The color difference is a quantitative measure of how the perception of color varies, based on three key attributes: lightness (L*), hue (a* and b*), and chroma. Differences in lightness indicate variations in brightness, while differences in hue reflect changes in the color's tone (such as red or blue). Chroma differences represent the intensity or vividness of the color. Accurate color difference evaluation is crucial in industries like manufacturing and commerce, especially for color matching and quality control.
In 1931, the CIE (Commission Internationale de l'Éclairage) introduced the CIE-RGB color space, which represents all visible colors using combinations of red, green, and blue. However, this system had a major drawback: it often produced negative values when calculating tristimulus values, making it less practical. To overcome this issue, the CIE-XYZ color space was developed. It uses imaginary primary colors X, Y, and Z that don’t correspond directly to real visible colors, but they allow for more consistent and usable calculations.
The XYZ system provides a foundation for defining colors, but it is not intuitive for human perception. The Y value in XYZ corresponds to luminance, while X and Z relate to chromaticity. To normalize the values, they are often expressed as x, y, and z, where x + y + z = 1. This normalization helps in representing color coordinates more effectively, though it doesn’t fully capture perceptual uniformity.
To address this, the CIE-L*a*b* color space was developed. It is a nonlinear transformation of the XYZ system, designed to align better with human color perception. In this space, L* represents lightness, a* represents the red-green axis, and b* represents the yellow-blue axis. These values can be calculated from XYZ using specific formulas, as shown below:
$$
L^* = 116 \cdot f\left(\frac{Y}{Y_n}\right) - 16
$$
$$
a^* = 500 \cdot \left[f\left(\frac{X}{X_n}\right) - f\left(\frac{Y}{Y_n}\right)\right]
$$
$$
b^* = 200 \cdot \left[f\left(\frac{Y}{Y_n}\right) - f\left(\frac{Z}{Z_n}\right)\right]
$$
Where $ f(t) = \begin{cases}
t^{1/3}, & t > \left(\frac{6}{29}\right)^3 \\
\frac{t}{3\left(\frac{6}{29}\right)^2} + \frac{4}{29}, & t \leq \left(\frac{6}{29}\right)^3
\end{cases} $
The CIE-LCH color space is derived from CIE-L*a*b*, using L (lightness), C (chroma), and H (hue) as its components. This makes it more intuitive for everyday use, as it aligns with common descriptions of color. The relationship between L*a*b* and LCH is given by:
$$
C^* = \sqrt{a^{*2} + b^{*2}}
$$
$$
H^* = \tan^{-1}\left(\frac{b^*}{a^*}\right)
$$
Color differences between two samples can be calculated using ΔE*, which represents the total difference between two colors. The formula for ΔE* is:
$$
\Delta E^* = \sqrt{(\Delta L^*)^2 + (\Delta a^*)^2 + (\Delta b^*)^2}
$$
This metric allows for precise comparison of colors in industrial settings. A larger ΔL* indicates a lighter color, while a smaller ΔL* means darker. Similarly, a larger Δa* suggests redder tones, and a larger Δb* indicates yellower tones. Understanding these values helps in ensuring color consistency across products and materials.
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