Luminescent materials are typically described by their luminescent color. Due to psychological and physiological factors, people’s perception of color varies. Even normal vision varies. To quantitatively describe a color and measure it using physical methods instead of the human eye, a chromaticity diagram is used. The color of a phosphor is typically expressed using color coordinates. Any color H0 can be quantitatively expressed using the three primary colors: blue (x0), green (y0), and red (z0):
Commonly used color coordinates have the x-axis on the horizontal and the y-axis on the vertical. With these coordinates, a point on the chromaticity diagram can be identified. This point accurately represents the color of the light emitted. In other words, chromaticity coordinates precisely represent the color. Because chromaticity coordinates have two numbers and are not intuitive, color temperature is often used to roughly represent the color of a lighting source.
（1.1）
The values of x, y, and z are related to the plane equation:
(1.2)
Only two of these values are independent of each other. Therefore, a color is generally represented by (x, y), which is called its color coordinates. The NTSC (National Television Systems Committee) specifies the color coordinates of standard red as (0.67, 0.33), standard green as (0.21, 0.71), and standard blue as (0.14, 0.08). Pure white light has color coordinates of (0.33, 0.33).
Chromaticity coordinates
The colors in the diagram include all colors that can be found naturally. This is a two-dimensional plane diagram, a plane composed of an xy rectangular system. It was designed to accommodate people’s habit of discussing variable relationships in a plane coordinate system. The process of designing this diagram involved many mathematical transformations and calculations. The significance and function of this diagram can be summarized in two sentences: (1) It represents the basic laws of color vision. (2) It represents the general laws of color mixing and decomposition.
Coordinate system – x, y rectangular coordinate system
x——indicates the relative value related to red.
y——indicates the relative value related to green.
z——represents the relative value related to blue. And z=1-(x+y)
Shape and outline
The shape is a tongue, sometimes also called a “tongue curve.” The closed area enclosed by the tongue’s outer curve and the bottom straight line is the trajectory of all visible monochromatic colors. Each point represents the color of a specific wavelength, ranging from 390nm to 760nm. The corresponding wavelengths of some characteristic color points are marked next to the curve. For example, in the figure, 510nm, 520nm, and 530nm are shown. The bottom straight line connects the 390nm point to the 760nm point, which is called the purple-red line.
color
This is a color map, and the colors within the area include all physically achievable colors.
Application value – quantitative expression of color
Color is represented by (x, y) coordinates. White should be included in the concept of “color”.
The significance of several characteristic points of the chromaticity coordinate diagram
(1) Point E – the coordinate point of the equal-energy white light point. Point E is a mixture of three primary colors with the same stimulus light energy. However, the luminous flux of the three is not equal. The CCT of point E is 5400K.
(2) Point A – the chromaticity coordinate point of a standard white light source specified by CIE. This is a pure tungsten filament lamp with a color temperature value of CCT=2856.
(3) Point B – a standard light source coordinate point specified by CIE. The CCT of point B is 4874K, representing direct sunlight.
(4) Point C – a standard daylight source coordinate point confirmed by CIE (daylight). The CCT of point C is 6774K.
(5) Point D – sometimes also marked as D light source is called typical daylight, or reconstructed daylight; CCT = 6500K.
Three special lines
(1) Blackbody color temperature trajectory: In the middle of the tongue-shaped curve, across the white area, there is a downward-curving curve. This is the blackbody color temperature trajectory. This curve represents the trajectory of the color change of a blackbody at different temperatures. The color temperature range is from 1000K to infinity. However, in practice, the range of 1000K-1400K is commonly used.
(2) Monochromatic light trajectory: This is the tongue-shaped curve in the chromaticity coordinate diagram, which is the trajectory of the color corresponding to the wavelength of visible light. Any point on the curve represents the wavelength of a light and the color it represents.
(3) Purple-red line: A straight line connecting the two ends of the tongue-shaped curve. The locus of the color after mixing red and purple is called the purple-red line.
Chromaticity coordinate partitioning
The area enclosed by the tongue-shaped curve is divided into 20 color zones. Within each zone, the colors are considered to be basically the same. Each color zone has an average dominant wavelength, or a complementary dominant wavelength, and has a corresponding English name. Their English-Chinese names are as follows:
- Red 2. Pink 3. Reddish Orange 4. Yellowish Pink 5. Orange 6. Orange-Yellow 7. Yellow 8. Reenish Yellow 9. Yellowish Green 10. Yellowish Green 11. Green 12. Bluish Green 13. Greenish Blue 14. Blue 15. Purplish Blue 16. Purple Violet 17. Reddish Purple 18. Purplish Pink 19. Purplish Red 20. Central Area – White Light Area
Complementarity of light and color
If two colors of light, when mixed in a certain proportion, produce white light, then the two colors are said to be complementary. In a chromaticity coordinate diagram, any straight line that passes through the white region can be found to represent a pair of complementary colors. Of course, a pair of complementary colors can also be found at either end of a line that passes through the equal-energy white light point E. In a chromaticity coordinate diagram, the color of the light at any two points will always be the result of a straight line connecting them. If the straight line does not pass through the white region, the colors of the two points cannot be considered complementary.
Mixture of white light with other colors of light—dominant wavelength and complementary color dominant wavelength
By mixing white light with an appropriate spectral color, any desired color of light can be obtained. If the white light selected is the isoenergetic white light at point E. Select any point C, connect CE and extend it, and intersect it on the monochromatic trajectory line. The wavelength of the monochromatic light at point C’ is called the dominant wavelength of the light at point C. The dominant wavelength λ represents the dominant hue of the spectral color at each point on the line. If point A within the FEN triangle is selected, connect EA, but do not extend it in the direction of A. Instead, extend the line to the upper left and intersect it at point A’ on the monochromatic trajectory line. The wavelength of point A’ is called the complementary color dominant wavelength of point A. The complementary color dominant wavelength also represents the dominant hue of the color at each point on line AA’.
Quantitative expression of color depth
Hues in the color sphere are similar to inter tones in music. A musical piece might have notes like C and F, and in colorimetry, the dominant wavelength represents hue. Just as musical notes have high and low pitches, these notes correspond to color depth in colorimetry. Color depth is represented by the excitation purity Pe (see the figure in Section 11). Clearly, on the line, the color is darkest at point C’, gradually fading to white, reaching point E, where it becomes completely white.
Mixing of colored light
The xy chromaticity coordinate diagram can be used to represent the color mixing relationship between any two colors of light.
These are two spectral colors on the chromaticity coordinates. To mix two lights, simply connect the two points to form a straight line, and the resulting color point must be somewhere on this line.
Color tolerance
On an xy chromaticity coordinate diagram, each point represents a specific color. The color of any point should be different from that of its neighboring points. However, if the points are too close together, the human eye cannot distinguish them. Only when the distance between two points is large enough can we perceive the difference between them. The maximum range of color changes that the human eye cannot perceive is called color bandwidth. Some studies have shown that the color bandwidth is not the same at different locations on the chromaticity coordinate diagram. The blue area has the smallest bandwidth, and the green area has the largest bandwidth. In other words, equal distances in different areas of the chromaticity diagram do not represent visually equal chromaticity differences. This is a defect of the chromaticity coordinate diagram.
Color temperature and chromaticity coordinate calculation method
First calculate the color coordinates. To do this, you must first have the spectrum P(λ).
Then the spectrum P(λ) is multiplied by the three stimulus functions X(λ), Y(λ), and Z(λ) corresponding to the wavelengths respectively and then added together to obtain the three stimulus values, X, Y, and Z.
Then the color coordinates x=X/(X+Y+Z), Y/(X+Y+Z)
Generally, the spectrum is from 380nm to 780nm, with an interval of 5nm, and a total of 81 data.
X(λ), Y(λ), and Z(λ) are functions specified by CIE, corresponding to the spectrum, with 81 data each, which can be found in colorimetry books.
Then calculate the color temperature, for example, the chromaticity coordinates x=0.5655, y=0.4339.
The chromaticity coordinates of the “blackbody locus isotherm” are Myler, color temperature, on the blackbody locus (xyuv), and outside the blackbody locus (xyuv). Let’s use xy data as an example.
1. For the convenience of expression, x on the bold locus is written as XS and y as YS, and x outside the bold locus is written as XW and y as YW.
First calculate the slope K of each row, K=(YS-YW)/(XS-XW), and write it on the edge of the table.
For example:
My lead 530 slope K1 = (.4109-.3874)/(.5391-.5207) = 1.3352
The slope K2 of the My lead 540 is (.4099-.3866)/(.5431-.5245)=1.2527
My lead 550 slope K3 = (.4089-.3856)/(.5470-.5282) = 1.2394
2. Find the point x=.5655, y=.4339 between which two isotherms it is located, that is, the distance between this point and the two isotherms is one positive and one negative.
If you don’t know its approximate color temperature, the calculation will be complicated; because you said it is a sodium lamp, then its color temperature is between 1800 and 1900K.
Use the following formula to calculate the distance D1 from this point to the Myrtle 530, 1887K isotherm
D1=((x-YS)-K(y-XS))/((1+K×K) square root)
=((.4339-.4109)-1.3352(.5655-.5391))/((1+1.3352×1.3352) square root)
=(.023-.03525)/(1.6682)=-.0073432
Then calculate the distance D2 from this point to the Myrtle 540, 1852K isotherm
D2 = ((.4339-.4099)-1.2527(.5655-.5431))/((1+1.2527×1.2527) square root)
=(.024-.02806)/(1.6029)=-.0025329
Because D1 and D2 are both negative, they are not found.
Then calculate the distance D3 from this point to the Myrtle 550, 1818K isotherm
D3 = ((.4339-.4089)-1.2394(.5655-.5470))/((1+1.2394×1.2394) square root)
=(.025-.02293)/(1.6029)=+.0013005
D2 is negative and D3 is positive. We found it. D2 is recorded as M2 for 540 Myler and D3 is recorded as M3 for 550 Myler.
3. First, take the absolute value of the distance. According to the ratio, we can get the point M, the formula is
M= M2+D2(M3-M2)/(D2+D3)
=540+.0025329(550-540)/(.0025329+.0013005)
=540+.025329/.0038334
=540+5.607=545.607
(Related) color temperature = 1000000/545.607 = 1833K
4. Answer: The (relative) color temperature at the point x=.5655 and y=.4339 is 1833K
Light, Context, and Environment
Color never exists in isolation. It is affected by other colors, and surroundings, and it changes over time.
Different light sources have different color temperatures.
- Daylight (5000K–6500K): neutral and balanced.
- Incandescent (≈2700K): warm and yellowish light.
- Fluorescent (≈4000–5000K): cool and bluish light.
Color constancy allows people to adapt to the color changes in light, but poorly enough so that photos look off-color.
Perception can change the brightness of a color. This is caused by the colors next to it. This phenomenon is known as simultaneous contrast. Artists, photographers, and designers use this to create mood and depth.
How Many Colors Can the Human Eye See?
The human eye can perceive more than 10 million colors, thanks to the three types of cone cells in our eyes.
However, the potential for color vision varies. An estimated 1% of women are tetrachromats, having an extra cone, which may allow them to see up to 100 million colors. This variation in perception exemplifies the individuality of one’s reality.
https://www.threenh.com/Color_Knowledge/How-Humans-See-Experience-Color-Differently.html