Chapter 1 Introduction
1.4 Organization of this thesis
The thesis is organized as followings: The theories of colorimetry and design of color gamut are presented in Chapter 2. Basic colorimetry concepts for presenting CGV are described in this chapter. Additionally, this chapter also represents the criteria of four-primary color gamut design. In Chapter 3, the experiment of four-primary LED backlight platform is introduced in detail. Furthermore, the major instruments used to measure the color data and the simulate method are also described. After that, the experimental results, including the two test input color spaces and the discussions of comparison, are presented in Chapter 4. Finally, the conclusions and future work are given in Chapter 5.
Chapter 2
Principle of Color Gamut Design
The most primitive theory of colorimetric with respect to the CGV representation will be reviewed. Besides, the previous method of four-primary color gamut design will be interpreted briefly as well. Finally, the proposed method and the two test input color gamuts for evaluating the gamut designing methods will be introduced separately.
2.1 Colorimetry
Colorimetry is the science relating color comparison and matching. To describe colors in numbers or to provide the physical or psychophysical color match using a variety of measurement instruments are all about colorimetry. The matching in color of two light stimuli of different spectral power distributions under a given condition of observation can be predicted by using basic colorimetry. Over the years, The CIE has defined a set of standard observers and standard conditions for performing color matching experiments. The color matching functions defined by color matching experiment is the basis of colorimetry. Using this color matching functions, the various color spaces have been developed for denoting colors numerically [19], [20], [21].
A color space is a mathematical multidimensional coordinate system where each dimension corresponds to a color component. Mathematically, a color is a vector in a color space, and the color gamut of a device is the subset of available colors in the color space. A device-dependent color space is one in which the same combination of color values on two
device-independent color space, the same set of tri-stimulus values produces the same visual color on two different devices at the same viewing condition. As mentioned earlier, the color reproduction prefers to perform in the device-independent color spaces. The various device-independent color spaces are introduced in the following section.
2.1.1 CIEXYZ color space
In 1931, the CIE agreed on a device-independent standard color space called CIEXYZ, which was created in the need for describing colors in the mathematical equivalent way. The color was measured with tristimulus filters corresponding to the sensitivities of the receptors in the standard observer. The result was the functions of matching curves fitted to the detected wavelengths, as shown in Fig. 2-1. Then, the integrations of matching function multiplying the object and illumination reflectance were computed as tristimulus values: X, Y and Z.
However, the tristimulus values were virtual tristimulus, and describing color in the three dimensions was not convenient. A derived color space specified by x, y, and Y was known as the CIE xyY color space. As shown in Fig. 2-2, the x and y is the coordinate of specific color on X + Y + Z = 1 plane by using the following equations: [22]
The third coordinate, z, can be omitted by providing Y parameter which is a measure of the luminance of a color. As a result, the chromaticity description of any color by using just two coordinates on the projecting locus of that plane, the CIE xy chromaticity diagram, is
The CIEXYZ system is widely used to specify colors; however, the chromaticity diagram is highly non-uniform. In the CIEXYZ system, a vector of unit magnitude representing the difference between two chromaticties is not uniformly visible [23]. The CIEXYZ is not suitable for judging the color difference. So the CIELUV and CIELAB color spaces were developed for solving this problem.
2.1.2 CIELUV color space
The CIE 1960 u’,v’ (UCS) diagram was the first determined by the linear transformation of Yxy, in an attempt to produce a chromaticity diagrams, in which a vector of unit magnitude difference is equally visible at all colors as shown in Fig 2-3. Y is unchanged from XYZ or Yxy. The non-uniformity is reduced considerably, but the uniform brightness scale is not included.
Fig. 2-21. The volume of visible colors in the CIEXYZ color space, the triangle is on the X + Y + Z = 1 plane
Fig. 2-21. The matching functions fitted to the spectral responses of human eye
Fig. 2-3. The 1976 u’v’ chromaticity diagram and its color difference diagram
Base on the CIE 1960 u’v’ diagram, the CIE developed the CIE 1976 UCS diagram transformed from Yxy and defined the CIE 1976 L*u*v*(CIELUV) space involves the uniform lightness scale. The transform was given by
* 116 16
' 4 chromaticity coordinates of stimulus, the u’n and v’n are the chromaticity coordinates of reference white.
2.1.3 CIELAB color space
The CIE 1976 L*a*b* color space, abbreviated CIELAB, is another uniform color space that transformed from CIEXYZ color space and related to Munsell color system. Three color values L* (lightness), a* (red-green axis), b* (yellow-blue axis) calculated from the CIE tristimulus values. As shown in the follows:
* 116 ( ) 16
where Xn, Yn and Zn are also the tristimulus values for the reference white, and L* ranges from 0 to 100, where 0 is perfect black, and 100 is the reference white.
The counterclockwise angle between the positive a* axis and the vector from the origin to the color is referred to as hue angle. Hue angle hab and chroma C*ab are defined as follows:
*
The CIELAB color difference ΔE*ab between two points is calculated as the Euclidean distance:
*ab ( L*2 a*2 b*2)
ΔΕ = Δ + Δ + Δ (2-10)
Since the CIELAB is the uniform device-independent color space, the color gamut and the gamut mapping process usually represent in the CIELAB space.
2.2 Previous work - Wen’s method
Although many of multi-primary displays were proposed for wider gamut representation, there were only few papers discussed its color gamut design and method. As previous noted, the shape and volume of device gamut will affect the color reproducibility. In addition, the MPDs offer the flexibility to adjust and exhibit possible CGV, and need the constraint to overcome the color conversion. So a previous method for design the relative luminance of four-primary display to decide its color gamut was proposed by Wen [24].
Wen had proposed two criteria to solve this problem, one was the Maximum White Point Luminance (display luminance) requirement, and the other was Maximum CGV requirement.
Both of them were base on the basic white point requirement. A four-primary display was taken an example for showing the methods; it is the same condition with this thesis.
For the maximum white point luminance requirement, first of all, the gamut setting was basically meeting the white point of the choosing system. For conventional three primary displays, the relative luminances of primaries were uniquely determined by the white point of
combination of three primaries; the forward model refers to Eq. (1- 1) can be represented as
and refer to Eq. (1- 2) the relative luminance can be calculated by the backward model:
1
For the four-primary LED display which Wen used, the additive fourth color is yellowish-green, which is denoted in Gy, enlarging the gamut about 130% NTSC in 1931 CIE xy chromaticity diagram and 137% NTSC in CIE 1976 uniform chromaticity scale (UCS) diagram. To achieve the white point, the forward model refers to Eq. (1- 3) as shown following:
As previous noted, the backward model of four-primary in Eq. (2-13) can not be calculated. For solving the linear equations, there must add some constraint to reduce the
column of matrix. As the definition of white point is the equal energy of each primary, it can be achieved by the R=B=G=Gy setting, where the normalized white point luminance is the sum of four primaries, as shown following:
r g b y w 1
Y +Y + +Y Y =Y = (2-14)
where 0≤Y Y Y Yr, , ,g b y ≤1, and Yr, Yg, Yb, Yy are the relative luminances of each primary.
Furthermore, the simple tristimulus derived formula as shown following.
(1 x y)
As Eqs. (2-14) and (2-15) were applied for Eq. (2-13), the basic color conversion can get the backward model of relative luminance of four primaries:
1 that each combination of vertical line agrees with the white point setting, and the combination reduce to three primaries, when Yy at 0 and 0.715.
Fig. 2-4. Luminance Yr, Yg, and Yb plotted against Yy under the white point requirement (S.
Wen, Displays, 26, pp. 171-176, 2005)
In addition, the requirement of the maximum display luminance is taken for a set of available primary luminances. Considering the available luminance of each LED Yrm, Ygm, Ybm, and Yym, the white point is satisfied when the
g gm y ym
r rm b bm
r g b y
a Y a Y
a Y a Y
Y = Y = Y = Y =η (2-17)
, , ,
Max luminance i
0 , , , 1 , , , ,
Max luminance k
r g b y im k
r g b y
where ≤a a a a ≤ Y = i=r g b y
∑
(2-18)In Eq. (2-17), ar, ag, ab, and ay are the turning factor of red, green, blue, and yellowish-green primaries. To meet the maximum efficiency, the desired ηis preferred as large as it can be.
Therefore, the designed maximum efficiency of four LEDs ηmax is defined as
max( )y rm gm bm ym
r g b y
Y Y
Y Y
Y Min
Y Y Y Y
η = ⎧⎪⎨ = = = ⎫⎪⎬
⎪ ⎪
⎩ ⎭ (2-19)
where Min { } is the minimum function. By using Eqs. (2-16) and (2-19), the changed relative luminance of yellowish-green Yy can get the curve plotted in Fig. 2-5 from which the maximum efficiency ηmax of 0.908 at Yy=0.44 can be derived. Thus, the initial four-primary color gamut with maximum white point luminance requirement is defined, when Yy=0.44, Yr=0.3, Yg=0.24, and Yb=0.05, respectively.
Fig. 2-5. Luminance ratios Yrm/Yr, Ygm/Yg, Ybm/Yb, and Yym/Yy plotted against Yy (S. Wen, Displays, 26, pp. 171-176, 2005)
For the maximum CGV requirement, the gamut volume is present in the CIE Lab color space. By matching the white point setting, utilizing Eq. (2-16), the color gamut can be designed by the relative luminances of four-primary. In addition, the CGV can be calculated by the equation:
The color gamut volume is calculated in CIELAB color space when changing Yc value, which is plotted in Fig. 2-6 from which the maximum gamut volume of 1.61×106 at Yy =0.37 can be derived.
Fig. 2-6. The CGV (ΔΕ*ab3) of four-primary display plotted against Yy (S. Wen, Displays, 26, pp. 171-176, 2005)
With these two proposed criteria, the four-primary display gamut can be achieved for its preferred application. Since the two criteria have two different settings, finally, Wen concluded that, in practice, the design of the relative primary luminances may be a compromised result of the two additional requirements. However, the criteria perform the largest CGV and maximum display luminance, but they do not consider the input CGV. So it may be not a suitable design for color reproduction.
2.3 Proposed method
another key factor affecting the display color reproduction performance. Some paper [26]
provides the metrics to judge the gamut volume of display, which depicts that the gamut volume characteristics is judged with the input encoding CGV. With this concept, the proposed new criterion is taking the input color gamut into account, which is the maximum intersectional CGV.
Consequently, this thesis refers to the Wen’s method, with the maximum white point luminance requirement and adds the maximum input CGV intersection requirement. The method of designing the four-primary color gamut for reproducing maximum input encoded color was proposed. It compromised with the efficiency of maximum luminance, and performed the best gamut mapping resulted from input signal.
A four-primary-LED backlight in FS-FC LCDs was constructed to verify the proposed method, will be introduced in next chapter. The four primaries are red, green, blue, and cyan, denoted in R, G, B, and C separately. To meet the white point, the forward model modified from Eq. (2-13) is shown as follows:
w R G B C
The backward model of the relative luminance of four primaries modified from Eq. (2-16) is shown as follows:
1
max( )c rm gm bm cm
r g b c
Y Y Y Y
Y Min
Y Y Y Y
η = ⎧⎪⎨ = = = ⎫⎪⎬
⎪ ⎪
⎩ ⎭ (2-23)
According to the calculated result of Eqs. (2-22) and (2-23), the maximum white point requirement can be achieved by the specific relative luminance of four primaries. The proposed maximum input CGV intersection requirement which is calculating the CGV intersection with input CGV in the CIELAB color space. The test input CGV, the sRGB color space [27] and the “real world surface color” gamut by pointer [28], will be introduced in next section. Then, the 3D color gamut visualization and the intersectional CGV calculating simulation will be introduced in next chapter.
In summary, the design flow of proposed method is shown in Fig. 2-7. First, the measurement data of four-primary color should be made to build a color database. Then, start designing the relative luminance of each primary. The first step is to meet the basic white point requirement by referring to the input color white point. Second, consult with the measurement database, the maximum available ratio also be calculated. With the maximum white point luminance design, the initial four-primary CGV can be determined by the relative luminance setting. Finally, the input CGV is taken to compare with the initial four-primary CGV. The maximum intersectional CGV will be found by shift-adjusting the initial setting. As a result, the new relative luminance setting decides the final four-primary CGV.
Yes Yes
nono
Fig. 2-7. The design flow of proposed method
2.4 Test input color gamuts
For the requirement of maximum input CGV intersection, the test color gamuts here, are the standard RGB (sRGB) color space and the “real world surface color”. The sRGB adopt the HDTV standard and is widely used in most monitor gamut management. Furthermore, the real surface database collected by pointer contains most of the colors that people can see in the real world.
2.4.1 Standard RGB color space (sRGB)
In 1996, Hewlett-Packard and Microsoft proposed a standard color space, sRGB, for the usage on monitors, printers, and the Internet. The aim of this color space was to complement the current color management strategies by enabling a third method of handling color in the operating system and device drivers. The sRGB is a single default color space acting as a bridge provides the good quality and backward compatibility with unambiguous and efficient transmission. Nowadays, the sRGB color space has been standardized by the International Electrotechnical Commission (IEC) as IEC 61966-2-1 in 1999 [29]. Such a standard can dramatically improve the color fidelity in the desktop environment
The three major factors of the sRGB standard are the colorimetric RGB definition, the equivalent gamma value of 2.2 and the well-defined viewing conditions, along with a number of secondary details necessary to enable the clear and unambiguous communication of color.
The sRGB standard used the ITU-R BT.709-2 reference primaries and the CIE standard illuminant D65 reference white. The ITU-R BT.709-2 defined the parameter values of the HDTV standards for production and international program exchange. The primaries and reference white of sRGB standard are given in Table 2-1.
Table 2-1 Parameters of sRGB chromaticties
CIE chromaticities for ITU-R BT.709 reference primaries and CIE standard illuminant
Red Green Blue D65
x 0.6400 0.3000 0.1500 0.3127
y 0.3300 0.6000 0.0600 0.3290
z 0.0300 0.1000 0.7900 0.3583
Additionally, the standard adopted the transfer function (gamma 2.2) of typical CRTs.
Gamma is the non-linearity of the electro-optical radiation transfer function of CRTs; This transfer function describes how much luminance results from voltages applied to the CRT, and often expressed by a mathematical exponential power function parameter.
After defining the parameters of colorimetry, the sRGB color space is designed to match typical home and office viewing conditions rather than the darker environment typically used for commercial color matching. The viewing environment descriptions contain all the necessary information to provide conversions between the standard and target viewing environments, as shown in Table 2-2:
Table 2-2 Parameters of sRGB viewing environment sRGB viewing environment Parameters
Condition sRGB
Luminance level 80 cd/m2
Illuminant White x = 0.3127, y = 0.3291 (D65) Image surround 20% reflectance
Encoding Ambient Illuminance Level 64 lux
Encoding Ambient White Point x = 0.3457, y = 0.3585 (D50) Encoding Viewing Flare 1.0%
Typical Ambient Illuminance Level 200 lux
Typical Ambient White Point x = 0.3457, y = 0.3585 (D50)
2.4.2 Real-world surface colors gamut
In 1980, Pointer published an article titled “the gamut of real surface colours”, which collected 4089 measured surface color patches data enclosing most of the color in the real world. In this article all the data have been calculated using CIE Standard Illuminant C. The color patches contained the follows:
(1) Munsell Color-Cascade (non-fluorescent) (2) Surface color objects measured by Trussel (3) DuPont paint samples
(4) Graphic arts spot colors
As show in Fig. 2-8, the measurement color data was plotted in the CIE1931 xy chromaticity diagram. In addition, the data were converted into CIELAB coordinates, sorted into groups according to the hue angle, hab, and then represented as plots of lightness, L*, as a function of chroma, Cab*. Similar calculations were made using the equivalent CIELUV coordinates. Both of these two coordinates collection used the convex hull, the smallest polygon that enclosed the sets of data to surround all these color data as a real-world surface color gamut.
Fig. 2-8 The Pointer color gamut in CIE xy chromaticity diagram
This thesis used the sRGB and real-world surface color gamut in the CIELAB coordinate as input colors to evaluate the CGV setting of the four-primary LED backlight.
Therefore, through the quantitatively evaluation of two input color gamuts, the four-primary gamut was able to represent the color chart with as much color fidelity as possible.
Chapter 3
Experiment and Simulation
This chapter has been divided into two sections: experiment and simulation. The experiment section includes four-primary-LED backlight platform, measurement equipment, and the measurement data, which will be firstly described for establishing a color database. In the simulation section, the simulation method for evaluating the gamut characteristic will be described.
3.1 Experiment
In this section, a four-primary-LED backlight in FS-FC LCDs has been constructed to verify the proposed method. The related measurement equipment and measurement data would be shown later.
3.1.1 Four-primary-LED backlight platform
The four-primary-LED backlight platform, as shown in Fig. 3-1, was composed of an optical cavity, a constant-current driving board, and a Field-programmable gate array (FPGA) control board. These parts would be introduced separately.
Fig. 3-1. The photo of four-primary-LED backlight platform, which included (a) a optical cavity, (b) a constant-current driving board, and (c) FPGA control signal board
The optical cavity, a sample of LED-Direct-Backlight, which was composed of four high flux LEDs i.e. Luxeon Star LEDs. A set of diffusers were coverd on the four LEDs cavity. The main target was to mix the four-primary colors to obtain the best brightness and color uniformity in the center of the diffusers. The optical cavity and specifications of the selected LEDs from LUMINLEDS Corporation are shown in Fig. 3-2, where the peak wavelengths of red, green, blue, and cyan primaries were 625nm, 530nm, 470nm, and 505nm, respectively.
Optical Cavity Constant-current
Driving Board FPGA Control Board
The constant-current driving board designed to provide the constant current for each LED was expecting for the uniform color mixing result. As shown in Fig. 3-3, the circuit board was divided into four similar parts, and each part deriving one specific LED. The digital switch monitored the current which drives the LEDs, and the digital values were coded on eight bits digital/analog converter (DAC) resulting in 256 digital values. Moreover, the other circuits aided the LED driving IC providing different constant currents by the setting of each digit count.
Fig. 3-3. The photo of constant-current driving board and its description
The FPGA control board produced the time-sequential signal allowing the switching of the driving current for each LED. This board was connected to the electronic driving board.
By the Verilog coding, the digital count and the timing signal has been provided for each LED.
Cyan Part Green Part Blue Part Red Part
Digital Switch 8-bit DAC LED driving IC
3.1.2 Measurement equipment
The instrument used to realize the measurements was the Conoscope, as shown in Fig.
3-4. The Conoscope has different applications: luminance vs. viewing direction, chromaticity
3-4. The Conoscope has different applications: luminance vs. viewing direction, chromaticity