance from the incident spot to the detector; (θi, ϕi) are polar and azimuthal angle of incident light deviated from the normal of the surface on which light is incident; (θe, ϕe) are polar of and azimuthal angle of scattering light deviated from the normal. The configuration of BSDF measurement is illustrated as Fig. 4(a) . When one collimated light beam is incident on the surface of a specimen at an angle (θi, ϕi), the light beam is scattered (or diffused) forwards and backwards in all directions. Thus, an optical detector is continuously moved along a spherical (or hemisphere) orbit that is centered at the incident spot of the specimen so as to measure the optical flux densities Ψ in all directions. Consequentially, BSDF can be obtained by substituting Ψ into Eq. (1). As long as the collimated light beam is sequentially incident at different incident angles and the above steps are repeated, we can obtain a complete set of BSDF for all incident angles. In this study, BSDF is assumed independent of light spectrum in the visible range. Theoretically, once the complete set of BSDF of a specimen is obtained, the optical behavior of this specimen can be precisely predicted. Therefore, it is essential to obtain the complete set of BSDF of the LGP with microstructures thereon.Next, there are still two difficulties to be overcome. In this case, the microstructures are on the bottom surface of the LGP. Thus, when lights propagating in a LGP are incident on the microstructures, some lights directly reflect back; some lights emerging from bottom surface of the LGP are incident on a bottom reflector and then reflect back to the LGP, so we need to obtain two sets of BSDF for the two different conditions. The first difficulty is how to obtain the BSDF for the incident lights propagating in a LGP made of PMMA. Due to Snell’s law, it is not easy to let a collimated light beam incident on bottom surface of a LGP at a large incident angle in PMMA medium. However, most lights propagating in the LGP are incident on microstructures at large angles. Besides, some of the corresponding reflected scattering lights cannot emerge out of LGP to be detected due to TIR. So, in order to overcome the above issue, the ‘equivalent medium-immersed measurement’ was proposed. We put a hemisphere made of PMMA on the specimen (i.e. LGP) and fill the refractive-index-matched liquid between them, which is illustrated in Fig. 4(b). It should be noted that the well-designed hemisphere takes thickness of the LGP into account and let its geometry center exactly locate on the bottom surface of the LGP. When a collimated light beam aims at the geometry center of the hemisphere, the collimated light beam hardly deflects through the interface between air and PMMA, and is directly incident on the spot of the LGP at the geometry center of the hemisphere, and then all the reflected scattering lights go back to the air with very little refractive deflection. In this measurement, the incident light and reflected lights seem to propagate in the same medium as the LGP all the time without refraction and thus deflection. Hence, by this method, we can let a collimated light beam incident on the bottom of a LGP at all incident angles and obtain a complete set of BSDF within the medium of PMMA. For simplicity, the reflector is put underneath the LGP and they are referred as an integrated unit, so we just need to obtain one set of BSDF for this unit.
Next, the second difficulty is how to implement one set of BSDF for various density distributions of microstructures on a LGP. Since pattern density varies across a LGP while BSDF depends on pattern density, it seems necessary to implement different sets of BSDF for different pattern densities. However, it is time-consuming and ineffective. In this study, the concept of hexagonal pattern elements is proposed. Some test pattern areas consisting of microstructures are formed on a LGP, and the microstructures are arranged in hexagon array like a honeycomb. We only measure a set of BSDF of the pattern area with the highest pattern density of microstructures. This set of BSDF involves both effects of the microstructures and the rest bare bottom surface of a LGP. Then, this set of BSDF is applied to a hexagonal pattern element. For the region with the same highest pattern density of the LGP, it is exactly fully filled by such hexagonal pattern elements; for other region with lower pattern density of the LGP, it is only filled partially by the hexagonal pattern elements. In the case of pattern frequency modulation, because the region with lower pattern density has higher ratio of bare surface to total area, the number of the pattern elements should be proportionally reduced to keep the pattern density in accordance with the designed value. Alternatively, in the case of pattern size modulation, the size of the pattern elements should be proportionally shrunk to keep the pattern density in accordance with the designed value. It should be noted that the pattern density of the test pattern measured for BSDF must be higher than the highest pattern density in the practical case to avoid pattern elements overlapping each other in the case of pattern frequency modulation.
3. Simulation and model verification
In this study, the related parameters of the BLU sample are as follows: the dimension of the LGP made of PMMA is 265 mm (length) X 170 mm (width); thickness of the wedge-shaped LGP is 0.6 ~1.4 mm (the thicker is the light-entrance side); 32 pieces of LED with an interval of 8.38 mm, and its optical intensity is of Lambertial distribution; light-emitting surfaces of LED directly touch light-entrance surface of the LGP; all LED are attached on a light-bar housing made of aluminum; a white reflector (model No. E6SV, Toray) is underneath the LGP; a diffuser sheet is put on the LGP; two prism sheets are put on the diffuser sheet and their microstructure directions are orthogonal to each other. The LGP is injection-molded, and the microstructures are formed on a stamper in advance by laser etching and then transformed onto the bottom surface of the LGP by injection molding. In order to save computing time in simulation process, only a stripe region of a 25.14 mm X 170 mm (simply called ‘long stripe’) is simulated for luminance uniformity across BLU, and a stripe region of a 50.28 mm X 30 mm (simply called ‘entrance region’) is simulated for hot-spot phenomena. The boundary conditions of those regions are set optical reflection or absorption to be equivalent to practical conditions. Except for size of the simulation region, all conditions in simulation are the same as the BLU. In this study, the software for optical simulation is OPTISWORKS [17], and the equipment for optical luminance measurement is BM7 (manufactured by TOPCON Corp. Ltd.); they both are widely used in optical industry. In experiment, the BM7 is setup 500-mm distance above the BLU and 0.1° field-view angle to measure head-on luminance. In measurement, the backlit module on a stage is moved in xy plane and the measurement interval is 1 mm. In the simulation, all the parameters are kept the same as those in measurement except the acceptance angle is a little larger in simulation. The purpose of adopting a larger acceptance angle in simulation is to gather more lights to reduce numerical fluctuation and error. Next, the simulation results are compared with experiment measurements.
The luminance distribution of simulation and measurement for the entrance region are shown in Fig. 5 . Figure 5 shows that simulation result is similar measurement result. Because the active area (viewable area) starts at 4 mm away from the entrance side of the LGP, we focus on the area from 4 mm to 8 mm away from the entrance side in order to check if the hot-spot phenomena exist. In Fig. 6 , the luminance contrast ratios (Low/High, i.e. Dark/ Bright, simply called ‘L/H contrast) of the simulation and experiment results at different sampling lines (4, 6, 8 mm away from the entrance side, respectively) are plotted, and we can find that simulation results are much accordant with measurements. In general, human eyes can easily perceive hot-spot when the L/H contrast is lower than 0.9, so the error of simulated luminance contrast ratio should be kept under 10% for safe design. In Fig. 6, the maximum difference between simulation and experiment results are under 8%, so our model can work well for hot-spot check. Figure 7 shows the luminance uniformity across long stripe of the LGP, and the trend of the simulation result substantially fits the measurement. Although there exists some difference (10%, maximum) between simulation and measurement, it is still acceptable for uniformity optimization. In addition to the above achievements, our optical model has advantage of saving time for ray-tracing. In general, the time-consuming for ray-tracing is related to the profile and texture of the microstructure. With more complicate profile and rough texture, time-consuming for ray-tracing is longer. In this case, our model can save time more than 70% compared with the geometry-based model.
4. Summary
In summary, a method is proposed for highly precisely simulating the optical behavior of a LGP with adopting LED as light source, especially for the LGP possessing microstructures with rough texture and rugged edges. The simulation results demonstrates their highly accordance with experimental measurements. We successfully simulate luminance for the entrance region and long stripe of a LGP, respectively. Both simulation results differ from the experiments less than 10%. Besides, our model can save time more than 70% compared with the geometry-based model in this case. This model based on BSDF measurement is proved its effectiveness not only for luminance uniformity evaluation but also for hot-spot check. As LED is going to rapidly replace CCFL for light source of edge-lit BLU and thus hot-spot becomes a very concerned issue, this method will be more important and valuable in the recent future.
Acknowledgments
This study was partially sponsored by National Science Foundation of China (NSFC) under Grant No. NSC 99-2221-E-003-020.
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