The evaluation of color aberration is based on the color difference equation that can visually visualize the color aberration, and the relevant color aberration formula is obtained by the International Commission on Illumination through a large number of color visual judgment and color aberration comparison psychological experimental data, which can be measured and calculated by color measuring instruments to achieve more accurate digital expression. This article introduces the typical color difference formulas in the colorimeter and their respective advantages and disadvantages
1.Cielab chromatic aberration formula
The CIELAB color difference formula is one of the color difference formulas recommended by CIE in 1976 for industrial applications. CIE uses the Euclidean distance of the CIELAB color space to express the magnitude of the difference between two colors, and the CIELAB color difference formula (e*ab) is defined as:
where L*, A*, and B* are the coordinate differences between the test sample (b) and its standard sample (S) in CIELAB 3D space.
Chromatic aberration can also be expressed by the chromaticity difference value c*ab and the hue angle difference value hab in the polar coordinates, where, c*ab, e*ab and l represent the length of the line segment, the unit is the same, only hab, is in the unit of angle, you need to convert the hue angle difference hab (in degrees) to the hue difference h*ab (the same unit as l* and c*ab), the formula is as follows:
Among them, the chromaticity difference c*ab and the hue angle difference hab are defined as follows:
Although the CIELAB space is not an ideal uniform color space, and the results of the CIELAB formula are not completely consistent with the results observed by the human eye, compared with other chromatic aberration formulas, the CIELAB chromatic aberration formula has great advantages in the performance of large chromatic aberration, and it is relatively simple in the expression of the formula, so it has been widely used.
2.CMC chromatic aberration formula
On the basis of the correction of the CIELAB chromatic aberration formula, the CMC chromatic aberration formula adjusts the size and shape of the chromatic aberration elliptical in each hue direction according to the visual relationshipThe relationship between chromaticity difference change and luminosity is improved, so that colors with different chroma have different chromatic aberration tolerances. The ellipses near the non-colored regions are smaller, and the ellipses with high chroma are larger, and the chromatic aberration tolerance is proportional to the change in chroma. The lightness weight factor L and the chroma weight factor C are introduced to meet the needs of different applications. The color difference expression for CMC(L:C) is:
Among them, L*S, C*AB,S and HAB,s are the standard indicators for determining color difference, and L*AB, H*AB and c*ab are all calculated by the CIELAB formula. When the L:C ratio is set to 1:1, it means perceptible color aberration, and if it is set to 2:1, it means that color aberration is acceptable.
The CMC chromatic aberration formula corrects the main defect in the CIELAB chromatic aberration formula, i.e., the defect of chromaticity position dependence, which is greatly improved from the CIELAB formula. In the CMC formula, the luminosity difference is weighted by the luminosity position, the chroma difference is weighted by the chroma position, and the chromatic difference is weighted by the chroma position and the hue angle.
3.CIE94 chromatic aberration formula
The chromatic aberration formula is an improved form of the CMC(1:C) chromatic aberration formula, and its structure is similar to that of the ΔE*CMC(L:C) chromatic aberration formula, which is calculated as follows:
In the formula, δl*, c*ab, and h*ab represent the difference in brightness, saturation, and color between the two colors, respectively. The parameter factors kl, kc and kh can be selected according to different evaluation objects and evaluation conditions, and the parameter factor values under the reference conditions are all 1. When the observation conditions change, each parameter can be individually changed to accommodate the visual change of each color component (lightness, chroma, hue).
The CIE94 chromatic aberration formula follows the idea of change parameters, and gives a better reference for the brightness, saturation and hue of the three elements that are related to color differences. For example, the parameter factor for evaluating the brightness of textiles is 2, while the recommended value of the lightness parameter factor in the printing industry is 14. In these two cases, the values of the other two are the same as those under the reference condition.
4.CIEDE2000 color aberration formula
The CIEDE2000 chromatic aberration formula is obtained through a large number of visual experiments and chromatic aberration evaluation experiments on the basis of the chromatic aberration formulas such as CIELab and CIE94. Rather than creating a new uniform color space in the critical region of the human eye, the CIE2000 chromatic aberration formula redefines the chromatic aberration calculation method so that the calculated value of chromatic aberration is closer to that of the human eye in the entire CIELAB (L*A*B* CHROMATICITY SPACE). On the basis of the formula for calculating the primary chromatic difference, the new chromatic aberration formula also cites three new weight coefficients sl, sc and sh, which represent the degree of difference in the direction of luminance l*, saturation c* and hue h*, respectively. The calculation formula is as follows:
where kl, kc, kh are the correction factors, l'、c'、h'is the l between the two samples'、c'and h'Arithmetic mean. If the absolute difference between the hue angles of the two samples is not more than 180°, the above equation is used to calculate directlyIf the absolute difference between the hue angles of the two samples is greater than 180°, subtract 360° from the larger hue angle and calculate it.
1.Advantages and disadvantages of the CIELAB color aberration formula.
Advantage: The chromatic difference between two colors is expressed by the Euclidean distance between the two color points.
Disadvantages: The calculation results are not always consistent with the visual perception (for example, a pair of light yellow samples and a pair of dark gray samples, both of which have a color difference value equal to 1, but the visual inspection will feel that the difference between the dark gray samples is several times greater than that of the light yellow samples.) ）
2.Advantages and disadvantages of CMC color difference formula.
Advantages: The lightness weight function l and the chroma weight function c are introduced, and the uniformity of the CIELAB color space is improved.
Disadvantages: In the a*b* plane, the c-axis of the calculated tolerance ellipse is all pointing towards the origin, while the tolerance ellipse of the visual evaluation result.
3.Advantages and disadvantages of the CIE94 color difference formula.
Advantages: The lightness weight function l and the chroma weight function c are introduced, and the uniformity of the CIELAB color space is improved.
Disadvantages: In the a*b* plane, the c-axis of the calculated tolerance ellipse is all pointing towards the origin, while the tolerance ellipse of the visual evaluation result.
4.Advantages and disadvantages of the CIEDE2000 color difference formula.
The CIEDE2000 color difference formula is a modification of the CIE94 color difference formula, which has the following characteristics:
1) The a* axis of the near-neutral color gamut was re-calibrated, and the performance of neutral color was improved
2) Modify the brightness weight function in the CIE94 formula to an approximate V-shaped function
3) The hue angle is considered in the hue weight function, which reflects that the hue compatibility limit varies with the hue of the color
4) Contains an ellipse selection to reflect the phenomenon that the chromatic aberration tolerance ellipse does not point to the center point in the blue area.
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