How to measure? As mentioned above, we define the basic units in the measurement process:
So we choose a specific intensity &; After the wavelength to be measured, hit the left side of the field of view, and constantly adjust the intensity and proportion of [unit RGB] light to achieve the same color sense as that to be measured. Finally, the following relationship is obtained: (Explanation: The reason why the red component is negative is that when some spectral colors projected into the half field of view match the three primary colors of the other half field of view, the matching can only be realized by adding the red primary color to the spectral color half field of view. In other words, the red light at this time is loaded on the whiteboard to be tested on the left side of the experimental diagram. If the amount of colored light added to the right side is designated as positive, then the left side is correspondingly negative. )
So we can use geometric methods to express visible light of any wavelength:
Normalization:
Then we have the relation of r(λ)+g(λ)+b(λ) = 1, which will exist as a plane in the graph 1, and we call it the unit plane:
Back to the train of thought, when we get the spectral trajectory of monochromatic visible light by projection in three-dimensional rgb space, for the sake of mathematical simplification, we simplify the three-dimensional space into two-dimensional space: (the point with the wavelength of 540 ~ 700nm in the figure actually contains the wavelength of 700 ~ 780nm) A straight line with a slope of 45 degrees indicates that the blue intensity value (blue chromaticity value) is 0 at this time, and you can ponder it if you are interested).
Let's ignore the red line in figure 6 and get a spectral trajectory inclined to the negative semi-axis of R after descending to two-dimensional space. Why do you think of this? (Because the red stimulus value will be negative in figure 1. ) In this oblique spectral trajectory coordinate system, if the colors are represented by corresponding red, green and blue, negative numbers will appear, and the expression and mixing of colors will be very chaotic. So scholars decided to change a coordinate system to represent the spectral trajectory of visible light: if we change three colors to describe visible light, then the new three primary colors can be connected into a triangle and wrapped inside (for xz-yz coordinate system). The representation of the spectral trajectory of visible light is no longer negative, and (X)(Y)(Z) can be understood as three new primary colors of invisible light, which can be produced in different proportions.
(X)(Y)(Z) How to choose? Can I wrap a triangle around our visible spectrum at will? No problem, whether or not to make a complete triangle and how to make a complete triangle are all artificially determined and designed to solve a certain problem. There is no absolute answer, only the optimal solution in a certain situation.
Based on I, (x) (y) and (z) are actually biased towards red, green and blue respectively. When describing color, it is directly proportional to the three primary colors of RGB system. Since r(λ)+g(λ)+b(λ) = 1, a chromaticity coordinate value can be omitted when representing a certain color, and correspondingly, a value can be omitted in (X)(Y)(Z), so we can use the omitted value to represent the brightness situation.
Which one should I choose?
Select (y) for green.
Why?
Because the human eye is most sensitive to the wavelength of green light (described in "Talking about the technical realization of color (Part I)"), the relative brightness (rather than quantity) ratio of the three primary colors in RGB system is:
lr:LG:lb = 1:4.59:0.060 1
This means that the RGB system with the same intensity has three primary colors, blue gives people a very dark feeling and green gives people the brightest feeling. Therefore, it is also reasonable to set the ratio of primary color Y to brightness and green in color (the greater the value of color Y, the brighter the human eye feels, which means the higher the ratio of green in color).
In addition, because color matching also includes brightness matching, the brightness equation can be obtained by substituting the relative brightness of the three primary colors.
LC = lr+4.59lg+0.060 1lb. When lC =0, b = 1-r -g is brought in, corresponding to the line corresponding to XZ (Y = 0 at this time).
It is approximately equal to g = (-0.94/4.54)r-(0.06/4.54), so XZ is determined, and then XY and ZY lines are determined.
Based on ii, the spectral trajectory is basically a straight line from 540nm to 700nm on the RGB chromaticity diagram. By mixing two colors on this line, various spectral colors between the two colors can be obtained. The XY side of the new XYZ triangle should coincide with this straight line, because the spectral trajectory only involves the changes of (x) primary colors and (y) primary colors, not (z) primary colors, so the XY line is determined.
The third lines YZ and CIE are straight lines tangent to a point with a wavelength of 503nm. Its equation is also easy to get.
So our (X)(Y)(Z) triangle is determined! Which is that red line in figure 6. We got the CIE 193 1 XYZ system!
Let's take a look at its relationship with RGB coordinate system:
And (1/3, 1/3)E still corresponds to our white point.
What are the points on this spectral trajectory? How to understand?
The point of the trajectory corresponds to the color of a certain wavelength and the frequency point of a wave corresponding to visible light; How about superposing two different wavelengths of light in a certain proportion? The superposition of light, that is, the superposition of waves, is not a linear superposition of wavelength or frequency. Think about the origin of Fourier series. The light produced by the superposition of different lights is the light in our trajectory.
Then we fill in the spectral trace.
When the light source directly emits some light to be measured, the relative spectral power distribution of the light is obtained after measurement, as follows:
(Obviously, the light source is "light superposition with different weights" in the 375-780 band. If it is a point on the spectral trajectory, the relative spectral power distribution should be a pulse function. )
It can also be obtained from the spectral tristimulus value (absolute value) curve of CIE 193 1 XYZ system. We can get the stimulus values of light sources X, Y and Z through integration.
Get the chromaticity coordinates of the light, and finally we get the familiar "saddle" diagram:
Let me leave you a few questions: What is the function of this CIE 193 1 XYZ system? How to apply this system? Where is this system applied? (I will answer later, but it should be after a lot of content)