Research ArticleApplication of Virtual Display Technology of LCD BacklightSpectrum Optimization Algorithm Based on Linear Programming

Yuan Cui , Zhuyang Chen, Cheng Huang, and Qian Gao

School of Electric Information Engineering, Jiangsu University of Technology, Changzhou 213001, China

Correspondence should be addressed to Yuan Cui; cuiyuan@jsut.edu.cn

Received 23 March 2021; Revised 18 April 2021; Accepted 15 May 2021; Published 26 May 2021

Academic Editor: Yong Deng

Copyright © 2021 Yuan Cui et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to make the color of image display more realistic, optimize the use of energy, and improve the light efficiency of the modulethrough reasonable spectral distribution, this paper proposes a backlight spectral optimization algorithm based on linearprogramming. With the goal of maximizing the backlight luminous efficiency, the theoretical maximum of the luminousefficiency of the backlight spectrum can be achieved by constructing a linear programming model. The research process is toobtain the optimal distribution of transmittance spectrum by linear programming method on the premise of ensuring the colorgamut standard of display system. The results show that the light efficiency can be increased to 335.5 lm/W, while the originallight efficiency of the system is less than 150 lm/W. With the goal of maximizing the light efficiency, light sources with narrowbandwidths such as lasers and quantum dot materials can be used to simulate and reconstruct these characteristic wavelengths.There will be easier to approach the ideal optimization spectrum and achieve the theoretical maximum luminous efficiency of610.8 lm/W.

1. Introduction

In recent years, many display devices have been introduced.In particular, the digital flat panel display technology repre-sented by the LCD has been rapid developed [1, 2]. Forfurther improving the effect of the display device andenhancing the performance of the display, the color gamut,as an important indicator of the display quality, will becomethe focus in the research area of display. At the same time, thepolarizer and color filter in the LCD panel structure have ahuge impact on the luminous efficiency, which lead to thelow light effect. At present, RGB color light source canremove the color filter to improve the luminous efficiency,but there are still some limitations. As the light source ofthe display, the spectral components contained in the back-light spectrum will directly affect the final color renderingeffect. The backlight spectrum is the key to color gamutexpansion as well. In this paper, a linear programming-based algorithm is proposed for optimization of the backlightspectrum. Through constructing a linear programmingmodel, the spectrum distribution of the primary colors of

any display and the calculation of the limit value of the lightefficiency can be optimized.

The rest of this paper is arranged as follows: Section 2studies the structure of liquid crystal display and the phe-nomenon of metamerism; Section 3 illustrates the optimiza-tion model of the backlight spectrum; Section 4 reports theanalysis of the backlight optimization model. Finally, Section5 concludes the proposed algorithm and presents severalaspects of future work.

2. Structure of Liquid Crystal Device andPhenomenon of Metamerism

Since the liquid crystal layer cannot emit the light, the tradi-tional LCD uses a multilayer module for reconstruction ofthe image bymodulating the backlight through diffusers, polar-izers, liquid crystal layers, and filters. According to the distribu-tion of the backlight light source, common modules can bedivided into two types: edge type and direct type [3, 4]. Theschematic diagram of these two structures is shown in Figure 1.

HindawiWireless Communications and Mobile ComputingVolume 2021, Article ID 9947288, 12 pageshttps://doi.org/10.1155/2021/9947288

As for the edge type, the backlight source is placed on theside of the liquid crystal panel. The light guide plate is usedfor color mixing and can directly couple the light to the liquidcrystal panel as the input light energy. However, in the directtype, the light emitted from the backlight is reflected by thereflector. After that, the light is dispersed upward throughthe diffuser. Eventually, the light can be transmitted fromthe front side. Taking the direct backlight structure as anexample, the basic structure of the module and the transmit-tance level of each layer are shown in Figure 2. Comparedwith the direct type, the side type has a lower overall utiliza-tion rate of the light energy due to the energy loss of the lightguide plate [5, 6].

Because of the multilayer structure of the module, thereare only 5% of the light from the direct type module thatcan be emitted by the screen for forming the final image. Thismeans that the utilization rate of light energy in the LCD sys-tem is rather low. To ensure the quality of the reconstructedimage, most of the light is absorbed or uniformed by variousmaterials during the layer-by-layer modulation. This phe-nomenon not only exacerbates the heating problem of thedisplay but also increases the power consumption of thedevice. Generally, the luminous efficiency (lm/W) is used asan index to measure the electro-optical conversion efficiencyof the light source. The luminous efficiency can be calculatedas follows:

η = kÐ 780380Φ λð ÞV λð ÞdλÐ 780

380Φ λð Þdλ: ð1Þ

In which, the coefficient k represents the maximum opti-cal efficiency, i.e., 683 lm/W, which is also the luminous effi-ciency value when human watches the yellow-green light(555 nm). ΦðλÞ is the radiance spectral energy distributionof the light source. VðλÞ is the light efficiency function ofhuman eyes’ optical spectrum. In the LCD system, whetherit is a traditional CCFL backlight or a new LED backlight,the luminous efficiency of the device does not exceed150 lm/W, and the luminous efficiency of the whole systemdoes not exceed 10 lm/W.

The light emitted from the backlight of the flat panel dis-play system is filtered by the module. Under the CIE-1931

XYZ color space, the color is calibrated by its color coordi-nates ðx, yÞ. Equation (2) for calibration is given as follows:

X =ð780380

Φ λð Þ�x λð Þdλ,

Y =ð780380

Φ λð Þ�y λð Þdλ,

Z =ð780380

Φ λð Þ�z λð Þdλ,

x = XX + Y + Z

,

y = YX + Y + Z

:

8>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>:

ð2Þ

In which, X, Y , and Z represent the tristimulus values ofthe red, green, and blue channels, respectively. ΦðλÞ is thespectral distribution of the color. −x ðλÞ, −y ðλÞ, and −z ðλÞare the standard observations of X, Y , and Z.

Deduced from the integral calculation of the color coor-dinates, there are infinite possibilities for the color lightspectrum distribution that meets the color coordinates. The-oretically, if the color coordinates ðx, yÞ are the same andhave the same brightness, the human eyes cannot distinguishthem and will judge these colors as the same color. This phe-nomenon is also elaborated by Glassman’s law [7–9]. In fact,whether in daily life or the industrial production, most of thecolors are metameres [10, 11]. This phenomenon is muchmore common, especially in the industries such as printing,dyes, and painting. Since the actual color perception of thehuman eye is directly related to the tristimulus value insteadof the spectral composition, the optimization of many lightsources and spectral analysis can be achieved by using themetamerism. For instance, the metamerism can be used forimproving the color accuracy of the multiprimary color dis-play systems [12]. Wyszecki et al. proposed the concept ofmetamerism black to decompose the spectral reflectance ofobjects [13]. Cohen et al. proposed an Rmatrix mathematicalmodel for spectral reconstruction calculations [14, 15]. Sim-ilarly, metamerism also provides the possibility to optimizethe backlight of liquid crystal displays.

Protector sheet

Prism sheet (H)

Prism sheet (V)

Diffuser sheet

CCFL

CCFL reflector

Light guideReflectorFrame

(a) Edge type

Protector sheet

Prism sheet (H)

Prism sheet (V)

Diffuser sheet

Backlight

(b) Direct type

Figure 1: Schematic of the LCD module structure.

2 Wireless Communications and Mobile Computing

The energy consumption of displays is used as anotherimportant indicator. In the optimization, the light efficiencyof the display is used as a reference indicator to measurethe quality of the backlight spectrum, and the high luminousefficiency light source is of great significance for the display.Normally, the power consumption of the general liquid crys-tal display (LCD) backlight accounts for most of the entirepower consumption. Backlight modulation can also be usedto improve the luminous efficiency of LCD module, such asflicker backlight technology and scanning backlight technol-ogy. Flicker backlight is to make the backlight glow only for acertain period in a frame instead of continuously illuminated.This method can reduce energy consumption but may lead toa decrease in the overall image brightness, which makes thebrightness output of the backlight more demanding. Basedon the flickering of the backlight, scanning backlight addsthe process of controlling the phase of the backlight; that is,lighting up and closing the backlight at the phase when theLCD pixel are completely on and completely off. The advan-tage of backlight scanning is that the light energy utilizationof the backlight is high and can obviously improve the phe-nomenon of LCD image motion blur, but in order to achievea constant background light brightness, it is necessary toimprove the brightness of the scanned background light.Therefore, the reduction of the power consumption causedby the backlight source is crucial. The utilization of LCDswith higher light efficiency in portable devices can improvethe endurance of the device under the same battery capacitywhich can enhance the practicability and competitivenessof the product.

Besides, the spectral optimization of the display backlightsource is also applicable to the field of lighting. In recentyears, with the development of cities, the fossil energy hasbecome increasingly tense. The prices of the conventionalenergy, such as oil and coal, have continued to rise. In partic-ular, international oil prices have reached to the peak leadingto an increasingly severe energy supply situation. The sus-tainable development and utilization of energy has attractedmore and more attention. Lighting is one of the main areas

where humans consume energy. Therefore, it is of great sig-nificance to achieve energy saving in the lighting field [16].For alleviating the ever-increasing energy crisis, the “greenlighting concept” has been proposed internationally in theearly 1990s. The Energy Independence and Security Act of2007 (EISA2007) signed by the United States specificallyrequires the inclusion of the “Next Generation Lighting Ini-tiative” (NGLI) [17]. Currently, European and Americanmarkets generally adopt the Energy Star (ES) indicatorjointly promoted by the US Department of Energy and theUS Environmental Protection Agency [18], China, alsobegan to implement the promotion of “green lighting pro-jects” in 1996 [19, 20]. An important step to realize this planis to develop and promote efficient and energy-saving light-ing fixtures. Saving the electricity for lighting, reducing thelighting pollution, and establishing a high-quality, efficient,economical, comfortable, safe, and reliable lighting systemare beneficial to the whole system. The high-efficiency light-ing source means that the source consumes less energy underthe same light output. It is of great significance to save energyand reduce power costs.

Compared with the lighting, the color gamut rangeshould be taken into consideration in the display systemwhile improving the light efficiency. Otherwise, the imagequality of the display will be affected due to the decrease incolor saturation, which will be harmful to the final qualityof the display. By using the metamerism, the simulationand optimization of the spectral distribution of the lightsource can be achieved with the optimal light efficiency.

3. Optimization Model of theBacklight Spectrum

The reconstruction of color images of LCD can be achievedby mixing multiple primary colors. Under the premise ofensuring the color gamut area, the light efficiency of thedisplay should be maximized. The optimized spectrum ofeach primary color is the basis for the optimized spectrumof the entire backlight. Based on the passive light-emittingprinciple of LCD, the light of the display received by theviewer is the backlight by passing through the liquid crystallayer and the filter. The absorption of other optical film layerssuch as polarizers can be treated as a fixed value. In order toachieve a real simulation effect, the spectral distribution ofthe backlight, ΦBLðλÞ, the transmittance line distribution ofthe filter, TCFðλÞ, and the transmittance distribution of theliquid crystal, TLCðλÞ, should be set as unknown parameters.Since these three parameters are unknown, solving the func-tion directly can be very difficult [21]. In order to simplify theprocess, the optimization of the process can be divided intothree steps. Step one is the spectrum optimization of the pri-mary color light. Step two is the spectral synthesis of the dis-play optimization backlight; the final step is the spectraldistribution of the color filter transmittance. During the pro-cess, the optimized result in each step can be the basis of thenext calculation. In the first step of optimization, the trans-mittance spectrum of the color filter and the liquid crystalcan be set as an ideal state, i.e., 100%. Following these threesteps, the optimized spectral distribution of the backlight

Transmittance ~ 5%

Color filter: 30%

Polarizer: 45%

Optical films: 70%

Backlight

Figure 2: Structure of the LCD backlight module and thetransmittance of each layer.

3Wireless Communications and Mobile Computing

and the corresponding distribution of the filter and the trans-mittance spectral of the liquid crystal can be obtained.

3.1. Spectral Optimization of Primary Colors. The spectrumoptimization of the primary colors is the basis of the displaybacklight optimization. As for displays that comply with aspecific color gamut standard, the color coordinates of eachprimary color have been determined. Each color coordinateof the primary color is different and vary with each other.Optimizing a certain primary color is equal to optimize thecolor light spectrum distribution of any known color coordi-nate. The calculation of color coordinates and light effectscan refer to equation (1) and equation (2). −w ðλÞ is the whitespectrum curve value. ΦðλÞ is the spectral distribution of thecolor. −x ðλÞ, −y ðλÞ, and −z ðλÞ are the standard observationsof X and Y . According to the principle of metamerism, thereare countless chromatic light spectrum distribution, ΦðλÞ,that satisfy the given color coordinate theoretically. Withthe goal of maximizing the light efficiency, finding one ormore optimized distributions among countless kinds of spec-tral distributions and improving light efficiency while satisfy-ing the color perception are the task of optimization ofprimary colors. Using the chromaticity formula, the problemcan be transformed into the following mathematical model.Assuming that the functionΦðλÞ satisfies the following equa-tions, we should find ΦðλÞ when η reaches to the maximum.

�w λð Þ = �x λð Þ + �y λð Þ + �z λð Þ,ð780380

Φ λð Þ x�w λð Þ − �x λð Þ½ �dλ = 0,ð780380

Φ λð Þ y�w λð Þ − �y λð Þ½ �dλ = 0,

8>>>>>><>>>>>>:

ð3Þ

η = kÐ 780380Φ λð Þ�y λð ÞdλÐ 780380Φ λð Þdλ

: ð4Þ

The solution of equation (3) is in the form of a functiondistribution, which is a functional problem. The tristimulusvalues, xðλÞ, −yðλÞ, and −zðλÞ, are subjective experimentalstatistical results. There is no recognized analytical formulacorresponding to it. In order to simplify the solution processand reduce the difficulty of the solution, the idea of functiondiscretization is used to reconstruct all the function distribu-tions into discrete functions. The integral operation is con-verted to accumulation operation [22, 23]. Eventually, theproblem can be transmitted into a discrete function for anonlinear programming model. Assuming that the discretefunction ΦðλÞ satisfies the following equations, we shouldfind ΦðλÞ when η reaches to the maximum.

�w λð Þ = �x λð Þ + �y λð Þ + �z λð Þ,

〠780nm

λ=380nmΦ λð Þ x�w λð Þ − �x λð Þ½ � = 0,

〠780nm

λ=380nmΦ λð Þ y�w λð Þ − �y λð Þ½ � = 0,

8>>>>>>>><>>>>>>>>:

ð5Þ

η = k∑780nmλ=380nmΦ λð Þ�y λð Þ∑780nm

λ=380nmΦ λð Þ: ð6Þ

The discrete functions involved in which all have thesame sampling rate. Taking into consideration of the calcula-tion accuracy and time, the sampling interval is set as 1 nm inthis paper. In addition, due to the physical meaning of thefunction, the value of each wavelength inΦðλÞ is the intensityof the energy distribution. Therefore, the value ofΦðλÞ is non-negative, i.e., ΦðλÞ ≥ 0, (380 nm ≤ λ ≤ 780 nm). Eventually,the nonlinear programming problem takes equation (6) asthe objective function, which contains 401 unknown parame-ters, 2 equality constraints, and 401 inequality constraints.

The nonlinear programming problem is solved bysubstituting the corresponding constraints and objectivefunctions. After normalization, the solution is the optimalrelative spectral power distribution of any color light. In thesolving process, it is necessary to substitute the spectral dis-tribution data for satisfying the color coordinates as the ini-tial value. If the initial value is unknown, the approximatecolor coordinates can be substituted into the calculation.However, the value calculated by the first optimization maynot be the best result. The first optimization result can beused as an initial value and then substituted into the mathe-matical tool for the next round of calculation. The result aftertwo iterations will converge to the final optimal result. Thefinal result maximizes the light efficiency under the premisethat the color coordinate is unchanged. Figure 3 shows theoptimized results of a certain white light (color coordinates(0.271, 0.234)). Before the optimization, the theoreticalluminous efficiency of the original spectral distribution ofthe illuminator is 237.6 lm/W. After the optimization, thetheoretical luminous efficiency is increased to 321.8 lm/W.

Through the optimization, the spectral distribution of thecolor light represented by any point other than the edge inthe tongue diagram of the color gamut in the CIE-1931XYZ color space can be optimized [24, 25]. Figure 4 showsthe optimized contour distribution of the tongue diagramwith the maximum light effect. The optimizable range coversthe entire tongue-shaped chart color gamut, which provides abasis for the spectrum optimization of the primary colors andthe backlight of the display.

3.2. Synthesis of Backlight Spectrum. As for traditional dis-plays, the standard of the color gamut provides four sets ofcolor coordinates for the four primary colors, i.e., red, green,blue, and white field. For example, in the NTSC standard(National Television Standards Committee, American Stan-dard Television Broadcast Transmission and ReceptionProtocol), the color coordinates of red, green, blue, and whiteare specified as ðxr , yrÞ = ð0:67, 0:33Þ, ðxg, ygÞ = ð0:21, 0:71Þ,ðxb, ybÞ = ð0:14, 0:08Þ, and ðxw, ywÞ = ð0:31, 0:316Þ. Briefly,the standard color coordinates of each primary color shouldbe calculated. Then, the aforementioned steps can be used toconstruct an equivalent nonlinear programming problem.After that, the constructed nonlinear programming problemcan be solved. Eventually, the optimal spectral distribution ofthe light efficiency of each primary color can be obtained.Taking the NTSC standard as an example, the optimized

4 Wireless Communications and Mobile Computing

spectral distributions of the three primary colors, i.e., ΦrðλÞ,ΦgðλÞ, and ΦbðλÞ, are shown in Figure 5. The theoreticallight effects of the three primary colors after the optimizationare 330.8 lm/W, 612.9 lm/W, and 101.9 lm/W, respectively.

Since the color coordinates of the white field are alsospecified in the color gamut standard, the relative intensityof each primary color spectrum needs to be calculated after

obtaining the optimized spectrum of each primary color.To tackle this issue, the synthesized white should be exactlyequal to the color coordinates of the white field when the pri-mary colors reach the maximum. Meanwhile, the light inten-sity of each primary color should be used to maximize thetotal brightness in the white field. The gain coefficients ofthe three primary colors of red, green, and blue channels

0

0.2

0.4

0.6

0.8

1

380 430 480 530 580 630 680 730 780

Rela

tive s

pect

ral i

nten

sity

Wavelength (nm)OriginalOptimized

Figure 3: The optimized spectral distribution of the white light with color coordinate of (0.271, 0.234).

0.8

0.7

0.6

0.5

0.4

600

500

400

300

200

100

0.3

0.2

0.1

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Light efficiency (lm/W)

X

Y

Figure 4: The contour map of the maximum light efficiency.

5Wireless Communications and Mobile Computing

can be set as nr , ng, and nb. In order to ensure the white fieldcolor coordinates, the intensity coefficient should satisfy thefollowing equations:

ygybYr xr − xwð Þh i

nr + yrybYg xg − xw� �� �

ng + yrygYb xb − xwð Þh i

nb = 0,

ygybYr yr − ywð Þh i

nr + yrybYg yg − yw� �h i

ng + yrygYb yb − ywð Þh i

nb = 0:

8><>:

ð7Þ

In which, Yr , Yg, and Yb represent the luminous flux ofthe three primary colors in the optimal spectral distributionof light efficiency, respectively. The expression of these threeparameters is given as follows:

Yr = 〠780nm

λ=380nmΦr λð Þ�y λð ÞΔλ,

Yg = 〠780nm

λ=380nmΦg λð Þ�y λð ÞΔλ,

Yb = 〠780nm

λ=380nmΦb λð Þ�y λð ÞΔλ:

8>>>>>>>>>>><>>>>>>>>>>>:

ð8Þ

In which, Δλ = 1 nm. The total luminous flux, Yw, of thewhite field of the display is expressed as the sum of the lumi-nous fluxes of the three primary colors:

Yw = nrYr + ngYg + nbYb: ð9Þ

On the premise that the color temperature of the whitefield does not deviate and in order to maximize the bright-ness of the white field, equation (7) can be set as theconstraint condition, and equation (9) can be set as the objec-tive function. In order to maximum the solution of equation(9), a linear programming problem can be proposed for solv-ing the gain strength of each primary color. It should be

noted that each gain coefficient is nonnegative, i.e., nr ≥ 0,ng ≥ 0, and nb ≥ 0. Besides, the final constructed linear pro-gramming problem contains three unknown parameters,two equality constraints, and three inequality constraints.By using some calculation tools, nr , ng, and nb can be solved.Taking the NTSC standard as an example, the brightness ofthe white field formed by the combination should be the larg-est when the white field color coordinates are (0.31, 0.316),nr = 0:8875, ng = 0:5742, and nb = 1:0000.

After obtaining the spectral intensity gain coefficients ofeach primary color, the optimized spectra of all primarycolors are combined into the display backlight spectrumaccording to the coefficient ratio. Due to the passive lightemitting principle of liquid crystal displays, the backlight ofthe display should pass through filters for selecting the spe-cific wavelength. Therefore, the final backlight spectrumvalue at a certain wavelength is the maximum value of theoptimized spectrum of all primary colors at that point. Thefinal optimized backlight spectrum BLðλÞ is given as follows:

BL λð Þ380nm≤λ≤780nm

=max nrΦr λð Þ, ngΦg λð Þ, nbΦb λð Þ,� �: ð10Þ

In which, the optimized backlight spectrum distributionsynthesized by the NTSC standard is shown in Figure 6.The theoretical light efficiency of the optimized backlightspectrum is 335.5 lm/W.

3.3. Spectral Optimization of the Transmittance of the Filter.Due to the passive light emitting principle of the LCD, thebacklight of the display should be selected by passing throughfilters. A large amount of backlight energy is absorbed by thefilter layer causing a low lighting efficiency. Based on theaforementioned principle, the optimization of the transmit-tance distribution of the filter can also be achieved by con-structing a linear programming problem [26, 27]. Assumingthat the spectral distribution of the display backlight is BLðλÞ,the transmittance distribution functions of the red, green,

0.0

0.2

0.4

0.6

0.8

1.0

380 430 480 530 580 630 680 730 780

Rela

tive s

pect

ral i

nten

sity

Wavelength (nm)

RedGreenBlue

Figure 5: The optimized spectral distribution of the red, green, and blue channel under the standard of NTSC.

6 Wireless Communications and Mobile Computing

and blue filters are CFrðλÞ, CFgðλÞ, and CFbðλÞ, respectively.According to the provision of the color gamut standard, thefinal color coordinate calculation of the primary color lightreceived by the human eyes meets equation (11) as follows:

�w λð Þ = �x λð Þ + �y λð Þ + �z λð Þ, CFw λð Þ = CFr λð Þ + CFg λð Þ + CFb λð Þ,

xr =∑780nm

λ=380nmBL λð ÞCFr λð Þ�x λð Þ∑780nm

λ=380nmBL λð ÞCFr λð Þ�w λð Þ, yr =

∑780nmλ=380nmBL λð ÞCFr λð Þ�y λð Þ

∑780nmλ=380nmBL λð ÞCFr λð Þ�w λð Þ

,

xg =∑780nm

λ=380nmBL λð ÞCFg λð Þ�x λð Þ∑780nm

λ=380nmBL λð ÞCFg λð Þ�w λð Þ, yg =

∑780nmλ=380nmBL λð ÞCFg λð Þ�y λð Þ

∑780nmλ=380nmBL λð ÞCFg λð Þ�w λð Þ

,

xb =∑780nm

λ=380nmBL λð ÞCFb λð Þ�x λð Þ∑780nm

λ=380nmBL λð ÞCFb λð Þ�w λð Þ, yb =

∑780nmλ=380nmBL λð ÞCFb λð Þ�y λð Þ

∑780nmλ=380nmBL λð ÞCFb λð Þ�w λð Þ

,

xw = ∑780nmλ=380nmBL λð ÞCFw λð Þ�x λð Þ

∑780nmλ=380nmBL λð ÞCFw λð Þ�w λð Þ

, yw = ∑780nmλ=380nmBL λð ÞCFw λð Þ�y λð Þ

∑780nmλ=380nmBL λð ÞCFw λð Þ�w λð Þ

:

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

ð11Þ

Since the backlight is determined, the difference in thetransmittance spectrum of the filter will directly determinethe luminous efficiency of the display. Therefore, the optimi-zation of the luminous efficiency is equal to the maximization

of the luminous flux. The luminous flux of the brightness ofthe white field, i.e., Y , can be calculated as follows:

Y = 〠780nm

λ=380nmBL λð ÞCFw λð Þ�y λð Þ: ð12Þ

Since there are three independent spectral distributions,each solution contains 401 unknown parameters, if the sam-pling interval is set as 1nm. In order to simplify the problem,the three functions can be combined into one function, andthis function can be solved by some mathematical tools. Thesynthesis process is to connect the transmittance distributionfunctions of the red, green, and blue filters in sequence to forma discrete function, i.e., CFallðmÞ, containing 1203 elements.The synthesis equation (13) is given as follows:

CFall mð Þ = CFr 380ð Þ,⋯CFr 780ð Þ, CFg 380ð Þ,⋯CFg 780ð Þ, CFb 380ð Þ,⋯CFb 780ð Þ� �:

ð13Þ

Taking equation (13) as the function to be solved, equation(11) and equation (12) can be transmitted into:

0

0.2

0.4

0.6

0.8

1

380 480 580 680 780

Rela

tive s

pect

ral i

nten

sity

Wavelength (nm)

NTSC (optimized backlight spectrum)

Figure 6: The optimized spectral distribution of the backlight under the standard of NTSC.

A =

BL 380ð Þ �x 380ð Þ − xr �w 380ð Þð Þ ⋯ BL 780ð Þ �x 780ð Þ − xr �w 780ð Þð Þ 0 ⋯ 0 0 ⋯ 0BL 380ð Þ �y 380ð Þ − yr �w 380ð Þð Þ ⋯ BL 780ð Þ �y 780ð Þ − yr �w 780ð Þð Þ 0 ⋯ 0 0 ⋯ 0

0 ⋯ 0 BL 380ð Þ �x 380ð Þ − xg �w 380ð Þ� �⋯ BL 780ð Þ �x 780ð Þ − xg �w 780ð Þ� �

0 ⋯ 0

0 ⋯ 0 BL 380ð Þ �y 380ð Þ − yg �w 380ð Þ� �

⋯ BL 780ð Þ �y 780ð Þ − yg �w 780ð Þ� �

0 ⋯ 0

0 ⋯ 0 0 ⋯ 0 BL 380ð Þ �x 380ð Þ − xb �w 380ð Þð Þ ⋯ BL 780ð Þ �x 780ð Þ − xb �w 780ð Þð Þ0 ⋯ 0 0 ⋯ 0 BL 380ð Þ �y 380ð Þ − yb �w 380ð Þð Þ ⋯ BL 380ð Þ �y 780ð Þ − yb �w 780ð Þð Þ

BL 380ð Þ �x 380ð Þ − xw�w 380ð Þð Þ ⋯ BL 780ð Þ �x 780ð Þ − xw�w 780ð Þð Þ BL 380ð Þ �x 380ð Þ − xw�w 380ð Þð Þ ⋯ BL 780ð Þ �x 780ð Þ − xw �w 780ð Þð Þ BL 380ð Þ �x 380ð Þ − xw �w 380ð Þð Þ ⋯ BL 780ð Þ �x 780ð Þ − xw �w 780ð Þð ÞBL 380ð Þ �y 380ð Þ − yw �w 380ð Þð Þ ⋯ BL 780ð Þ �y 780ð Þ − yw�w 780ð Þð Þ BL 380ð Þ �y 380ð Þ − yw�w 380ð Þð Þ ⋯ BL 780ð Þ �y 780ð Þ − yw �w 780ð Þð Þ BL 380ð Þ �y 380ð Þ − yw �w 380ð Þð Þ ⋯ BL 780ð Þ �y 780ð Þ − yw �w 780ð Þð Þ

26666666666666666664

37777777777777777775

,A ⋅

CFall 1ð Þ⋯

CFall 1203ð Þ

2664

3775 =

0⋯

0

2664

3775,

Y = k BL 380ð Þ�y 380ð Þ,⋯,BL 780ð Þ�y 780ð Þ, BL 380ð Þ�y 380ð Þ,⋯BL 780ð Þ�y 780ð Þ, BL 380ð Þ�y 380ð Þ,⋯, BL 780ð Þ�y 780ð Þ½ � ⋅CFall mð Þ:

ð14Þ

7Wireless Communications and Mobile Computing

In addition, the value of the function CFallðmÞ is thetransmittance of the material, which should fall in theinterval (0, 1), i.e., 1 ≥ CFallðmÞ ≥ 0 (1 ≤m ≤ 1023). Finally,the linear programming problem contains 1203 unknownparameters, 8 equality constraints, and 2406 inequalityconstraints. The optimized distribution of CFallðmÞ can besolved. The first to 401th values, the 402th to 802th values,and the 803th to 1203th values of the solution correspond tothe red filter, green filter, and blue filter, respectively. By comb-ing these three sets of transmittance spectral distribution andthe known backlight, the color coordinates of the three pri-mary colors of the red, green, blue, and white field are all thesame, and the light efficiency reaches the maximum.

Through the proposed method, the transmittance opti-mization spectral distribution of any known backlight ofthe three primary color filters can be solved. Taking the spec-tral distribution shown in Figure 7(a) as an example, usingNTSC color gamut standard, the abscissa is taken as the

wavelength length, and the ordinate is taken as the relativespectral intensity to calculate the relative intensity of RGB tri-color at the corresponding wavelength. Finally, the transmis-sion spectrum line of the three primary color filters isoptimized, and the results are shown in Figures 7(b)–7(d).The final light efficiency is 197.1 lm/W.

If the backlight spectrum is the result shown in Figure 6,the corresponding optimized transmittance distribution ofthe filter can also be obtained. The result is shown inFigures 8(a)–8(c).

Since the energy of the optimized backlight spectrumshown in Figure 6 is concentrated in some narrow bandwidths,the energy of the backlight can be retained to the maximum ifthe transmittance of the color filter at the corresponding wave-length is in a high-pass state. The light efficiency of the overallmodule can reach to the theoretical limit value of 335.5 lm/W.Compared with the common backlight, the loss of the lightenergy caused by the filter is smaller and easier to achieve.

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CFr

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CFb

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(d) The blue channel

Figure 7: The optimization results of transmission spectrum line of the three primary color filter.

8 Wireless Communications and Mobile Computing

4. Analysis of the Backlight Optimization Model

According to the metamerism in colorimetry, the optimiza-tion of any color light spectrum and the LCD backlight spec-trum can be achieved by constructing linear programmingequations. However, from the simulation results, the spec-trum with the theoretical maximum light effect has the char-acteristic of pulsed distribution. Since the liquid crystaldisplays is commonly used in the traditional LCD backlightsource, the spectrum is difficult to approach the theoreticallimit in practical applications. Then, the characteristics ofthe optimal spectral distribution of monochromatic light willbe discussed. Combined with the new quantum dot backlighttechnology, the optimization of the spectrum in the applica-tion of improving the display backlight will also be discussed.

4.1. Characteristic of Optimization of Primary Colors.According to the aforementioned algorithm, any color lightwith known color coordinates can be optimized. Via the sim-ulation of many colored lights, the distribution characteris-tics of the optimized spectrum of monochromatic light canbe found. For a fixed color coordinate, the spectral distribu-tion with the greatest light effect is often concentrated intwo segments or a very narrow range, showing a pulse-likedistribution. The power of the remaining wavelengths is zero.These wavelengths of zero value mean that they areineffective or less effective to a given color coordinate.Therefore, the optimized backlight spectrum should avoidletting the power distribute at these wavelengths for reducingthe waste of the light energy. The feature of the pulseddistribution simplifies the process of the optimized spectrum.Therefore, the wavelength and the relative intensity of thepulse can be used to determine an optimized spectrumdistribution. In Figures 9(a)–9(c), the pulse wavelength and

the relative intensity of the optimized spectrum of threeprimary colors under the NTSC standard in Figure 5 is anno-tated, respectively.

It can be seen from Figure 9 that the optimized spectrumfor color coordinates (0.67, 0.33) (NTSC standard red) con-tains a main peak at 611 nm. The optimized spectrum forcolor coordinates (0.21, 0.71) (NTSC standard green) con-tains a main peak at 538 nm and a secondary peak at454 nm, where the intensity is 13.0% of the main peak. Thecolor coordinate (0.14, 0.08) (NTSC standard blue) opti-mized spectrum contains a main peak at 460nm and a sec-ondary peak at 521nm where the intensity is 30.2% of themain peak. These wavelengths of the main peaks are closeto the optimization results obtained by Senfar Wen, accord-ing to the color difference statistical algorithm [28, 29].

The wavelength positions and relative intensities of themain and secondary peaks of the optimized spectra vary withthe color gamut. According to the algorithm discussed above,for any given gamut standard, the characteristic peak posi-tion of each primary color can be obtained. In the actualapplication, the backlight spectrum should be adjusted tothe corresponding main and secondary peak positions, andthe relative intensity should be maintained to continuouslyapproach the theoretically optimized spectrum. Eventually,the light efficiency of the backlight can be improved whenthe color gamut is unchanged.

4.2. Optimization of the Quantum Dots. As for the optimizedspectrum characteristics of the pulsed distribution, the tradi-tional broad spectrum light source is difficult to achieve. Inaddition to lasers, new quantum dot materials offer great pos-sibilities for approaching the ideal spectrum. As for fitting theideal backlight, quantum dot materials should be used tomeet the wavelength of the primary and secondary peaks in

380 480 580 680 780Wavelength (nm)

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(a) The red channel

380 480 580 680 780Wavelength (nm)

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CFg

(b) The green channel

380 480 580 680 780Wavelength (nm)

0%20%40%60%80%

100%Tr

ansm

ittan

ce

CFb

(c) The blue channel

Figure 8: The result of filter transmittance lines for optimizing backlight spectrum.

9Wireless Communications and Mobile Computing

the optimized spectrum. The relative intensity of each pri-mary color can be controlled by changing the concentrationof the quantum dot materials. However, even for quantumdot materials, the spectrum is not strictly in the pulse distri-bution. In the mathematical model, Gaussian distributioncan be used to simulate the spectrum [30, 31]. Equation(15) is given as follows:

ΦQD λð Þ = e−ln 2 λ−λpð Þ/dð Þ2 : ð15Þ

In which, λp represents the center wavelength of thequantum dot spectrum, and d represents the half-wavewidth. In order to study the approximation degree of fittingand optimizing backlight by using quantum dot materials,under the NTSC green standard, the simulation results isshown in Figure 10.

The results show that the position and relative intensityof the main and secondary peaks are consistent with the idealspectrum. The half-wave width of the main peak is 3 nm, andthe secondary peak is 1 nm. The actual color coordinates of

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Figure 10: The simulation spectrum of the quantum dot backlight.

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NTSC_red (0.67, 0.33), 𝜂 = 330.7440 lm/W

611 nm

(a) The red channel

NTSC_green (0.21, 0.71), 𝜂 = 612.99 lm/W

538 nm

454 nm,13%

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NTSC_blue (0.14, 0.08), 𝜂 = 101.87 lm/W

456 nm

521 nm,30.2%

(c) The blue channel

Figure 9: The wavelength and relative intensity of the optimized spectral distribution of the NTSC standard.

10 Wireless Communications and Mobile Computing

the simulated waveform are (0.21, 0.71), and the luminousefficiency is 610.8 lm/W. The simulated waveform almostcoincides with the ideal waveform. The luminous efficiencyis improved on the premise that the green color coordinateremains unchanged, showing the importance of the positionof the main peak of the spectrum. However, the half-wavewidth of the actual quantum dot material is wider than thesimulation one. The excessively wide spectral distributionwill not only generate unnecessary energy consumptionbut also affect the reproduction of the target color.Figures 11(a) and 11(b) show the variation curves of theluminous efficiency and the chromatic aberration with half-wave width, respectively. The chromatic aberration is charac-terized by the distance between two color coordinate points,i.e., Δu′v′, under the CIE-1976 u′v′ color space.

It can be seen from Figure 11 that as the half-wave widthof the quantum dot material increases, the chromatic aberra-tion of the fitted waveform continues to increase, and thelight efficiency continues to decrease. In order to correct theerror caused by the half-wave width, it is necessary to furtheradjust and optimize the primary and secondary positions ofthe waveform on the basis of the original waveform.

5. Conclusion and Future Work

In summary, based on the aforementioned results, using themetamerism of the human visual system, this paper proposesa linear programming-based algorithm for optimization ofthe backlight spectrum within the range of any given displaysystem color gamut. On the premise of keeping the colorgamut of the display system, the maximum theoretical lumi-nous efficiency of the backlight is calculated by the proposedalgorithm. The simulation results provide a design referenceand characteristic standard for the future low-power display.At the same time, this paper shows that the utilization ofnarrow-bandwidth light sources such as lasers and quantumdot materials can make it easier to approach the maximumvalue of theoretical light efficiency. Besides, as the bandwidthof the nonideal backlight source increases, the positions ofthe primary and secondary peaks of the original optimizedwaveform may shift. Therefore, the next research can be

focused on optimization of the algorithm by using the spe-cific material. In addition, it needs to be further consideredthat the Gaussian function spectral distribution characteris-tics should be combined in the spectral distribution optimi-zation design. At the same time, by reasonably changingsome parameters and constraints in the metamerism equa-tion, targeted simulation optimization is realized, and theerror is continuously reduced.

Data Availability

The data in this paper are valid and available from the corre-sponding author.

Conflicts of Interest

This paper does not contain any conflict of interest.

Acknowledgments

The study is supported by the National Natural Science Foun-dation of China (61601208) and the Industry-university-research cooperation project of Jiangsu Province (Grant No.BY2018139).

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