//Logo Image
Author: Yeh-Liang Hsu, Chia-Chieh Yu, Yao-Tung Wang, Ming-Hsiu Hsu (2008-12-11); recommended: Yeh-Liang Hsu (2010-06-09).
Note: This paper is published in Journal of the Chinese Institute of Engineers, Vol. 32, No. 5, pp. 717-725, July 2009.

Uniform luminance design of the direct-type backlight unit of liquid crystal displays

ABSTRACT

Light efficiency optimization of a direct-type backlight unit (BLU) of the liquid crystal display (LCD) is considered in this paper. The purpose of this research is to obtain the greatest uniformity in a direct-type BLU, while the brightness is maintained in a satisfactory level.

It is difficult to find a numerical optimization algorithm that is readily applicable to this problem because of the existence of discrete variables, implicit objective functions and constraints, or even binary constraints. The sequential neural-network approximation (SNA) method is designed specifically for this type of engineering design optimization problem. In this paper, a two variable LCD BLU design example is presented first to illustrate the design process using the SNA method. Then a four variable LCD BLU design optimization problem is solved.

Keywords: backlight unit, light efficiency optimization, luminance uniformity, sequential approximation method (ME21)

I.      INTRODUCTION

The liquid crystal display (LCD) has become the mainstream display component in various digital consumer products from cellular phones, personal digital assistants (PDA), notebook computers, to television sets. The backlight unit (BLU) module provides a light source for transmission type LCD. Based on the location of the light sources, BLU modules can be classified into two categories: edge-type BLU and direct-type BLU. The edge-type BLU module mounts the light source lamp (such as cold-cathode fluorescent lamp, CCFL) at the top or the bottom edge of the LCD. A light guide plate is used to guide the light from edge-light into surface-light. One advantage of the edge-type BLU module is that it is thin. However, the edge-type BLU is not able to produce enough brightness, and is often used for small or mid-sized LCDs.

For products requiring large-sized LCDs, television sets for example, the direct-type BLU module is commonly used. The direct-type BLU module places a number of CCFLs directly behind the LCD panel in a parallel configuration. The core components of a direct-type BLU include a reflective sheet, a light source module (CCFLs and clamps), a diffuser plate, and a prismatic sheet sandwiched between two diffuser sheets.

Brightness and luminance uniformity are the major performance indices of the BLU. While the direct-type BLU module provides greater brightness, the uniformity of luminance is an important issue to be considered. Automatic optical inspection (AOI) systems are used to measure the performance of the BLU in industry. Luminance uniformity is a measure of how well the luminance remains constant over the surface of the screen. “Sampled uniformity”, which compares several discrete points on the screen to provide a quick check of the uniformity, is the measuring scheme commonly used in industry.

Figure 1 shows the 9 symmetrical sampling points (P1~P9) which divide the LCD screen into small squares. The center luminance is measured at center point (P5). The “9-point uniformity” is defined by the minimum luminance measured at the 9 sampling points divided by the maximum luminance measured at the 9 sampling points, as shown in Eq. (1).

        9-Point Uniformity (Luminance uniformity) =        (1)

Note that from Eq. (1), the perfect luminance uniformity is 100%.

Fig. 1 Nine symmetrical sampling points on the LCD screen

Brightness and luminance uniformity depend on the shapes, locations and dimensions of the optical components of the BLU. Researchers have been trying to change the locations of the lamps and the shapes of the reflectors in order to improve the brightness and to achieve uniform luminance. Chan et al. (2003) developed a special reflector for direct-type BLUs to improve the light efficiency, which achieved a 33% increase in luminance. Park and Lim (2001) experimented with four types of reflector structures, including flat reflectors, V-shape reflectors, U-shape reflectors and W-shape reflectors in direct-type BLUs. They found that the distance between the lamp and the diffuser surface is proportional to the luminance uniformity.

In practice, experimental methods are used to find a design with acceptable luminance uniformity by LCD manufacturers. Optical simulation tools have also been used to avoid high cost iterations needed during the experimental design process. The use of the simulation tools helps engineers to speed up BLU design by replacing physical mockups with virtual models created by simulation tools during the BLU design process. However, design modification to improve luminance uniformity is still based on the experience of the engineer, and is tested in a “trial and error” manner using the simulation tools.

Optimization processes combining optimization algorithms with optical simulation tools have been introduced into edge-type BLU design to achieve a uniform luminance. Cheng and Pedram (2004) proposed a technique aims at conserving power by reducing the backlight illumination while retaining the image fidelity through preservation of the image contrast. This concurrent brightness and contrast scaling optimization problem was solved subject to constraint on contrast distortion. Choi et al. (2004) considered an ink density optimization problem in order to produce a uniform distribution of luminaries on the front face of BLU. The ink density pattern was represented by a 3rd-degree polynomial function. Four coefficients of the polynomial function were the design variables. The Nelder-Mead direct search method was used in this study to solve the optimization problem. Cassarly and Irving (2005) developed a hybrid optimization approach that combines a mesh feedback optimization method with a classical optimizer to design the extraction pattern for an edge-type BLU. The design variables of their work include density, size and spacing of extraction patterns on a light guided plate. Park and Ko (2007) optimized the emitting structure of multi-channel-type flat fluorescent lamps (FFLs) combined by a lenticular-lens-patterned diffuser plate by the ray tracing technique for best luminance uniformity.

In this paper, a uniform luminance design optimization problem for direct-type LCD BLU under maximum brightness constraints is considered. Fig. 2 shows the critical dimensions of a BLU in top view. The design parameters C (thickness of the diffuser plate), D (diameter of the lamps), E (thickness of the inner diffuser sheet), F (thickness of the prismatic sheet), G (thickness of the outer diffuser sheet), LU (size of the display), and LQ (number of lamps) are defined by the manufacturers. The design variables a (angle of the reflector), b (distance between a lamp and one side of the reflector), h (height of the enclosure), lb (width of the bottom side of the reflector), p (distance between two lamps), and lp (distance between a lamp and bottom side of the reflector) are to be decided by the designer. Design variables p and lb can be expressed in terms of other parameters and variables as:

        ,                                                                                           (2)

        .                                                                              (3)

Thus there are only 4 independent design variables a, b, h, and lp. Variables p and lb can be obtained using Eqs. (2) and (3) after the optimal values of the 4 independent design variables a, b, h, and lp are obtained.

Fig. 2 Critical dimensions of a BLU in top view

The design goals for the BLU are to achieve higher luminance uniformity and to satisfy the luminance requirement of the manufacturer (for example, luminance at each of the 9 sampling points has to be higher than 9,000 lux in this case). This design problem can be formulated as follows:

        max. Uniformity(x)

        s.t.    Brightness(x)=1,                                                                              (4)

where x is the vector of design variables described above. In industry, the design variables are often discrete variables. The function Uniformity(x) is the 9-point uniformity defined in Eq. (1), and the Brightness(x) is the constraint on the luminance of the 9 sampling points of LCD. Both functions are “implicit functions,” that is, the functions cannot be expressed in an analytical function in terms of design variables. Both functions are evaluated by the optical simulation tools.

In Eq. (4), the constraint Brightness(x) can be expressed as 9 inequality constraints for the 9 sampling points. Instead of using 9 implicit constraints, this constraint is expressed in a simplified, binary form of “pass-or-fail,” “feasible-or-infeasible” in Eq. (4). If the current design x satisfies the brightness requirement of the LCD (luminance at each of the 9 sampling points is higher than 9,000 lux), then Brightness(x)=1, otherwise Brightness(x)=0. This binary constraint “Brightness(x)=1” alone defines the feasible domain of the optimization problem. This type of binary constraint is useful in many engineering design applications where the final design has to pass certain critical tests. The results of the tests are often simply “pass-fail”, without precise function values.

The Sequential Neural-Network Approximation (SNA) method was developed by the authors (Hsu et. al, 2001; Hsu et. al, 2003) to handle engineering design optimization problems with discrete variables, implicit functions and binary constraints. The SNA method was also applied to reduce the weight of aluminum disc wheels under fatigue constraints (Hsu and Hsu, 2001). The SNA method is revised here to handle the LCD BLU optimization problem. In the previous version, the objective function was treated as an explicit function and the neural network was only used to simulate the boundary of the feasible domain of the optimization problem. In the revised SNA method, two back-propagation neural networks are trained first to simulate the objective function and the feasible domain formed by the implicit constraints using a few representative training data samples. A sample of training data consists of three pieces of information: a design point (i.e., a set of values for the design variables), objective function value at this design point, and whether this design point is feasible or infeasible. A search algorithm then searches for the “optimal point” of the simulated objective function in the feasible domain simulated by the neural network.

This new design point is checked against the true implicit constraints to see whether it is feasible, and the new training data sample is then added to the training set. The neural network is trained again with this added training data, in the hope that the network will better approximate the objective function and the boundary of the feasible domain of the exact optimization problem. Then the search algorithm searches for the “optimal point” of the new simulated objective function in the new approximated feasible domain again. This sequential approximation process continues in an iterative manner, until the same “optimal design point” is obtained repeatedly and no new training point is generated. A restart strategy is employed to start the search process from different feasible initial points, so that the method may have a better chance to reach a global optimum.

In this paper, the optical simulation software Speos (Optis, 2008) is used to simulate the brightness and uniformity of the LCD. A two variable LCD BLU design example is presented first to illustrate the design process using the SNA method. Then a four variable LCD BLU design optimization problem is solved.

II.  OPTIMIZING LIGHT EFFICIENCY OF A BACKLIGHT UNIT

The basic idea of sequential approximation methods is to use a simple sub-problem to approximate the hard, exact problem. The solution point of the simple sub-problem is then used to form a better approximation to the hard, exact problem for the next iteration. In an iterative manner, it is expected that the solution point of the simple approximate problem will get closer to the optimum point of the hard exact problem.

In the SNA method, the optimization problem in Eq. (4) is approximated by an approximate problem below:

        max. UniformityNN(x)

        s.t.    BrightnessNN(x)=1,                                                                  (5)

where the UniformityNN(x) and BrightnessNN(x) are the neural network simulations for Uniformity(x) and Brightness(x), respectively. Note that UniformityNN(x) simulates the function values of Uniformity(x), while BrightnessNN(x) simulates the feasible domain formed by Brightness(x)=1.

In this paper, the “real” optimization model in Eq. (4) is denoted Mreal, and the approximate model simulated by neural network in Eq. (5) is denoted MNN. MNN is a “simple” model, because once the training of the neural networks is completed the computational cost of evaluating UniformityNN(x) and BrightnessNN(x) is much less than that of evaluating the Uniformity(x) and Brightness(x).

In the SNA method, a set of initial training points is used to train the neural network so that the neural network can simulate a rough map of the whole design domain. The set of initial training points should reasonably represent the whole design domain. Orthogonal arrays are used here because they are geometrically balanced in coverage of the experiment region with just a few representative experiments.

As described in Section I, there are 4 independent variables in this problem: lp, b, h, and a. For demonstration purposes, variables lp and b are assumed to be fixed in this section. Variables h and a have 9 possible discrete values:

h = {12.2, 14.2, 16.2, 18.2, 20.2, 22.2, 24.2, 26.2, 28.2} mm

a = {30, 35, 40, 45, 50, 55, 60, 65, 70} degrees

The ranges of the design variables were obtained from the engineering experience of the LCD manufacturer. In this example, the ranges of both variables were divided into 8 equal sections. Other discrete values (e.g., uneven discrete values) are also possible.

Table 1 shows the initial training points determined by a three-level orthogonal array. The values of Uniformity(x) and Brightness(x) are evaluated by the optical simulation software Speos.

Table 1 The initial training points of the 2-variable example

h (mm)

a (degree)

Uniformity(x)

Brightness(x)

12.2

30

0.67

1

12.2

50

0.87

0

12.2

70

0.95

0

20.2

30

0.48

1

20.2

50

0.76

1

20.2

70

0.89

0

28.2

30

0.33

1

28.2

50

0.68

1

28.2

70

0.86

0

After the initial training set is generated, two back-propagation neural networks, UniformityNN(x) and BrightnessNN(x), are trained to simulate objective values and the feasible domain formed by the constraint using the initial training data.

Figure 3 shows a typical three-layer neural network is used in the SNA method. The size of the input layer depends on the number of variables and the number of discrete values of each variable. In this example, there are 2 design variables, with 9 discrete values each. Thus a total of 18 neurons are used in the input layer. Each neuron in the input layer has value 1 or 0 to represent the discrete value each variable takes, as will be explained later. There is only a single neuron in the output layer. In UniformityNN(x), the output neuron takes the value of Uniformity(x), which is between 0 and 1. In BrightnessNN(x), the output neuron represents whether this design point is feasible (the output neuron has value 1) or infeasible (the output neuron has value 0).

Fig. 3 The architecture of the neural network

The number of neurons in the hidden layer depends on the number of variables in the input layer. There are 12 neurons in the hidden layer in this example. The transfer functions used in the hidden and output layer of the network are both log-sigmoid functions. The neuron in the output layer has a value range [0, 1]. For BrightnessNN(x), after the training is completed, a threshold value 0.25 is applied to the output layer when simulating the boundary of the feasible domain. In other words, given a discrete design point in the search domain, the network always output 0 (if output neuron’s value is less than the given threshold) or 1 (otherwise) to indicate whether this discrete design point is feasible or infeasible.

Figure 4 shows the neural network representation of the center point (h, a)=(20.2, 50) of the discrete search domain in UniformityNN(x) and BrightnessNN(x). A cross represents a “0” in the node, and a circle represents a “1” in the node. For illustration purpose, the 18 input nodes are arranged into two rows to represent the two design variables. The first 5 nodes in the first row have a value of 1 to show that the first variable h has the discrete value of 20.2. In the second row, the first 5 nodes have a value of 1 to show that the second variable a has the discrete value of 50. As shown in Table 1, checking with Uniformity(x) and Brightness(x), (h, a)=(20.2 50) is a feasible design point and its objective value is 0.76.

Note that in this representation, discrete values of the variables are embedded and neighboring nodes have very similar input patterns. Moreover, there has to be at least one feasible design point in the set of initial training points. Otherwise there will be no feasible domain after the training is completed.

Fig. 4 The neural network representation of the center point (h, a)=(20.2, 50) of the discrete search domain

The computational effort required in neural network training is critical. If the computational cost required in neural network training is larger than that of evaluating the implicit constraints, then the SNA method will lose its advantage. Here all the training data are represented in a clear 0-1 pattern, which makes the training process relatively fast. A quasi-Newton algorithm, which is based on Newton’s method but does not require calculation of second derivatives, is used for the training. In our numerical experience, the error goal of 1e-6 is usually met within 100 epochs, even for cases with many training points.

III.  SEARCHING IN THE NEURAL-NETWORK APPROXIMATE MODEL

Using the 9 initial training points in Table 1, Fig. 5 shows the approximation by MNN after the initial training has been completed. The 9 nodes enclosed by square brackets are the initial training points, and the contours are approximated objective values by UniformityNN(x). There are 81 possible discrete combinations in the search domain. A circle represents that the design is feasible determined by BrightnessNN(x), and a cross represents the design is infeasible determined by BrightnessNN(x).

Fig. 5 The approximation by MNN after the initial training has been completed

A search algorithm starts to search for the optimum point of MNN. Fig. 6 is the flow chart of this discrete search algorithm. As discussed earlier, there has to be at least one feasible design point in the set of initial training points, so the search algorithm can always start from a feasible design point. If a new design point obtained from the previous iteration is a feasible design point in Mreal, it is used as the starting point in the current search. If the new design point is infeasible in Mreal, then the same starting point used in the previous iteration is used again in the current search.

As shown in Fig. 6, a usable set Uj is formed from neighboring discrete nodes of the current search point xj (j=0 for the starting point). There are m=3n-1 nodes in Uj, where n is the number of design variables. Then the components in Uj are sorted by the “distances” to xj in a descending order, thus Uj={u1, u2, u3, …, um}. Note that by “distance”, we don’t mean the absolute distance ||uk-xj||. Instead, we mean the number of variables in uk that have different discrete values from xj. Therefore this sorting is the same for all discrete points, given the number of total design variables, and does not require any computation. The node that has a larger “distance” to xj has a higher priority to be searched first.

Pick a node uk from Uj. Two conditions are checked: “if uk is feasible in MNN?” and “if f(uk)<f(xj)?” If both conditions are satisfied, uk is a better feasible point than xj, and we move on to uk and start the next iteration (j=j+1). On the other hand, if either of the two conditions is not satisfied, then we check the next node in Uj (k=k+1). When we reach the end of Uj (k=m), there is no better feasible point in Uj, and xj is output as the optimum (at least locally) point.

Fig. 6 Flow chart of the search algorithm

In the LCD BLU example discussed in this section, the feasible design point (h, a)=(20.2, 50) is used as the starting point because it has the best objective value (0.76) among all design points in the initial training set. The search algorithm terminates at a new design point (h, a)=(20.2, 60). This new design point is then evaluated in Mreal. Using the optic simulation software Speos, this new design point is determined infeasible, and the objective value is 0.81. Thus, a new training point {(20.2, 60), infeasible, 0.81} is added to the set of training points, and the neural-network is trained again. After the second training is completed, MNN is updated with 10 training points. The search algorithm then starts to search for the new optimum point in MNN again.

The iteration continues, with one more training point added into the set of training points in each iteration. The whole process terminates when the same design point is obtained repeatedly and no new training point is generated. In this design case with two design variables, the SNA method terminates after 4 iterations. Fig. 7 shows the approximate model MNN trained by 13 design points, including the 9 initial training points (nodes enclosed by square brackets in Fig. 7) and 4 new design points obtained during the iterations (nodes enclosed by diamond brackets in Fig. 7). Again in Fig. 7, a circle represents that the design is feasible determined by BrightnessNN(x), and a cross represents the design is infeasible determined by BrightnessNN(x). The optimum point found by the SNA method is (14.2, 50), and the uniformity of luminance is 0.82.

Fig. 7 Approximate model MNN trained by 13 design points

Figure 8 shows the iteration history of this example. The design points enclosed by circles are the feasible design points. Note that a total of 13 points out of the 81 (9×9) possible combinations (16%) are evaluated to obtain this optimum design. No gradient calculation is required. To ensure a better chance of reaching a global optimum, the searching process is restarted from other feasible points (12.2, 30), (20.2, 30), (28.2, 30), (28.2, 50) in the initial training set. In this example, all restart search processes terminate at the same optimum design point (14.2, 50) in one iteration.

Fig. 8 Iteration history of the 2-variable example

IV.   LIGHT EFFICIENCY OPTIMIZATION WITH 4 DISCRETE DESIGN VARIABLES

Figure 9 outlines the SNA method described in the previous section. The set of initial training data S0 with at least one feasible point is given. A back-propagation neural network is trained to simulate the objective function and a rough map of the feasible domain formed by the implicit constraints using S0, and the initial optimization model MNN is formed There has to be at least one feasible point in S0, such that MNN has a feasible domain.

Starting from a feasible point s, the search algorithm described in Figure 6 is used to search for the solution point xj of MNN in the j-th iteration. The search algorithm has to start from a feasible design point. There can be several feasible design points in S0, and the one with lowest objective value is used first. The new solution point xj is then evaluated to see whether it is feasible in Mreal, and whether xj = xj-1. If not, this new solution point xj is added to the set of training points S, and the neural network is trained again with the updated data set. Then the search algorithm is used to search for the solution point in the updated MNN again. With the increasing number of training points, it is expected that the feasible domain simulated by the neural network in MNN will get closer to that of the exact model Mreal, and the solution point of MNN will get closer to the optimum point.

If the feasible solution point xj generated in the current iteration is the same as xj-1, no new training point is generated. The set of the training point since S, and consequently MNN, is not updated. The current search has to be terminated because we will be getting the same solution point.

As shown in Fig. 9 after the process is terminated, a restart strategy is employed to start the search process from different feasible initial points in S0. The iterations continue until all feasible points in S0 have been used as initial starting points. Finally the feasible design point with the lowest objective value in S is output as the optimal solution.

Fig. 9 Flow chart of the SNA method

In this section, all 4 design variables (lp, b, h, and a) are considered. Each design variable has 9 possible discrete values:

h = {12.2, 14.2, 16.2, 18.2, 20.2, 22.2, 24.2, 26.2, 28.2} mm

b = {4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0} mm

lp = {3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5} mm

a = {30, 35, 40, 45, 50, 55, 60, 65, 70} degrees

Table 2 shows the 9 initial training points determined by the orthogonal array. The design point (20.2, 20.0, 7.5, 70) was used as the starting point because it has the best objective value (0.67) among all feasible design points in the initial training set. Following the same procedure described in the previous section, the optimal design point was obtained after 27 iterations using the SNA method. The optimal design point is (12.2, 16.0, 5.5, 50), and uniformity of luminance improves to 0.85, which is higher than that in the previous section with two design variables.

Figure 10 shows the iteration history in this example. After the optimal design point was found, the searching process was restarted from other feasible points (12.2, 30), (20.2, 30), (28.2, 30), (28.2, 50) in the initial training data to ensure a better chance of reaching a global optimum. However, as shown in Fig. 10, no better design points were found during the restart process. In the optimization process using the SNA method, 36 training points (including 9 in the initial training, and 27 during the iterations) out of the 6561 (94) possible combinations (0.55%) were evaluated.

Table 2 The initial training points of the 4-variable example

h (mm)

b (mm)

lp (mm)

a (degree)

Uniformity(x)

Brightness(x)

12.2

4.0

3.5

30

0.82

0

12.2

12.0

5.5

50

0.92

0

12.2

20.0

7.5

70

0.91

0

20.2

4.0

3.5

30

0.95

0

20.2

12.0

5.5

50

0.60

1

20.2

20.0

7.5

70

0.67

1

28.2

4.0

3.5

30

0.83

0

28.2

12.0

5.5

50

0.32

1

28.2

20.0

7.5

70

0.33

1

Fig. 10 Iteration history of the 4-variable example

V.   CONCLUSION

A uniform luminance design optimization problem for direct-type LCD BLU under maximum brightness constraints was considered in this paper. It is difficult to find a numerical optimization algorithm that is readily applicable to this problem because of the existence of discrete variables, implicit objective functions and constraints, or even binary constraints. The SNA method is designed specifically for this type of engineering design optimization problem. In the SNA method, the precious function evaluations of the implicit functions (by optical simulation software Speos in this case) are accumulated to progressively form a better approximation to the real optimization problem using the neural network. Only one evaluation of the implicit constraints is needed in each iteration. No sensitivity calculation is required.

In the 4-variable design example presented in this paper, the uniform luminance of the LCD BLU improves from 0.67 (the highest value among all feasible design points in the initial training set) to 0.85, a 27% improvement. Only 36 design points out of the 6561 (94) possible combinations, or 0.55% of the possible discrete design points were evaluated.

In the design of LCD BLU, optical simulation tools have been used to avoid high cost iterations needed during the experimental design process. This paper demonstrates that, combined with the SNA optimization method, designs with optimal luminance uniformity, while satisfying the brightness requirements, can be obtained systematically, with the fewest calls to the optical simulation tools. The SNA method has been coded into a software package that is readily available for design engineers.

NOMOCLATURE

a              angle of the reflector

b              distance between a lamp and one side of the reflector

C             thickness of the diffuser plate

D             diameter of the lamps

E              thickness of the inner diffuser sheet

F              thickness of the prismatic sheet

G             thickness of the outer diffuser sheet

h              height of the enclosure

lb             width of the bottom side of the reflector

lp             distance between a lamp and bottom side of the reflector

LQ           number of lamps

LU           size of the display

m             the number of nodes in Uj

Mreal         the real optimization model

MNN         the approximate model simulated by neural network

n              the number of design variables

p              distance between two lamps

Pi             symmetrical sampling points of LCD screen

S0             the set of initial training data

S              a new training data

s               a feasible point in S0

Uj           a usable set which is formed from neighboring discrete nodes of the current search point xj

uk                 the vector of design variables in Uj

xj             the vector of discrete design variables

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