Real surface color gamut as the input

The input color gamut is replaced with real surface color gamut which was introduced in section 2.4.2. Similar to last section, the results from fulfilling of the three criteria will be shown separately.

4.2.1 Maximum white point luminance

For a real surface color gamut, the white point C decided by the maximum luminance and relative ratio of each primary is the starting point for defining the color gamut of a display.

Using the measured database and Eq. (2-22), the white point of illuminance C can be achieved by different combinations of relative luminance setting. The varied Yc was applied to Eq.

(2-22), and plotted curve, as shown in Fig. 4-10, was resulted. Each vertical line in the diagram is under the white point requirement, e.g. when the relative luminance sets at vertical line 1, which Yc=0.19 Yr=0.295, Yg=0.447, and Yb=0.068, the mixing result will agree with the illuminance C white point coordinates. It is also noticed that the LED backlight reduces to three primaries for the cases of Yc= 0 and 0.62. Because Yc is the luminance of comprises of blue and green spectral components, the required luminance of blue and green primaries decrease as Yc increases. On the other hand, the required luminance of red primary is increased with Yc. Therefore, the varied Yc lies on the range of two boundaries.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

X: 0.62 Y: 0.003176

Yc

Luminance

Yg

Yb Yr Vertical Line1

Fig. 4-10. Plots of luminances Yr, Yg, and Yb as functions of Yc under the white point requirement

In addition, if considered the available luminance ratio of each LED at the white point C, the luminance ratios as functions of Yc are shown in Fig. 4-11 by Eqs. (2-22) and (2-23).The minimum ratio of 0.96 at Yc=0.19 is the maximum efficiency ηmax defined by Eq. (2-23).

Besides, the designed efficiency of four LEDs, η, is plotted in Fig. 4-12 by applying the varied Yc to Eq. (2-23) for the comparison. As shown in Fig. 4-12, the maximum efficiency ηmax of 0.9598 at Yc=0.19 can be derived. Thus, the initial four-primary color gamut with maximum white point luminance requirement is defined, when Yc=0.19 Yr=0.295, Yg=0.447, and Yb=0.068, respectively.

0 0.1 0.2 0.3 0.4 0.5 0.6

under the white point requirement

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 4-12. The available LED efficiency plotted against Yc under real surface gamut input

4.2.2 Maximum four-primary CGV

The maximum CGV of four-primary display was also considered in Wen’s method. The

0.0 0.1 0.2 0.3 0.4 0.5 1.55x10⁶

1.60x10⁶ 1.64x10⁶ 1.68x10⁶ 1.72x10⁶

Four-primar CGV

(

3

)

Yc

Max CGV

color gamut volume was calculated in CIELAB color space by Eq. (2-20) with varied Yc

value, as shown in Fig. 4-13. The maximum gamut volume of 1.69×10⁶ at Yc=0.25 can be derived. The maximum four-primary CGV with white point requirement is defined, when Yc=0.25, Yr=0.299, Yg=0.385, and Yb=0.066, respectively.

Fig. 4-13. The four-primary CGV plotted against Yc under the real surface gamut input

4.2.3 Maximum input CGV intersection

According to the design flow of proposed method in Fig. 2-7, the initial four-primary CGV was achieved by fulfilling of the maximum white point luminance requirement. In addition, the initial four-primary CGV with different relative luminance setting was compared with the input gamut. The intersectional CGV of four-primary LED backlight and real surface color gamut was also derived by Eq. (2-20). Then, the intersectional CGV plotted against the shifted Yc value is shown in Fig. 4-14. Obviously, the maximum value is achieved when Yc

from the initial value shift from 0.19 to 0.07. By using Eq. (2-22), the relative luminances are Yc=0.07, Yr=0.287, Yg=0.57, and Yb=0.072, respectively.

-2 -1 0 1 2 3 4 5.5x10⁵

6.0x10⁵ 6.5x10⁵ 7.0x10⁵ 7.5x10⁵ 8.0x10⁵

Intersectional CGV

Yc shifted value

shift 1.2

Max Intersection

Fig. 4-14. Plot of intersectional CGV as a function of the shifted Yc value under real surface gamut input

The 3D CGV visualization of initial four-primary and real surface color gamut were presented in CIELAB color space by q-hull algorithm simulation for the observation, as shown in Figs. 4-15 and 4-16. Besides, the intersectional CGV visualization by combining the two color gamuts is shown in Fig. 4-17 from which some part of real surface color gamut is not included in the four-primary color gamut.

Fig. 4-15. 3D visualization of four-primary gamut in CIELAB color space with different angle of (a) top and (b) side view

(a) (b)

Fig. 4-16. 3D visualization of real surface color gamut in CIELAB color space with different angle of (a) top and (b) side view

Fig. 4-17. 3D CGV Intersection of four-primary gamut and real surface color gamut

4.2.4 Summary

With the real surface color gamut as input, the three criteria are performed by the value setting shown in Table 4-4. The relative luminance of each primary and the digital level setting were listed. In addition, for the convenient comparison, the curves based on three criteria are plotted in Fig. 4-18.

Real surface gamut

Four-primary gamut (a)

CGV=8.57+e6 (b)

1.54x10⁶

Table 4-4 The relative luminance setting of each criterion with real surface gamut input

Yr Yg Yb Yc

Ratio 0.295 0.447 0.068 0.19

Level 255 252 230 218

Ratio 0.299 0.385 0.066 0.25

Level 225 190 195 255

Ratio 0.287 0.57 0.072 0.07

Level 197 255 195 58

Relative luminance

Fig. 4-18. Efficiency, four-primary CGV, and the intersectional CGV plotted against Yc for comparison with real surface gamut input

As shown in Table 4-5, the comparisons of computed data are based on three criteria including the maximum efficiency, four-primary CGV, and intersectional CGV. The first row

is 0.96, the four-primary CGV is about 1.684 x 10⁶, and the intersectional CGV is about 91.5

% of real surface CGV. Besides, the second row fulfills the maximum CGV requirement at Yc=0.25, the maximum efficiency is 0.84, the four-primary CGV is about 1.865 x 10⁶, and the intersectional CGV was about 90.9% of real surface CGV. Furthermore, the third row fulfills the maximum intersection CGV requirement at Yc=0.07, the maximum efficiency is 0.76, the four-primary CGV is about 1.646 x 10⁶, and the intersectional CGV was about 92.1 % of real surface CGV. Obviously, each criterion has the largest value, which will be discussed in next section.

Table 4-5 The compared results of each criterion

TEST INPUT Criteria Used Yc η_max Four-primary CGV (ΔΕ_ab³)

Intersectional CGV (with test input ) Max White Point

Luminance 0.19 0.96 1.685x10⁶ 91.5% Input CGV Max CGV 0.25 0.84 1.690x10⁶ 90.9 % Input CGV The Proposed

Design 0.07 0.76 1.646x10⁶ 92.1% Input CGV

"Real Surface Color "

With the three criteria setting, the LED backlight was set to achieve the white point illuminance C and measured the color difference. As shown in Table 4-6, the measured color

difference in Δu’v’ is lower than the minimum perceptible limit. Consequently, the designed relative luminance is also acceptable.

Table 4-6 The color difference with the reference white C in CIE 1976 UCS diagram of each criterion