Illustrating the Helmholtz-Kohlrausch effect of quantum dots enhanced LCD through a comparative study

JI Hong-lei，CHENG Shang-jun，LI Peng-fei ，ZHANG Yan，GE Zi-yi，ZHONG Hai-zheng

（1. Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201；2. University of Chinese Academy of Sciences, Beijing 100049；3. School of Materials Science & Engineering, Beijing Institute of Technology, Beijing 100081；4. R & D Center, TCL Electronics Co., Ltd., Shenzhen 518000, China；5. Ningbo Excite Technology Co., Ltd., Ningbo 315000, China）

Abstract: Helmholtz-Kohlrausch effect (H-K effect) describes the influence of color purity on the perceived brightness of a colored object. Quantum dots (QD) based backlights can enhance the color quality of Liquid Crystal Display (LCD) with improved perceived brightness due to the well-known H-K effect. However, the H-K effect of QD embedded TVs (also known as QLED TV) has not been fully demonstrated. In this paper,we investigated the H-K effect of QLED TVs through a comparative study between QLED backlights and YAG-LED backlights. By comparing the viewers’ experimental results with the Kaiser and Nayatani model,we demonstrate that a QLED TV shows significant H-K effect. To achieve the same perceived brightness with YAG-LED TV, the physical brightness of QLED TV was greatly decreased to 75% for pure red, 86%for pure green, and 74%-88% for bright colorful images. Moreover, QLED TVs are strongly preferred over YAG-LED TVs even when both QLED TV and YAG-LED TV show the same perceived brightness. The results imply the bright future of QLED TVs toward healthly displays.

Key words: QLED TV; Helmholtz-Kohlrausch effect; perceived brightness; display; colority

1 Introduction

The display is an important technology for information communication. Display technology has developed well in the past 20 years. As a key parameter for describing the performance of display screens, color gamut represents the largest range of colors that a screen can display, which was defined by the International Commission on Illumination(CIE) in 1931. The colored triangle in the color space is the gamut limit of a screen[1]. The National Television System Committee (NTSC) is one of the standard color gamuts, which indicates the subset of all colors that should be generated[2]. The color gamut of conventional Liquid Crystal Display(LCD) with LED backlight is usually less than 70%NTSC because of the broad emission of Yttrium Aluminum Garnet (YAG) phosphor[3-4]. Quantum Dots (QDs) are nanoscale semiconductor crystals with narrow-band emission, tunable color and high quantum yields, which can improve the color quality of LCD displays[5-7]. The color gamut of QD embedded TVs (also known as QLED TVs) can reach up to 120% NTSC[8-13]. In 2013, Sony[14]and QD Vision first showed QLED TVs at the Consumer Electronics Show (CES). Later on, many companies launched their own QLED TV products[15-17], including TCL, Samsung, Hisense, etc. In 2020, more than 10 million QLED TVs were sold. In comparison with the rapid commercialization of QLED TV products, the investigation of their color performance lagged off.

The Helmholtz-Kollosch effect (H-K effect)refers to the phenomenon that the perceived brightness of color increases with the increase of color purity[18-20]. Tsujimura et al. showed that the H-K effect is involved in OLEDs[21]and a similar phenomenon has been reported in LED projectors[22-23].Although it is expected that QLED TVs have a more significant H-K effect[24-25], the H-K effect of QLED TV has not been comprehensively studied. In this paper, we investigated the H-K effect of QLED TV through a comparative study between QLED backlights and YAG-LED backlights. By comparing the results of an observational study with the Kaiser and Nayatani model, we illustrated the influence of color gamut on the perceived brightness of QLED TVs.

2 Models for calculating the H-K effect

According to the literature, perceived brightness (the sensation) does not always vary linearly with luminance[26]. Luminance is a measurable physical concept, while the perceived brightness is affected not only by the light source itself, but also by the viewing environment and the psychological factors of the viewer. Helmholtz defines color purity (%P) which can be expressed in the following equation:

whereNis the location of the white reference point,Sis the color point being evaluated, andDWis the dominant wavelength. For different colors with the same dominant wavelength, the brightness/luminance ratio (B/L ratio) increases with an increase in color purity%P[18]. The H-K effect reveals the relationship between brightness and chroma, and was theoretically described by Dowling and Nayatani et al..

2.1 Kaiser model

In 1986, Kaiser summarized the experimental results[27-29]and proposed the Kaiser model[30]. In the Kaiser model, two terms have influence on brightness: a color component (F) and the luminance component log (Y). The equations are as follows:

whereL**is the perceived brightness,x,yare the CIE 1931 color coordinates. When the perceived brightness of the two screens is the same, theRBratio of the physical brightnesses can be expressed as equations (4)～(5):

whereY2/Y1is the measured value,is the theoretically calculated value.RBrepresents the luminance ratio of the two screens when their perceived brightness are the same.F1andF2can be calculated by the color coordinates.Y1andY2represent the luminance of the two screens when their brightness is the same.

2.2 Nayatani model

The Kaiser model describes the relationship between perceived brightness and color purity without considering the influence of the environment. Nayatani proposed a mathematical model to calculate the H-K effect in 1991 and further improved it in 1997. Nayatani showed that the model should not only consider the light itself, but also consider the influence of the environment[31-32]. The H-K effect was described by using equation (6):

whereLis the luminance of the test chromatic light,andLeqis the equivalent luminance of the reference white light.

wherev′andu′are the CIE 1976v′andu′chromaticity transformed form chromaticity (x,y) of the test chromatic light, andv′candu′care thev′andu′chromaticity of the reference white light.

whereLais adapting luminance of the environment.KBris a coefficient for specifying the adapting-luminance dependency of the H-K effect.

In equation (10),suvis the metric saturation of test chromatic light withx,y. The Nayatani model considers the luminances of both the light source and the environment. The γVACcan be regarded as the B/L ratio. The viewer’s brightness perception experiment is carried out according to the above two models, and the calculation results were discussed with a comparison of that against the experimental results.

3 Experimental section

In our work, a TCL 55F8 (YAG TV) and a TCL 55C715 (QLED TV) were selected for testing.For simulating normal indoor lighting conditions,we created a lighting environment of around 150 lx in a darkroom. Twelve viewers were invited for the test, of which 8 were men and 4 were women of ages 20?35 years. The visual acuity (or corrected visual acuity) of all volunteers was greater than 1.0,with no color blindness or color weakness. The specific experimental environment referred to GY/T134'The method of the subjective assessment of the quality of digital television picture'[33], as shown in Table 1.

Tab. 1 Key parameters of test environment表1 測試環境參數

3.1 Solid color experiment

Figure 1(a) shows the schematic diagram of the solid color experiment. The QLED TV and YAG TV were placed in the same horizontal plane and the viewing angle is kept the same for both of the TVs.Three colors R, G, B were emitted through the same HDMI source. The luminance of the QLED TV was adjusted by the viewers to match the perceived brightness of the YAG TV. Based on the measured luminance of the QLED TV and the YAG TV, the perceived brightness QD/YAG ratio was calculated.

Fig. 1 (a)Schematic diagram for the solid color experiment; (b) schematic diagram for the multicolor experiment圖1 （a）純色實驗測試示意圖；（b）彩色實驗測試示意圖

3.2 Multicolor experiments

We selected two groups of pictures for the test.Group I contained colorful pictures with red flowers and green leaves. Group II had plain pictures with a field and a portrait.

To avoid variation in the chip, we used a modified TV to display different color gamuts as shown in Figure 1(b). The edge-lit TV used separated light guide plate and the optics film from the middle to realize different color gamut on the left and right.The luminance on the left and right side can be adjusted by controlling DC sources. For the same viewers, the luminance of the YAG TV was adjusted to get the same perceived brightness on both the QLED TV and YAG TV.

3.3 Subjective preference experiment

Twenty observers were invited for a subjective preference experiment with 10 test pictures that are symmetric or nearly symmetric. The experiment was carried out under 200 nit, 270 nit and 350 nit perceived brightnesses (the measured luminance was different).

4 Results and discussion

4.1 Results and discussion of solid color experiment

Figure 2(a) (color online) shows the emission spectra of the QLED and YAG-LED TVs. The yellow and blue lines represent the white spectrum of the QLED and YAG TVs. The Full Width at Half-Maximum (FWHM) of the QLED TV is about 27 nm for green emission and 26 nm for red emission,which is much narrower than that of the YAG TV.Figure 2(b) (color online) shows the color gamut of QLED TV and YAG TV, indicating that the color gamut of the QLED TV is higher. The white color coordinates of the QLED TV and the YAG TV are consistent.

Fig. 2 (a)White light spectrum and (b) color gamut of QLED TV and YAG-LED TV圖2 量子點電視與YAG電視的（a）白光光譜及（b）色域圖

Figure 3 (color online) shows the measured and calculated brightness ratio (QD/YAG) under different luminances. The dots represent the measured values, the black dotted lines represent the average measured values, the green and blue dotted lines represent the theoretical values calculated according to the Kaiser model and the Nayatani model respectively. The smaller QD/YAG ratio represents the more significant H-K effect. Since the blue light of both the QLED and YAG TVs generated by the GaN chip, the blue light perception only shows a slight difference. In this work, we focus on the H-K effect of red light and green light. It can be seen that the measured average values of red and green are 0.75±0.04 and 0.86±0.04, indicating that the H-K effect of a QLED TV is very significant, in particular for red. By comparing the calculated values based on the Kaiser model and the Nayatani model,the Nayatani model of red is consistent with the measured values, while the Kaiser model in green is consistent with the measured values.The measured values were different from the theoretical values,which may be explained by the differences of individual viewers as well as the test environment. The perceptual differences may be due to the color perception ability differences of different people[34].

Fig. 3 Comparison of theoretical calculation results and measured values of brightness ratio (QD/YAG) in solid color experiment圖3 純色實驗QD/YAG的理論值與實測值對比

4.2 Results and discussion of multicolor experiments

To study the H-K effect of QLED TV, two groups of test pictures were applied for further comparison. Group I consists of colorful pictures with red flowers and green leaves. Group II has plain pictures with fields and portraits.

Figure 4 (color online) shows the QD/YAG of colorful and plain pictures under different luminances. The red and green dashed lines represent the QD/YAG of red flowers and green leaves, the purple and yellow dashed lines represent the QD/YAG of portrait and field. The results show that the H-K effect becomes weaker and flattens in the range of 200 nit to 500 nit for colorful images. The H-K effect of colorful images is more pronounced than that of plain images, and the smallest QD/YAG of red images can reach 0.74. For plain pictures,QLED TV and YAG TV have the same color performance. These results indicate that the display of colorful pictures in a QLED TV creates more acute perception for brightness.

Fig. 4 The curves of QD/YAG of different pictures in multicolor experiment圖4 彩色實驗不同圖片QD/YAG實測值對比曲線

4.3 Subjective preference experiment

We further carried out the subjective preference experiment. Figure 5 (color online) shows the results of viewers' preference ratio for the QLED TV and the YAG TV under the same perceived brightness. The experimental results show that, under the same perceived brightness, the QLED TV is generally preferred. The proportions of subjects who preferred QLED TV at 200 nit, 270 nit and 350 nit are 54.3%, 55.0% and 58.0%, respectively.Even though the perceived brightness of the QLED TV and the YAG TV were kept the same, the viewers still preferred the QLED TV. The QLED TV had a great advantage in red and green pictures. As many as 73.8% of subjects preferred the QLED TV when its luminance was 350 nit, while YAG TV had an advantage in blue and yellow pictures. As luminance increased, the preference for the QLED TV grew. In addition, the preference results were not affected by the genders of the subjects.

Fig. 5 Preferential ratio under the same perceived brightness圖5 相同感知亮度下的主觀喜好比例

5 Conclusion

In conclusion, we investigated the H-K effect of a QLED TV through a comparative study between QLED backlights and YAG-LED backlights. The results of the solid color experiment were analyzed by considering the Kaiser model and the Nayatani model. The influence of color gamut on perceived brightness and subjective preference was discussed based on the experimental results of multicolor tests. The results indicated that the QLED TV exhibits significant H-K effect, and the perceived brightness was significantly higher than that for the YAG TV. Under the same perceived brightness, the average measured brightness ratio QD/YAG for red and green were 0.75±0.05 and 0.86±0.04. The minimum brightness ratio QD/YAG of colorful pictures was 0.74. Under the same perceived brightness, the QLED TV with a higher color gamut was more popular, and that preference grows strong as the brightness increases. Under the same perceived brightness, the QLED TV is not only less luminant, but also more popular with viewers. This conclusion is of significant importance for developing healthier LCD screens[35].

In addition, it is worth noting that China's LCD industry has become the world's largest, accounting for 70% of the world's LCD output in 2020.Quantum dots backlight technology is the core technology of the extended LCD industry[36-37]. This study provides a theoretical basis for the popularization of quantum dots technology.

——中文對照版——

1 引 言

顯示技術是信息交互的重要媒介，過去的20年中，顯示技術層出不窮。色域是影響顯示器色彩表現的關鍵指標，也是消費者選擇產品時的首要考慮因素，它代表顯示器所能展現的最大色彩范圍。1931年，國際照明委員會（International Commission on Illumination，CIE）首次定義了色彩空間，紅綠藍三基色對應色點所圍成的三角形代表顯示器的色域，其面積越大，即色域越高，可顯示 的 色 彩 越 多[1]。NTSC（National Television Standards Committee）是美國國家電視標準委員會制定的高清電視顯示標準[2]。傳統的液晶顯示器（LCD）大多使用基于YAG熒光粉的白光LED作為背光源，白光LED光譜是決定顯示色域的主要因素，使用YAG-LED的液晶顯示器的色域一般小于70% NTSC[3-4]。量子點是納米尺寸的半導體晶體，具有發光波長窄、顏色可調、量子產率高等特點[5-7]，可顯著提升顯示的色彩品質，搭載量子點背光的液晶顯示器色域高達120%NTSC[8-13]。2013年，SONY[14]和QD Vision公司率先在國際消費電子展（CES）展出了搭載量子點背光技術的液晶電視（量子點電視，QLED），隨后，TCL、三星、海信等廠商也紛紛推出了量子點電視[15-17]，2020年，量子點電視的銷量已經超過千萬臺。

亥姆霍茲-科爾勞施效應（簡稱H-K效應）指的是人眼對色光的感知亮度隨著色純度的增加而提升的現象[18-20]，是表征顯示器件色彩特性的重要特征。柯達OLED研發部的Tsujimura等人報道了有機發光二極管（OLED）中的H-K效應[21]，Liao等人報道了LED投影儀中的H-K效應[22-23]。盡管人們很早就預測量子點電視擁有更顯著的H-K效應[24-25]，然而尚沒有針對量子點電視H-K效應研究的報道。本論文通過觀看者亮度感知實驗，對比了YAG熒光粉白光LED背光電視（YAG電視）和量子點電視的H-K效應差異，根據Kaiser模型與Nayatani模型分析純色實驗的測試結果，并通過彩色實驗探究了顯示器的色域對感知亮度與主觀偏好的影響。

2 H-K效應理論與數學模型

在顯示領域，物理亮度（Luminance）和感知亮度（Brightness）的概念有所不同，物理亮度是一個可測量的物理概念，不考慮人眼的感知，而感知亮度不僅受到光源自身影響，還受到觀看環境、觀看者的心理因素等影響[26]。Helmholtz定義了色純度（%P）：

式中，S是評估色點，N是白點的色坐標位置，DW是主波長。對于主波長相同的不同色點，其色純度%P越高，感知亮度/物理亮度（B/L值）越高[18]。H-K效應揭示了亮度與色度之間的關系，為了更好地量化此效應，Dowling與Nayatani等人提出了不同的數學模型來描述H-K效應。

2.1 Kaiser模型

Kaiser等人基于實驗結果，提出了Kaiser模型[27-30]。感知亮度L**主要受兩個因素影響，即顏色分量F和物理亮度分量log(Y)。其公式表示如下：

其中，Y表示顏色的物理亮度，x，y為顏色的CIE 1931色坐標。當兩塊物理亮度不同的屏幕（Y1與Y2）具有相同的感知亮度時，其物理亮度比值被稱為感知相對亮度，用RB表示，RB如式（5）所示：

其中，Y2/Y1為實測值，為理論計算值。RB表示感知亮度相同的情況下，兩塊屏幕物理量度的比值。實驗中，F1與F2可通過色坐標求得，進而得出理論計算值；通過調節兩塊屏幕的亮度使二者的感知亮度相同，再測量實際屏幕的物理亮度可得到Y1與Y2，進而可求得RB。

2.2 Nayatani模型

1991年，Nayatani提出計算H-K效應的數學模型，并在1997年進一步完善，Nayatani認為，模型不僅需要考慮待測光本身，還需要考慮環境的影響[31-32]。本實驗在Nayatani模型的基礎上，提出H-K效應的計算模型：

式中γVAC用于衡量待測光的H-K效應，Leq是與測試光感知亮度相同的白光物理亮度，L是測試光的物理亮度。

式中v′與u′為待測光在CIEUV空間中的色坐標，可由x，y轉換得到，vc′與uc′為白光在CIEUV空間中的色坐標。

式中La為環境亮度。

綜上，Nayatani模型通過測定環境光、待測光與參考光的參數，獲得γVAC值。本論文根據上述兩種模型開展了觀看者亮度感知實驗，通過實驗測試結果與模型計算結果的對比，分析了量子點電視的H-K效應。

3 實驗部分

選取TCL 55F8（YAG電視）和TCL 55C715（量子點電視）做為樣機，分別代表普通LCD電視和量子點LCD電視。為了模擬客廳使用環境，在暗室中創建了150 lx左右的光照環境。邀請11名觀看者參加測試，年齡在20～35歲之間。所有觀看者的視力（或矯正視力）均大于1.0，無色盲和色弱。具體實驗環境參照GY/T134 《數字電視圖像質量主觀評價方法》[33]，如表1所示。

3.1 純色實驗

純色實驗場景如圖1（a）所示，將量子點電視和YAG電視置于同一水平桌面上，使觀看者處于兩臺電視機的中垂線上，且與兩臺電視機視角一致。采用相同的HDMI信源，依次輸入R、G、B3個純色畫面。固定YAG電視的亮度不變，觀看者通過調試量子點電視亮度使其與YAG電視的感知亮度一致，并同時實測量子點電視和YAG電視的物理亮度，二者的物理亮度之比用“QD/YAG”表示。

3.2 彩色實驗

在純色實驗的基礎上，將畫面替換為兩組彩色畫面。一組為鮮艷畫面：紅花與綠葉；一組為平淡畫面：田野與人像。為了便于觀測者觀察，所有試驗圖片均為軸對稱圖形。

為了去除機芯對畫質的影響，展示不同畫質的電視機必須保持機芯統一。本實驗采用兩臺TCL 65C8（側入式機型），分別做以下改裝：（1）導光板從中間一分為二，量子點膜只保留左半邊，左邊均采用藍色LED燈條；右邊采用YAG燈條；為了防止左右兩邊光互相干擾，導光板分界線處貼有導光板側面反射膜。（2）燈條通過直流源供電，以實現左右兩邊亮度不一致；（3）樣機在顯示白場畫面時，確保左右兩邊白場色點、色溫一致。改裝好的樣機與測試示意圖如圖1（b）所示。調節量子點電視燈條的電流，使之可以處于200 nit、300 nit、400 nit、500 nit任意檔位，觀看者調節YAG電視燈條的電流使其感知亮度與量子點電視相同，測量YAG電視的物理亮度，計算QD/YAG值。

3.3 主觀喜好實驗

邀請20名觀看者進行測試，使用賣場宣傳視頻的10幅截圖，所有圖形均為左右對稱或接近左右對稱。進行200 nit、270 nit和350 nit等感知亮度（實測亮度不一樣）下的喜好實驗。

4 結果與討論

4.1 純色實驗結果與討論

兩臺樣機的白場色點保持一致，圖2（a）（彩圖見期刊電子版）給出了兩臺樣機的光譜圖，黃線與藍線分別表示量子點電視與YAG電視的白光光譜，量子點電視的光譜半峰寬更窄；圖2（b）（彩圖見期刊電子版）給出了兩臺電視機的色域圖，量子點電視的色域更高。

圖3（彩圖見期刊電子版）給出了不同亮度下的QD/YAG實測值與模型計算值，圓點表示實測值，黑色虛線表示實測值平均值，綠色虛線與藍色虛線分別表示根據Kaiser模型與Nayatani模型計算得到的理論值，理論計算值與實測值越小，HK效應越明顯。由于量子點電視和YAG電視的藍光都是由GaN芯片發出的，藍光感知的差異非常小，本文主要對比了紅光與綠光的H-K效應。從實驗數據可以看出：紅、綠光的實測平均值在分別為0.75±0.045、0.86±0.040，說明量子點電視的H-K效應非常顯著，特別是紅光。通過對比Kaisar模型與Nayatani模型的計算值可知，Nayatani模型在紅色與實測值更吻合，Kaisar模型在綠色與實測值更吻合。實測值與理論值存在差異的原因可能是抽樣總體和實驗設置的不同。Kaiser模型和Nayatani模型基于白種人，而本文的測試結果基于黃種人，人種眼睛的差異可能是造成上述感知差異的主要原因[34]。

4.2 彩色實驗結果與討論

為進一步研究量子點電視的H-K效應，本實驗采用兩組測試畫面做進一步對比研究，一組為鮮艷畫面：紅花與綠葉；一組為平淡畫面：田野與人像。

圖4（彩圖見期刊電子版）給出了不同亮度下彩色與平淡畫面的QD/YAG值，紅色與綠色虛線分別表示紅花與綠葉畫面的QD/YAG值，紫色與黃色虛線分別表示人像與田野的QD/YAG值。結果表明：對于鮮艷畫面，在電視燈條電流由200 nit提升到500 nit的過程中，H-K效應逐漸變弱并趨于平緩，鮮艷畫面的H-K效應比平淡畫面更顯著，紅花圖像的QD/YAG最小值可達0.74。對于平淡畫面，量子點電視與YAG電視的色彩表現能力相當。由上述結果可知：量子點電視對于鮮艷畫面的表現能力更強，給人更加明亮的感覺。

4.3 主觀喜好實驗

研究發現，在純色與彩色實驗中，即使量子點電視與YAG電視的感知亮度相同，同一畫面下，觀看者更加青睞量子點電視，本論文進一步開展了主觀喜好實驗。圖5（彩圖見期刊電子版）給出了相同感知亮度下，觀看者對量子點電視與YAG電視的喜好情況。實驗結果表明：同等感知亮度下，量子點電視總體占優勢，量子點電視在200 nit、270 nit、350 nit的喜好比例分別為54.3%、55.0%、58.0%；這種偏好與性別、與是否為背光行業人員無明顯關系；量子點電視在紅綠畫面具有很大優勢，在量子點電視亮度為350 nit時，紅綠畫面的喜好比例可達73.8%，YAG在藍黃畫面具有優勢；隨著電視亮度的提升，喜好量子點電視的人越來越多。

5 結 論

本論文通過觀看者亮度感知實驗，對比了YAG電視和量子點電視的H-K效應差異，根據Kaiser模型與Nayatani模型分析純色實驗的測試結果，并通過彩色實驗探究了顯示器的色域對感知亮度與主觀偏好的影響。實驗結果表明：量子點電視具有更為顯著的H-K效應，感知亮度明顯高于傳統YAG電視；在同樣的感知亮度下，紅、綠的QD/YAG的實測平均值分別為0.75±0.05、0.86±0.04；鮮艷畫面的QD/YAG最小值可達0.74；在相同感知亮度下，高色域的量子點電視更受歡迎，并且喜好趨勢將隨著亮度的增加而增加。總之，在同等感知亮度下，量子點電視不僅物理亮度低，而且更受用戶喜愛，對于健康顯示的發展具有重要意義[35]。

值得關注的是，中國液晶顯示產業已經位居世界第一，2020年液晶產量占全世界的70%。量子點背光技術是延長液晶產業的核心技術。我國的量子點顯示技術在國際上處于第一集團，在量子點LED領域的核心材料、器件以及集成方面都有了先發優勢[36-37]。此外，TCL、京東方等國內龍頭企業已于2020年發布了基于印刷技術的量子點電致發光顯示技術樣機。本研究為推廣量子點技術提供了理論依據。