As indicated in the previous section, the 1931 CIE x,y Chromaticity Diagram (or xyY diagram) was inadequate because the two-dimensional diagram failed to give a uniformly-spaced visual representation of what is actually a three-dimensional color space. We can see this problem clearly in the following illustration of the xyY chromaticity diagram:
Fig. 2-7 Nonuniformly-spaced visual representation of CIE x,y Chromaticity Diagram [13]
Each line in the diagram represents a color difference of equal proportion. The distances between the end points of each line segment are perceptually the same according to the 1931 CIE 2° standard observer. As shown in Fig. 2-7, the lines vary in length, sometimes greatly, depending on what part of the diagram they are in. This disparity in line length indicates the amount of distortion between parts of the diagram.
To correct this, a number of uniform chromaticity scale (UCS) diagrams were proposed. These UCS diagrams used a mathematical formula to transform the XYZ values or x,y coordinates to a new set of values (u,v) that presented a visually more accurate two-dimensional model. In 1960, CIE adopted one of these as the 1960 CIE u,v Chromaticity Diagram as shown in Fig. 2-8.
Fig. 2-8 1960 CIE u,v chromaticity diagram
Compared with the 1931 diagram in the aforementioned section, the effect was to elongate the blue-red portions of the diagram and relocate the illuminant (or white point) to decrease the visual disparity with the green portion.
However, this was still found unsatisfactory and in 1975, CIE proposed modifying the u,v diagram and supplying new (u’,v’) values. This was done by multiplying the v values by 1.5. Thus in the new diagram u’ = u and v’ = 1.5v. The resulting diagram was adopted as the 1976 CIE u’,v’ Chromaticity Diagram as shown in Fig. 2-9.
Fig. 2-9 1976 CIE u’,v’ chromaticity diagram
While the representation is not perfect (nor can it ever be), the u’,v’ diagram offer
ig. 2-10 Nonunif u’,v’ chromaticity
in the u’,v’ diagram represent the same as in the x,y illustration, only here
s a much better visual uniformity. This can be seen in Fig. 2-10 by comparing the following illustration of the u’,v’ diagram with the x,y diagram at the top of this section:
F ormly-spaced visual representation of CIE diagram [13]
The lines
we can see the lines are more uniform throughout the diagram. One other point to make about the CIELUV model is the replacement of the Y lightness scale with a new scale called L*. The Y scale is a uniform scale of lightness with equal steps between
each value. However, this kind of scale is not adequate to represent differences in lightness that are visually equivalent. For example, a difference between values of 10 and 15 on the Y lightness scale differ by the same magnitude as values of 70 and 75.
We do not see the values as being the same, however. We have much less ability to differentiate between degrees of lower values than we do of middle and higher values.
Using a mathematical formula, the Y values were translated to other values that are
.5 Color Difference
v color space is designed to be perceptually uniform, meaning that
he Luv space was designed specifically for emissive colors, which correspond to im
approximately uniformly spaced, but more indicative of the actual visual differences. The resulting scale, L*, models the Munsell system's scale of value. The major difference is that L* uses a scale of 0-100, while Munsell's Value uses a scale of 0-10. The L* lightness scale is used for CIELAB as well as CIELUV. The value of CIELUV lies in the fact that, like CIEXYZ and xyY, it is device-independent and therefore not restrained by gamut. It is an improvement over CIEXYZ and xyY in that it better represents uniform color spaces.
2
The CIE 1976 Lu
a given change in value corresponds roughly to the same perceptual difference over any part of the space. Using such a space for quantizing color values decreases the chance that any given step in color value will be noticeable on a display or hardcopy.
T
ages captured by a camera or computer graphics rendering program. However, we must modify the assumptions used by the CIE slightly, since we want to record high dynamic-range images independent of viewer adaptation. We therefore ignore
the part about luminance scale, using instead a log scale to cover a much larger range of values. We also ignore the part about dominant color and encode based on the absolute (u’,v’) coordinates.
Derived from Eq. (2-2), (u’ ,v’) is the color coordinate of a sample, (u
.Color-difference formula of CIE 1976 [13]：
>0.008856
.6 Just Noticeable Difference
is a number that stands for the minimum tolerance
n’, vn’) is the color coordinate of the reference white, X,Y,Z are the tristimulus of a sample, and Xn,Yn,Zn are the tritimulus of the reference white, Yn =100.
Eq. (2-3)
Just Noticeable Difference
human can percept between one and its neighbor color. Over the years, various metrics have been proposed to characterize the perceived color of polychromatic light [14]. One such metric for determining color is chromaticity. Chromaticity is used to define the perceived color impression of light, irrespective of its luminance (or
“photometric brightness”), in accordance with the standards of the CIE. The CIE 1931
chromaticity standard defines the hue and saturation of light based on a pair of xy coordinates that specify position in a chromaticity diagram. Color gamut of RGB LED and curve of Blackbody Locus are depicted Fig. 2-11. In Fig. 2-11, for each color (i.e., chromaticity), there is a “MacAdam ellipse” that defines a “just noticeable difference” (JND) between it and neighbouring colors.
Fig. 2-11 CIE 1931 xy chromaticity diagram
The size and orientation of these ellipses vary with color, and that why a linear transformation of the CIE chromaticity diagram, called the CIE 1976 Uniform Color Space (UCS), was developed to minimize these differences [15].
The transformation is given by:
3
is relatively constant for small differences in and anywhere a
Eq. (2-5) Eq. (2-4)
'
u v' long the
blackbody locus from 2000 to 6500 Kelvin (Fig. 2-11). Further, Δu'v'= 0.0015
offers a reasonable approximation of one JND within this range. American National Standards Institute (ANSI) and International Electrotechnical Commission (IEC) standards specify four MacAdam ellipses for fluorescent and HID lamps (Δu'v'= 0.006 ), but most major lamp manufacturers maintain chromaticity variations to in two or three MacAdam ellipses (at full rated light output and 25 ℃ ambient temperature) for quality control purposes. It is therefore reasonable to adopt two MacAdam ellipses, or Δu'v'= 0.005 , as a target tolerance for Just Noticeable Difference of LEDs [16].
Similarly, uvΔ is th
The
e deviation in color point (u, v) from the reference (ur, vr) in with
CIE 1960 UCS plane and is defined as:
2
This equation form is the same as Eq. (2-4). And Typical human eye can
.7 Recursive Approach
s the repetition of a process within a computer program. It Eq. (2-6) notice a color difference Δuv > 0.0035 in uv plane [12][17]. Hence the Just Noticeable Difference is regarded as 0.0035 in CIE 1960 UCS plane.
2
Recursive Approach i
can be used both as a general term, synonymous with repetition, and to describe a specific form of repetition with a mutable state. Therefore, recursive approach is an example of iteration, but typically set a declarative condition as desired condition.
Only when the desired condition reached will the recursive approach stop. In computer programming, recursive approach is coded in using ‘while loop’ or ‘if sentence’ frequently. Therefore, recursive approach method detailed in the third chapter is applied on feedback control system for LED light output stabilization. An example of flow chart of recursive approach to reach 100 is shown as Fig. 2-12.
Fig. 2-12 Flow chart of recursive approach to reach 100
.8 PWM and Duty Ratio
idth modulation (PWM) uses a square wave whose duty ratio is 2
2.8.1 PWM Pulse-w
modulated resulting in the variation of the average value of the waveform.
Fig. 2-13 Square wave, showing the definitions of ymin, ymax and D.
If we consider a square waveform f(t) with a low value ymin, a high value ymax
and a duty cycle D (Fig. 2-11), the average value of the waveform is given by:
∫
= 1
T0
f(t)dt y T
As f(t) is a square wave, its value is ymax for 0＜t＜D．T and ymin for D．T＜t
Eq. (2-7)
＜T. The above expression then becomes:
⎟⎟ ⎠
This latter expression can be fairly simplified in many cases where ymin = 0 as
y max
D
y = ⋅ . It is obvious that the average value of the signal (y) is directly dependent on the duty cycle D.
2.8.2 Duty Ratio
In a square wave of PWM signal (Fig. 2-12), the most important factor is duty ratio. The duty ratio D is defined as the ratio between the pulse duration (τ) and the period (T).
Fig.2-14 Definition of Duty Ratio in a PWM signal of rectangular waveform
2.9 Design Rules
The system structure is shown in Fig. 2-15. As soon as we adjust the variable transistor and set up desired LED light output, the processor will keep the electrical digital signal of desired color as setup value. Whenever the sensor senses the variation of LED light output by transferring electric digital signal into processor via (through) analog to digital converter, the feedback recursive function will be initiated and begin to run. Finally, by increasing or decreasing duty ratio of PWM signals of LCD driving current, the desired color is approached.
Fig.2-15 Feedback control system structure flow
2.10 Summary
In this chapter, we have described not only the history of LED, Photodiode, CIE and fundamental PWM theories, but also selected Δu'v'= 0.005 (Just Noticeable Difference) as our evaluation index. In addition, basic concepts of recursive approach have been explained as well. In the following chapter 3, the realization of feedback control system with recursive approach is going to be presented.
Chapter 3
System Implementation and Measurement
3.1 System Implementation
LED light output feedback control system is going to be established by combining several devices. According to the device functionalities and requirements, the whole system is divided into 7 sections shown in the system block diagram (Fig.
3-1). The setup value block represents that the desired color of LEDs is set up by adjusting the external variable resistor. Meanwhile, the system is initiated and begins to function. As soon as sensor senses the color variation in spite of manmade or naturally decayed and transfers electric digital signal into central processor through analog to digital converter, the feedback recursive function will be initiated and begin to run. Comparator program processor runs the recursive program and triggers the PWM signal generator and constant current driver to obtain the desired LED color.
Fig.3-1 System block diagram of LED light output feedback control system
3.1.1 Setup Value
The desired colors of RGB LEDs are set up by adjusting the external 10KΩ variable resistors of LED driver to change the driving current of LEDs. Because LED is a current-driven device, the color of LED will vary when the driving current is changed.
3.1.2 LED Array
(a) (b)
Fig. 3-2(a) Photograph and (b) Structure of LED [18]
Diameter 5mm RGB LEDs (Fig. 3-2) are used to conduct this experiment because of convenience of availability and ease of sensing the color variation (Bottom Emitting) without light guide structure. Optical characteristics of LEDs are shown in Table. 3-1. However, the choice of sensor is dependent on the optical characteristics of LEDs.
Table. 3-1 Optical Characteristics of LEDs
Red Green Blue
Wavelength (nm) 625 525 460
( x , y ) (0.68, 0.30) (0.18, 0.71) (0.12, 0.06)
3.1.3 Sensor
In order to fit the spectral sensitivity of LEDs and simplify the system complexity, 3-channel (R, G, B) photodiode color sensor is chosen to sense the color variation of LED array. The spectral response of sensor is shown in Fig.3-3. This photodiode color sensor features no sensitivity in the near infrared region. Its spectral response range is close to the human eye sensitivity. Therefore, such sensor is appropriate for the color sensing of LED array.
(a) (b)
Fig. 3-3 (a) Photograph and (b) Spectral Response of Photodiode Color Sensor [18]
Table. 3-2 Optical Characteristics of Photodiode Color Sensor [18]
Blue 400 to 500 nm
Green 480 to 600 nm Spectral Response Range（λ）
Red 590 to 720 nm
Blue 460 nm
Green 540 nm
Peak Sensitivity Wavelength（λp）
Red 620 nm
Undoubtedly, Photo Sensor and RGB LEDs are indispensable in this experiment, 3-in-1 high sensitivity photo diode and 5mm Lamp LEDs are chosen because their wavelengths correspond to each other (Tables. 3-1 and 3-2).
3.1.4 ADC (Analog to Digital Converter)
The purpose of the A/D converter (ADC0804) is to take analog input of senor signal in the range of 0 to 5V and digitize it into 8-bits to transfer into the Lattice microprocessor. Though the A/D converter is designed with clock inputs for a synchronous connection to a microprocessor, A/D converter can be used freely in color feedback control system. Fig. 3-4 shows the configuration of the ADC0804 in free-running mode.
To configure the ADC0804 to function in free-running mode, CS* and RD* are grounded and WR* and INTR* are tied together. The N.O. on the WR* and INTR*
pins stands for normally open. When the A/D is first turned on, the WR* and INTR*
must be momentarily grounded. CLK R is tied back to CLK IN. V+(VREF) is set as 5V and determines the input voltage range. AGND and DGND are tied together on the same ground plane. In this mode, the A/D will convert its input at pin 6 to the outputs DB0-DB7 within 135 ns.
In free running mode, only 8 output pins are connected to the Lattice microprocessor, freeing up pins that would have been used for clocking, chip select, etc, for use in other modules. In addition, free-running mode eliminates complicated synchronization and timing issues with the Lattice microprocessor has existed to run the chip at another sampling rate.
Fig. 3-4 Schematic for A/D Converter in Free-Running Mode
Fig. 3-5 Analog to Digital Bits Arrangement
Four 8-bits A/D converters are used to quantize the analog signals of photo sensor. Totally there are 32 bits to process, and the arrangement of 32 bits for color resolution is shown in Fig. 3-5. Two black solid circles represent unused empty bits,
whereas the other six white circles denote the bits shared in common by RGB color.
Consequently, 14 bits resolution for single color can be achieved.
3.1.5 Central Processor
Fig. 3-6 Functional Block diagram of Central Processor
Control processor (Fig. 3-6) is the kernel of the whole feedback control system, and it collects all electric digital signals to process.
While ( sensor_signal != setup_value) {
If (sensor_signal < setup_value) PWM_intensity = PWM_intensity + 1;
Else
PWM_intensity = PWM_intensity – 1;
}
The code shown above denotes the function of recursive program. Actually, central processor not only links the sensor signals to PWM generator, it also compares
sensor signal to setup value and decides the feedback signal. While loop begins to run when sensor_signal doesn’t equal setup_value. After that, when the sensor_signal is lower than the setup_value, the LED light output is getting weaker. At this moment, the PWM_intensity signal of LED driving current is assigned to be another increased one to enhance LED light output as feedback, and vice versa. As sensor_signal is higher than setup_value, the LED light output is getting brighter. At this moment, the PWM_intensity signal is assigned to be lower to decrease LED light output as feedback.
3.1.6 LED Driver
DD313 is a constant current driver designed for LED lighting application. This current driver incorporates three-channel constant current circuitry with current value set by three external resistors. The three enable pins are specifically designed for independent control over each of the three output terminals, which are R, G, B LED channels in the experiment. The fast response of the output current can adapt to high dimming resolution and high refresh rate applications up to 1MHz. The pin connection and description data of LED driver, DD313, are shown in Appendix (a).
The schematic diagram of LED driver, DD313, is shown in Fig. 3-7. 18V is applied to VLED. Five, Seven, and Nine LEDs are driven in series connection for Blue, Red, and Green color separately. The Constant-Current Outputs of DD313 for RGB LEDs are adjustable. Constant-current value of each output channel is set by an external resistor connected between the REXT(R, G, B) pin and GND individually.
Besides, varying the resistor value can adjust the current up to 500mA. The equation of REXT(R, G, B) and Output current is shown as follows:
Eq. (3-1) Iout(R,G,B) (A) = 0.5 (V) / REXT(R,G,B) (Ω)
Fig. 3-7 Schematic Diagram of LED driver, DD313 [19]
3.1.7 PWM Generator
PWM generator is used to switch Enable-Pins(ENR, ENG, and ENB) of LED driver to accomplish dimming function. DM413 is a PWM enabled LED driver specifically designed for LED lighting or display applications. DM413 incorporates shift registers, data latches, 3-channel constant current circuitry with current value set by 3 external resistors, and built-in oscillator for PWM functioning. Data and clock buffer outputs are designed for cascading another chip. Additionally the Output Polarity Reverse function is designed to adapt to high power LED applications. The pin connection and description data of PWM Generator, DM413, are shown in Appendix (b).
Configuration of PWM generator and LED driver is shown in Fig. 3-8. 5V is applied to VCC. The Duty Ratio of PWM signal can be adjusted by changing Pull-High Resistance. Due to 400 Hz of PWM wave, flicker can be avoided. Because 14 bits PWM generator is utilized, the driving current of LED is divided by 14 bits. If the driving current were 20 mA, then the PWM recursive current scale would be 1.2 μA.
20 (mA) ÷ 214 = 1.2 (μA) Eq. (3-2)
Fig. 3-8 Configuration of PWM generator and LED driver [20]
3.2 Measurement 3.2.1 Evaluation Index
Color difference in CIE 1976 color space is taken as evaluation index because this color space is more uniform than CIE 1960 color space. As described in Chapter 2, Eq. (2-5) is used to calculate the color difference. and are initial color coordinate of RGB LEDs at specific driving currents.
' 'v Δu
0
'
u v
0'
3.2.2 Measuring Instrument
CS-200 chroma meter is employed to measure color coordinate of RGB LEDs. It displays and outputs in luminance Lv (cd/m2) and chromaticity diagram (CIE 1976 UCS chromaticity diagram). The photograph and setting coordinate of CS-200 are shown in Fig. 3-9. According to the specification of chroma meter CS-200, measured data are 4 bits below point. Reliable accuracy is three bits below and the last bit is regarded as reference value. Therefore, worst error of color difference is 0.0012. The calculation is shown below.
'
Fig. 3-9 (a) Photograph and (b) color coordinate setting of CS-200 chroma meter
3.2.3 Measuring Criterion
data of LEDs are the initial values of each LED. When taking measurement, the data are accepted when brightness Lv are within 10%
variation. Such standard is according to the prior art. [5] After taking the forward voltages of RGB LEDs into account, Seven, Nine, and Five points color data are measured for Red, Green, and Blue LED Arrays separately. In the following, Color difference is calculated. Besides, average value of
'
measurement fluctuation. The measurement and experiment setting are depicted in
Figs. 3-10 and 3-11. LEDs are arranged on the left PCB board. Holes are distributed in order in the right PCB boards. In order to ensure measuring the identical points of LEDs, CS-200 chroma meter is used to take the measurement of LEDs through the measuring points.
Red Measuring
points Blue
Green
LED Array
Fig. 3-10 Measurement setting of CS-200 chroma meter and LED arrays
Oscilloscope Power Supply
LED Array
Chroma Meter CS-200
Feedback Control System
Digital Multimeter
Fig. 3-11 Experiment setting of recursive feedback control system
3.3 Summary
The system structure and functionality of each device have been elaborated, as well as the setting of measurement. Central processor, which is the kernel of the feedback control system, collects all electric digital signals to process, compares sensor signal to setup value of desired LED color and decides the feedback signal.
After deciding increasing or decreasing duty ratio of PWM signals to generate, the original desired color of LED is approached step by step. As a result, recursive
After deciding increasing or decreasing duty ratio of PWM signals to generate, the original desired color of LED is approached step by step. As a result, recursive