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This paper proposes an optimization method for designing a prism-pattern LCD light guide plate (LGP) using a neural-network optical model and a real-valued genetic algorithm to achieve excellent luminance uniformity in the exiting light. This newly developed method is proposed as a way of solving the complicated optimization work for non-image optics due to the numbers of ray tracing. First, a neural-network optical model is based on a back-propagation neural network. Then the neural-network optical model is incorporated into a real-valued genetic algorithm to optimize the distribution density of the prism pattern. The results show that the 13-point luminance uniformity reaches an outstanding 92.09%.
©2009 Optical Society of America
1. Introduction
The backlight module (BLM) provides a liquid crystal display (LCD) with a surface light source, which is converted from a point- or line-light source. A typical edge-type BLM [1], as shown in Fig. 1 , includes a light source, a light guide plate (LGP) and several optical films for scattering and condensing light. The light-scattering dots or pattern on the LGP scatter the reflected light rays travelling within the LGP such that the light rays are emitted from the LGP’s top surface as a surface light source. Thus, the design of the LGP’s light-scattering dots or pattern plays an important role in achieving a BLM at low cost with high brightness and high luminance uniformity.
To achieve better luminance uniformity, Ishikawa [2] proposed a dot-pattern designed in such a way that the distribution density of the light-scattering dots increases gradually with their distance from the light source. The rationale is that part of the light is scattered by the dots and comes out of the LGP, where it was propagated. Some researchers have also suggested a power function or a polynomial for the distribution density of the light-scattering dots [3,4]. However, the relevant works do not provide a method for determining the optimal distribution density of the light-scattering pattern for uniform luminance.
To assist the BLM design, the ASAP (Advance System Analysis Program) optical modeling software has been utilized [5]. To improve the uniformity of the exiting light for the LGP, Li et al. [6] also propose a method of designing the prism pattern for the LGP as a light-scattering prism pattern with the aid of ASAP simulation. The key to this method is to adjust the distribution density of the prism pattern at each sub-region of the LGP in such a way as to achieve an overall mean light flux. However, even though better uniformity of the exiting light is obtained, this prism-pattern design is not optimal.
The genetic algorithm is one commonly adopted method of searching multiple optimal parameters [7,8]. It was inspired by the Darwinian concept of the natural selection of species. The genetic algorithm, consisting of initialization, parent selection, crossover and mutation processes, is employed in order to generate a better population, i.e., better solutions.
This research proposes an optimization method for LGP prism-pattern design, using a neural-network optical model and a genetic algorithm. The optical model is based on a back-propagation neural network [9] intended to establish the relationship between the distribution density of the prism pattern and the exiting-light luminance of the LGP, by means of ASAP simulation. Since ASAP simulation is time-consuming, the neural-network optical model is adopted in the genetic algorithm, to take advantage of its rapid computational capacity. Then the real-valued genetic algorithm [10] is executed in order to search the optimal distribution density of the prism pattern based on the neural-network optical model, such that high uniformity of the luminance is achieved.
The comparisons between this proposed optimization method and previous approaches for LGP design are listed as follows:
- 1. The optimization method presented in this paper uses a neural-network optical model and a genetic algorithm. The neural network model serves to generate fitness values that are then used in the genetic algorithm for the purpose of optimization. However, the previous approaches obtain a good distribution density of the LGP light-scattering dots or pattern by adjusting the coefficients of a power function or a polynomial that represents the distribution density [3,4], or by adjusting the distribution density of the dots or pattern at each LGP’s sub-region in such a way as to achieve an overall mean light flux [6,11].
- 3. The optical simulation program ASAP is utilized in this proposed optimization method only to generate input-output pairs for the purpose of neural-network training. Our previous approach uses ASAP to establish an intensive lookup table for obtaining a good distribution density of the LGP light-scattering dots or pattern for each sub-region by interpolation [6,11].
- 4. In addition to the triangular-prism pattern, the trapezoid-prism pattern is considered in this optimization method, whereas only the triangular one is taken into account in our previous approach [6].
The next section presents the design procedures of the prism pattern for an LGP, using a neural-network optical model and a genetic algorithm. Then the design of a 13.3-inch light guide plate is illustrated, using the proposed design method, and ASAP results are provided to validate the effectiveness of this design method. Finally some conclusions are drawn.
2. Procedures for LGP design
The optimization method proposed in this paper adopts a neural-network BLM optical model and a genetic algorithm. First, the back-propagation neural network is used to establish the BLM optical model. Then the real-valued genetic algorithm is performed to search for the optimal distribution density of the prism pattern on the LGP. The procedures for the LGP design can be stated as follows:
Step 1. With the aid of ASAP simulation, the characteristics of the prism pattern (i.e., triangular or trapezoid prisms, prism angle, prism depth, and prism spacing, etc., as shown in Fig. 2 ) are determined, so as to obtain the largest value or smallest variation of the exiting light flux or luminance.
Fig. 2 Prism-pattern characteristics: angle θ, spacing P, depth H, and top length a defined for a trapezoid prism pattern of an LGP.
Please note that the parameters of the prism pattern in Fig. 2 should be searched for at the same time since they may not be independent in this optimization problem. However, if the parameters are searched for at the same time, the optimization procedures become much complicated. Thus this optimization method tries to find one optimal parameter (i.e., distribution density of prism spacing) by assuming that the other parameters (i.e., prism angle and depth) are reasonably detected and then fixed. The rationale to optimize the distribution density of the LGP prism spacing instead of the other ones is that having different prism spacings for the sub-regions of the LGP is effective for achieving high luminance uniformity, and is easier to fabricate than the others.
Step 2. The whole LGP is divided into n equal regions (e.g., 13 regions for the LGP in Fig. 3(a) ). The input-output patterns for neural-network training and verification are generated by using orthogonal arrays and ASAP simulation for the purpose of implementing the neural network of a BLM model, as shown in Fig. 4 . The inputs to the neural network are n prism spacings corresponding to the n regions, and the outputs are the exiting-light luminance values at the central points of these regions (see Fig. 3(b)). Note that different regions possess different prism spacings, although inside each region the spacing value remains constant.
Fig. 3 (a) An LGP model is divided into thirteen equal regions with a cold cathode fluorescent lamp (CCFL) adjacent to region No. 1; (b) the luminance value of the central point in each region is considered.
Fig. 4 Structure of a neural network model with one hidden layer, where ωxh and ωhy are the weights, and θh and θyj are the bias values.
Step 3. The back-propagation neural network is trained to obtain its weightings and bias values by using input-output training patterns, and these are then verified by input-output verification patterns.
A back-propagation neural network [9] with one hidden layer is shown in Fig. 4. The initial weights are randomly generated, and then the neural network is trained to adjust the weights by minimizing the squared Euclidean norm of the error function via the steepest descent method [12]. The outputs at the h-th hidden neuron and j-th output neuron, Hh and Yj, are defined, using a sigmoid function as follows:
where and ωih and ωhj are the weights, θh and θj are the bias values, and Xi is the i-th input signal.Step 4. The real-valued genetic algorithm is utilized to search for the optimal prism-pattern distribution density, which provides the highest luminance uniformity of the LGP exiting light. In the search process, the neural-network optical model obtained from Step 3 is used to calculate the exiting-light luminance value in each region of the LGP, thus expediting the computation.
In the genetic algorithm, the fitness function is defined as the ratio of the minimum to the maximum luminance values at the central points of the n division of regions. The objective in performing the genetic algorithm is to maximize the value of the fitness function such that optimal luminance uniformity of the exiting light is achieved. The flowchart of the genetic algorithm is shown in Fig. 5 , and explained below in greater detail.
The initialization process randomly generates an initial population, in the beginning, which makes up the first generation of chromosomes. In each chromosome, there are n genes each of which represents one of the n prism spacings for the n regions of the LGP. Then the fitness values of the initial population are calculated by using the neural-network optical model. In parent selection, the roulette wheel parent selection is utilized to select the parent chromosomes from the initial population [8]. Then every pair of selected parent chromosomes goes through the crossover process to make two new chromosomes, called children, where the uniform crossover technique is adopted [8]. Following the crossover, once a probability check is passed, the mutation process is performed on these child chromosomes. The mutation process is to make sure that the corresponding solutions of the child chromosomes will not be trapped into a local maximum. Finally, in the process of selection for new population, the fitness values of the child chromosomes are calculated, and then the parent and child populations with higher fitness values are selected as the next generation. The above evolution processes are repeated until the preset number of iterations is reached or the best fitness value among the population converges at a certain value.
Step 5. The ASAP simulation is then conducted to verify the exiting-light luminance uniformity for the optimal prism distribution density obtained in Step 4.
3. Simulation
3.1 Simulation model
A LCD backlight module of size 294mm × 166mm (i.e., 13.3 inches) is considered. The structure contains a cold cathode fluorescent lamp (CCFL) light source (diameter 1.8mm, length 294mm) with a reflector (reflectivity 90%), a wedge-shaped LGP (transmission 91.4%, refraction index 1.49), with side and bottom reflection sheets (reflectivity 90%). The thick side of the LGP is 2.3 mm thick with a wedge angle of 0.4832°. A total of one hundred million rays are utilized in ASAP simulation. The top length a of the trapezoid-prism pattern in Fig. 2 is set as 0.01 mm when a trapezoid-prism pattern is utilized for a LGP.
The bottom surface of this LGP, which has a prism pattern, is divided into thirteen regions of equal area, as shown in Fig. 3(a).
3.2 Simulation results
The LGP design is performed according to the design procedures presented in the previous section “Procedures for LGP design,” of which the details are as follows.
In the first step, ASAP simulations are conducted to assist in the determination of the following three prism-pattern characteristics:
(1) Luminance plots are obtained for two LGPs, one with a trapezoid- and the other with a triangular-prism pattern, as shown in Figs. 6(a) and 6(b). Since the average luminance values for the LGPs with trapezoid and triangular prism patterns are 947.1 and 919.9 nit, respectively, the trapezoid prism pattern is considered.
Fig. 6 Luminance plots by ASAP with prism spacing P varying from 0.5mm to 1.5mm for (a) a trapezoid prism pattern; (b) a triangular prism pattern.
To see how good a measure of the lighting uniformity performed on the central line is (see Fig. 3(b)), ASAP simulation is conducted for an equal-spacing trapezoid-prism pattern (P = 0.9mm, θ = 95 °, and H = 0.02mm). The results in Table 1 show that the luminance value at the central line in each region has an error less than 1% compared to the average value of 30 points, and the corresponding standard deviation is also less than 1.1% of the luminance value at the central line. Thus, one can conclude that the luminance values at the 13 points of the central line give a good measure for calculating the luminance uniformity.
Table 1. Analysis of luminance values at 30 points of each region
(2) The exiting total light flux by ASAP simulation for different prism angles θ is shown in Fig. 7 . The largest exiting-light flux is obtained at θ = 80°, and thus θ = 80° is selected.
(3) Fig. 8 shows the luminance plots with prism depth H varying from 0.01mm to 0.05mm. The smallest luminance variation for all thirteen regions occurs at H = 0.02mm, and thus the prism depth is set at this value.
For the neural-network BLM optical model, the thirteen prism spacings for the thirteen regions are the inputs of the neural network, and the corresponding thirteen exiting-light luminance values at the central points of these regions are the outputs of the network, shown in Fig. 4. The configurations of the inputs for the neural network are generated from three sets of L27 orthogonal arrays, where each spacing has 3 levels (i.e., P = 0.7mm, 0.95mm, and 1.2mm). Then ASAP simulation is conducted for each configuration to obtain 81 sets of input-output patterns in total.
To train the back-propagation neural network, 72 out of 81 sets of input-output patterns are utilized. The transient errors of the network training are shown in Fig. 9 . From this figure, one can tell that the error is very small (less than 0.0001) when the training epochs reach 10429. Therefore, the training is finished at this epoch. Then the remaining 9 sets are used to verify the trained neural network, and the corresponding errors listed in Table 2 are very small (i.e., about 0.0005 or less). Thus the success of the neural network training can be inferred.
Table 2. The output errors of the trained neural-network optical model for 9 verification sets of input-output patterns.
The next step is to obtain the optimal distribution density of the prism pattern for the LGP by executing the real-valued genetic algorithm. The mutation rate is set as 0.01 in the mutation process. The genetic algorithm is run for 40,000 generations, and the convergence plot is shown in Fig. 10 . In Fig. 10, the fitness value is 54.14% for the first generation, and then increases rapidly during the first few generations. Then the fitness value increases gradually and finally converges to 94.99%. Thus the genetic algorithm effectively improves the fitness value from 54.14% to 94.99%.
Finally, ASAP simulation is conducted to verify the optimal distribution density of the prism pattern obtained by the genetic algorithm. The corresponding ASAP luminance plot is shown in Fig. 11 , and this plot shows that the 13-point luminance uniformity achieves an outstanding 92.09%. Note that the range of the luminance values for the color bar in Fig. 11 is from 862 to 968 nit. That is, Fig. 11 shows that the variation of luminance values within each region is much smaller. Figure 12 compares the luminance values of the central points in the 13 regions from the neural-network optical model with the ASAP simulation for the optimal LGP. In the figure, the luminance difference between them is from 1.80 to 28.16 nit, that is, less than a 3% error. This means that Fig. 12 validates the accuracy of the neural-network optical model.
Fig. 11 ASAP Luminance plot for the LGP with the optimal distribution density of the prism pattern obtained from the genetic algorithm.
Fig. 12 Luminance values at the central points of 13 regions using the neural-network optical model versus ASAP simulation for the LGP with the optimal distribution density of the prism pattern.
Regarding the typical time to run the relevant programs, if the C + + programs are executed on a desktop computer with a 2.66-GHz Intel Celeron CPU and 2GB 400-MHz DDR2 RAM, it takes about one minute to run the neural-network training program and about thirty minutes to run the genetic algorithm. When a faster computer is used, the time for running the neural-network and genetic algorithm programs would become much shorter. Thus one can conclude that it is quite efficient to obtain a better solution by adopting the proposed optimization method.
4. Conclusions
The results from the execution of the genetic algorithm show that the 13-point luminance uniformity reaches 92.09% for a 13-inch LGP. Thus it can be concluded that the optimal design method of the LGP, using the genetic algorithm and neural-network optical model provides an effective way to determine the distribution density of the prism pattern so as to achieve excellent luminance uniformity in the exiting light. In addition, it is also shown that the neural-network optical model possesses high accuracy in estimating the luminance values of the LGP such that the search process is effectively expedited.
References
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