The evaluation of color visually is tricky process, each person accepts or rejects color matches based on his/her color perception skills. In manufacturing, the subjectivity can cause the confusion and misunderstanding between customers, suppliers, vendors, production, and management. Due to this fact, the color measurement devices are important in many industries.
To make the color decisions, there is the demand to set the tolerances for how much perceived color difference is acceptable. Tolerances are used to control color, ensure consistency within a production run, and to minimize variability from one batch to another.
Methods for color interpretation
CIELAB, or L*a*b* values are counted from the tristimulus values (X,Y,Z), which are the base of all color mathematical models.
The 3D aspect of the CIELAB color space
The location of a color in the CIELAB color space is defined by a three-dimensional, rectangular coordinate system:
Once the L*a*b* position of a color is determined, a rectangular tolerance box can be drawn around it to indicate the acceptable color difference.
This color – a relatively dark (L* = 42.65, a* = -23.01, b* = 10.50) shade of greenish/blue – is defined by three numbers in the L*a*b* color model. Note that both a* and b* are negative, placing the measured dot in the green/blue quadrant. This method can cause some problems, because some colors may pass that shouldn't and some colors are acceptable even they may fail.
L*C*h° color difference calculations are derived from L*a*b* values, but mathematics convert the rectangular coordinate system to a cylindrical polar coordinate system.
This method is more closely to human perception of color, which reduces the chance of disagreement between human observer and instrumental readings or values.
CMC, CI94 and CIE2000
The most current and accepted tolerancing methods are elliptical – DECMC, CIE94, and CIE2000. These methods use the color difference calculations that are based on the color's location in color space. This provides better agreement between visual and instrumentally evaluation.
CMC Tolerancing Model
The image shows a slice of these three-dimensional color models. At the center is gray, and chroma increases while moving out in any direction. Red, with a hue angle of zero, is at the right. Moving counter-clockwise, the hues shift into oranges, then yellows, then greens, etc.
These tolerancing systems make tolerance ellipsoids in color space around the target color. The ellipsoid represents the volume of acceptance and automatically varies in size depending on position of the color in color space to more closely represent visual color perception. As you can see, the ellipses in the orange area of color space are longer and narrower than the broad and rounder ones in the green area. The size and shape of the ellipses also change as the color increases in chroma. These equations allow the user to vary the overall size of the ellipse to better match what is considered acceptable.
Author: Jana Loskotova