The working principle of the colorimeter is to simulate the visual system of the human eye, and use the analog integration optical system inside the instrument to integrate the tristimulus value of the spectral photometric data to obtain the mathematical expression of the color, so as to calculate the excellent value and the chromatic aberration of the contrast color. This article introduces the difference between CIERGB spectral tristimulus value and CIEXYZ spectral tristimulus value and the conversion between them
The CIERGB spectral tristimulus value is obtained by CIE with 317 normal visioners, using the red, green and blue primary colors specified by CIE, and the equivalent energy spectral color from 380 780nm. During the experiment, the number of red, green, and blue primary colors corresponding to the isoenergetic spectral color with each wavelength of the spectrum is called the spectral tristimulus value, which is denoted as r( )g( )b( ) Therefore, the color equation of the matching wavelength of the isoenergetic spectral color c( ) is: c( )=r( )r) + g( )r) +b( )r).
In order to better understand the above color equation, the data of the tristimulus value of the r( )g( )b( ) spectral and the unit amount (r) = 10000，（g）=4.5907，（b）=0.0601 is substituted into the above equation to obtain the relative brightness curve of the isoenergetic spectral color c( ), as shown in the figure below. The maximum value is c(555), i.e., c(555) (555)(r) + g(555)(r) + b(555)(r) = 1000。
As can be seen from the figure above, the relative brightness curve of the isoenergetic spectral color is the same as the photopic spectral luminous efficiency curve of the human eye. Since the maximum value of c( ) is c(555), c( ) can be understood as relative brightness. Assuming that in the matching experiment of isoenergetic spectral colors, the actual brightness of the three primary colors is r0( )g0( )b0( ), then there is:
r（λ）=r0（λ）/m（r）
g（λ）=g0（λ）/m（g）
b（λ）=b0（λ）/m（b）
where m=r0(555)+g0(555)+b0(555), which is the maximum brightness of the actual color light of the isoenergetic spectral color. Therefore, the tristimulus value of CIERGB spectral r( )g( )b( ) is the actual number of red, green, and blue primary colors corresponding to each wavelength of the spectrum, and is converted and normalized by unit quantity.
At =555nm, the brightness of isochromatic colors has a maximum value, indicating that the brightness of green is higher in isospectral colors, and a large amount of green light (ratio of 1.) is required when mixing white light with three monochromatic lights (primary colors) of red, green, and blue0000：4.5907：0.060), which indicates that the sum of brightness in the wavelength band of green light in the isoenergetic spectrum is larger, so green light is strongly representative in the isoenergetic spectrum.
The CIEXYZ spectral tristimulus value is obtained by the CIERGB spectral tristimulus value through mathematical transformation, which is denoted as the X( )Y( )Z( )CiERGB spectral tristimulus value r( )g( )b( ) Although the spectral color c( ) equation can indirectly reflect the relative brightness and waste of the isoenergetic spectral color, it is very unintuitive. In order to visually represent the brightness of a color, CIE stipulates that y( )= v( ), so y( ) not only indicates the number of green primary colors in the color light to be matched (isoenergetic spectral color). It also indicates the brightness of the color light to be matched, which is used to calculate the brightness characteristics of the color. Since y( ) conforms to the luminous efficiency of the photopic spectra, the ciexyz spectral tristimulus value x( )y( )z( ) represents the color visual characteristic parameter of the human eye in the calculation of the color chromaticity value of the object.
To overcome the disadvantage that the RGB color space does not produce all colors, and in some cases the color values can be negative, the International Commission on Illumination (CIE) in 1931 prescribed a new color system called the XYZ color space. It represents colored light as: c = x (x) + y (y) + z (z). where (x), (y), and (z) are the primary color quantities of the xyz color space, and x, y, and z are the trichromatic scale coefficients.
The xyz color space must meet the following three conditions:
1) The trichromatic proportional coefficients x, y, and z are all greater than zero;
2) The value of y is exactly the brightness of colored light;
3) When x=y=z, it still indicates standard white light.
According to the above conditions, the relationship between the RGB color space and the XYZ color space can be obtained:
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