Post by: Jan Lalek, Andrzej Rybczyński, Krzysztof Jeżowski
MacAdam tests
MacAdam conducted tests for a selection of 25 reference points on the CIE 1931 chromaticity diagram, as a result of which he established boundaries around the selected points where the average observer began to notice color differences with respect to the reference point. The tests were conducted along different directions of color change. The tests showed that the boundary points of color distinguishability, at which a certain percentage of subjects began to notice a color difference, form an ellipse around the reference point. The ellipses vary in size depending on the position on the chromaticity chart of the reference point. The dimensions of the ellipses are smallest for the color blue, while the largest for the color green. The dimension of the ellipse also depends on the assumed fraction of the population noticing the color difference. The higher the degree of the ellipse, the more likely it is that the color difference will be perceptible.
Degree 1 of MacAdam ellipse (sd = 1.0) – 68.26% of people will notice little color difference
Degree 2 of MacAdam ellipse (sd = 2.0) – 95.44% of people will notice slight color differences
Degree 3 of MacAdam ellipse (sd = 3.0) – 99.44% of people will notice color difference
The mathematical model created on the basis of MacAdam’s research allows for the determination of the ellipse of a given degree for a selected point on the CIE 1931 chromaticity chart. GL Optic Spectrosoft software, on the basis of the measurement result, allows to determine in which degree of MacAdam ellipse the tested source falls in relation to the adopted reference point.
In real conditions, the chances of perceiving color differences depend on many factors, such as individual sensitivity to visual stimuli, the intensity of the light source, lighting conditions, the colors of the observed objects, etc.
The smaller the degree of the ellipse in which the light source is contained, the greater the uniformity of its color relative to a reference point.
How to interpret MacAdam ellipses in practice?
Descriptively, the differences in color perception depending on the degree of MacAdam ellipse can be described as follows.
1 MacAdam ellipse: this value indicates very high uniformity. Color differences are barely noticeable; colors appear almost identical to the average observer.
2 MacAdam ellipses: this value means high color uniformity, but already with greater possibility of noticing color differences. To the average observer, the colors still appear fairly uniform, but when comparing two different light sources, the color differences can be quite noticeable.
3 MacAdam ellipses: This value is considered the standard value for most applications. Color differences are noticeable, but they are not large enough to affect the quality of lighting significantly.
4 MacAdam ellipses: this value indicates fairly low color uniformity, and color differences are already quite pronounced. To the average observer, the colors will already seem quite inhomogeneous and may affect the quality of lighting.
5 MacAdam ellipses: This value indicates low color uniformity. Color differences are very pronounced and will affect the quality of lighting in a negative way.
6 and 7 MacAdam ellipses: these values indicate very low color uniformity. Color differences are extreme and will affect the quality of lighting in a significant and negative way. Light sources that fall within these ellipses should not be used in professional applications.
According to ECODESIGN requirements, a minimum of 10 samples are used to check color uniformity. What is tested is the deviation from the chromaticity center point (cx and cy) declared by the manufacturer or importer, expressed in the size (degrees) of the MacAdam ellipse formed around the chromaticity center point (cx and cy).
Some manufacturers’ data sheets include the term SDCM which in these publications means MacAdam ellipse. This term is inconsistent with the guidelines in the normative documents.
