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2024-12-18
Color difference is an important parameter for color science quantification. It refers to the distance between different colors in a specific color space. It can be generally understood as the difference in color. It can be measured by a colorimeter and calculated using a specific color difference formula. So, what symbol is used to represent color difference? What are the calculation formulas for color difference? This article introduces them.
Chromatic Aberration
Color difference is represented by △E, △ represents difference, and E is the first letter of the German word Empfindung, which means feeling. The unit of color difference is NBS, which was established by the National Bureau of Standards of the United States and is now widely adopted by various countries. One NBS color difference unit is approximately equivalent to 5 times the visual color difference recognition threshold. Compared with the color difference value of two adjacent levels in the Munsell system, 1 NBS unit is approximately equal to 0.1 Munsell lightness value, 0.15 Munsell chroma value, and 2.5 Munsell hue value (chroma is 1); the difference between two adjacent colors in the Munsell system is about 10 NBS units. The difference between the NBS color difference unit and the color perception of people is described in the following table. It can be seen that the NBS color difference unit is valuable in industrial applications. New color difference formulas developed later often consciously adjust the unit to be close to the NBS unit. For example, the units of color difference formulas such as ANLAB40, HunterLab, CIELAB, CIELUV, etc. are roughly the same as the NBS unit (not equal), and not all color difference calculation formulas calculate color difference units that are NBS.
CIE ΔE*ab color difference perception threshold reference
There are many types of color difference calculation formulas, the most common ones are ΔE*ab, ΔE*uv, ΔE*94, ΔE*cmc, ΔE*00, etc., as follows
1.ΔE*ab color difference formula
The ΔE*ab color difference formula is the abbreviation of the CIELAB color difference formula. The CIELAB color difference formula is based on an approximately uniform three-dimensional color space, consisting of rectangular coordinates L*, a*, and b*, and is recommended for use by the International Commission on Illumination. This color difference formula is based on the CIELAB color space. If two colors are calibrated according to L*a*b*, the total color difference between the two is calculated as follows:
In the formula, ΔL* is the lightness difference; the difference between Δa* and Δb* is the chromaticity difference; △E*ab is the total color difference.
2.ΔE*uv color difference formula
The ΔE*uv color difference formula is derived from the linear transformation of the CIE xy chromaticity diagram. The purpose of the linear transformation is to improve the uniformity compared with the visual results. The CIE1976L*u*v* color difference formula is:
In the formula, ΔL* is the lightness difference; the difference between Δu' and Δv is the chroma; △E*uv is the total color difference.
3.ΔE*cmc color difference formula
The ΔE*cmc color difference formula is derived by modifying the CIELAB formula, and its formula is as follows:
Where: △L*, △C*, △H* are calculated by CIE1976LAB color difference formula, SL, SC, SH are weighted functions of lightness, chroma and hue, respectively, used to adjust the contribution of different lightness, chroma and hue to color difference. l and c are parameter factors, used to adjust the influence of different observation conditions on color difference. Selection of l and c values: For visual identification data of "perceptibility" of color difference, l=c=1 can be taken. For visual identification data of "acceptability" of color difference, l=2 and c=1 can be taken.
4.ΔE*94 color difference formula
The full name of the ΔE*94 color difference formula is "CIE1994 (△L*△C*ab△H*ab) color difference model", the formal abbreviation is CIE94, and the color difference symbol is △E*94. The △E*94 color difference formula is a modified form of the CMC (1:c) color difference formula, and its structure is similar to the ΔE*CMC (l:c) color difference formula. The calculation formula of this formula is as follows:
In the above formula, △L, △C*ab, △H*ab respectively represent the differences in lightness, chroma and saturation between samples, which are calculated by CIELAB color difference formula. The three parameters kL, kC, kH are the same as kl and kc in CMC (l:c) formula, and their values can be determined according to the specific object. In the printing industry, it is recommended to use kL=1.4, kC=kH=1; in the textile industry, when kL=2, kC=kH=1, the calculation result of CIE94 color difference formula is closer to visual evaluation.
5.ΔE*00 color difference formula
ΔE*00 color difference formula is the abbreviation of CIEDE2000 color difference formula, which is the latest color difference formula recommended by CIE based on CIELAB. Its color difference formula is as follows:
In the formula: KL, KC, KH are three constant parameters, which are defined according to the different test objects or the requirements of color quality control. In the textile industry, KL is generally 2, and KC and KH are generally 1; SL, SC, SH represent the weight coefficients of lightness, chroma and hue, respectively, which are used to correct the uniformity of the color space; RT represents the rotation function, which is used to correct the deflection of the main axis direction of the tolerance ellipse in the blue area of the color space. CIEDE2000 only redefines the calculation method of color difference, and does not establish a new uniform color space. For general industrial color difference evaluation, this formula can be used directly for calculation, and the calculation result can represent the perceived color difference.
