The CMC color system, more accurately known as the CMC (l:c) color difference formula, is a color tolerancing system developed to define acceptable color differences between a standard color and a sample color. It is widely used in industries where precise color matching is critical, such as textiles, paints, and plastics.
Understanding CMC Tolerancing
Unlike simpler color difference formulas (like basic Euclidean distance in a color space), CMC tolerancing is designed to correlate more closely with human perception of color differences. Human vision is less sensitive to differences in hue in some parts of the color spectrum (like green and blue) compared to others, and less sensitive to differences in chroma (saturation) or lightness depending on the color's position in the color space.
The CMC formula takes this perceptual non-uniformity into account. As specified in the reference, the CMC calculation mathematically defines an ellipsoid around the standard colour with semi-axis corresponding to hue, chroma and lightness. This ellipsoid represents the boundary of perceptually acceptable color difference around a target color.
- The Ellipsoid: Imagine a 3D shape around your standard color point in a color space like CIELAB. This shape is an ellipsoid, not a simple sphere.
- Semi-Axes: The axes of this ellipsoid are aligned with lightness (L*), chroma (C*), and hue (H*). The length of the ellipsoid's axes determines the permissible tolerance in each direction.
- Perceptual Weighting: The unique aspect of CMC is that the size and shape of this ellipsoid automatically adjust depending on the standard color's position in the color space. For example, for a color with high chroma, a larger difference in chroma might be allowed compared to a color with low chroma, reflecting human perception.
How CMC Tolerancing Works
When comparing a sample color to a standard color, the CMC formula calculates a single numerical value representing the "distance" between them. If this value is less than a specified tolerance limit (e.g., CMC 1.0 or CMC 0.5), the sample is considered an acceptable match.
The formula typically includes two parameters, 'l' and 'c', written as CMC (l:c). These parameters are ratios that allow weighting the importance of lightness differences versus chroma and hue differences.
- l (lightness): The weighting factor for lightness difference.
- c (chroma/hue): The weighting factor for chroma and hue difference.
Commonly, CMC (2:1) or CMC (1:1) is used.
- CMC (2:1): Gives lightness twice the importance of chroma and hue. This is often used for textiles where lightness variations are considered more critical.
- CMC (1:1): Gives equal importance to lightness, chroma, and hue differences.
Origin and Status
The CMC tolerancing system was developed by the Colour Measurement Committee of the Society of Dyers and Colourists in Great Britain. It became public domain in 1988, allowing its widespread adoption across industries.
Key Benefits of Using CMC
- Improved Agreement: Provides color difference values that correlate well with visual assessments by humans.
- Industry Standard: Widely accepted and used globally, especially in textile manufacturing.
- Perceptually Uniform: Accounts for the non-uniformity of human color perception across the color space.
Using CMC allows for more precise and consistent color quality control, reducing disputes and improving manufacturing efficiency.
Summary Table:
| Feature | Description |
|---|---|
| Type | Color Difference Formula / Tolerancing System |
| Purpose | Quantify acceptable color differences correlating with human perception. |
| Mechanism | Defines a perceptually uniform ellipsoid around a standard color. |
| Axes | Ellipsoid axes relate to Lightness, Chroma, and Hue. |
| Adjusts by | Automatically adjusts ellipsoid size/shape based on the standard color. |
| Parameters | Uses (l:c) weighting ratios (e.g., CMC 2:1, CMC 1:1). |
| Origin | Society of Dyers and Colourists (Great Britain). |
| Public Use | Became public domain in 1988. |
In essence, the CMC system moves beyond simple distance calculations in color space to provide a more nuanced and perceptually relevant measure of color difference, making it a vital tool for color quality management.
