What are MacAdam ellipses and how they affect LED color consistency

What Macadams Ellipses mean - for dummies...

MacAdam ellipses provide a guideline as to how accurate the average person’s color vision is, and how good they are at distinguishing between similar colors. MacAdam ellipses, like just about all photometric topics, are not absolute measurements based on some definable physical property such as weight, length or time; instead, they are derived from statistical measurements of the visual properties of samples of the population. There are no absolutes in vision science—just comparative statistics. All we can measure is how the value of a particular parameter compares to what the average person sees

Example on the diagram that shows a close up of the 3200 K point with the black body line and three sizes of MacAdam ellipses, 2-step, 4-step, and 7-step

See our range of 3 step macadam LED Strip

Explained in more detail...

SDCM is an acronym which stands for Standard Deviation Colour Matching. SDCM has the same meaning as a “MacAdam ellipse”. A 1-step MacAdam ellipse defines a zone in the CIE 1931 2 deg (xy) color space within which the human eye cannot discern the color difference. Most LEDs are binned at the 4-7 step level, in other words, you certainly can see color differences in LEDs that are ostensibly the same color.

MacAdam Ellipse The science behind color difference specifications was established by Dr. David MacAdam in 1942 [MacAdam, D.L., Visual Sensitivities to Colour Differences in Daylight, J.Opt.Soc.Am. 32, 247 (1942)].
MacAdam’s experiments relied upon visual observation of the so-called Just Noticeable Colour Difference (JND) between two very similar colored lights. Just Noticeable Difference is defined as the color difference where 50% of observers see a difference and 50% of observers do not see a difference. The zones with standard deviations of color matching (SDCM), were found to be elliptical in the CIE 1931 2 deg observer color space. The size and orientation of the ellipses varied greatly depending upon the location in the color space diagram. The zones were observed to be largest in the green and smaller in the red and blue.

Due to the variable nature of the color produced by white light LEDs, a convenient metric for expressing the extent of the color difference within a batch (or bin) or LEDs is the number of SDCM (MacAdam) ellipses steps in the CIE color space that the LEDs fall into. If the chromaticity coordinates of a set of LEDs all fall within 1 SDCM (or a “1-step MacAdam ellipse”), most people would fail to see any difference in color. If the color variation is such that the variation in chromaticity extends to a zone that is twice as big (2 SDCM or a 2-step MacAdam ellipse), you will start to see some color difference. A 2-step MacAdam ellipse is better than a 3-step zone, and so on.

It should be noted that SDCM ellipses are often shown in the CIE color space diagram at a ten times magnification (see image to left) because they would otherwise be too small to be seen clearly when viewed in the complete CIE diagram.
MacAdam’s experiments demonstrated that the size of an SDCM ellipse is quite small, which means that the human visual system is very good at discriminating color differences when viewing two light sources at the same time. If we consider the size of the 1-step SDCM ellipse at an arbitrary 3,000K color temperature, the CCT range is ±30K, and the corresponding u’v’ range (the chromaticity coordinates in the 1976 CIE Uniform Colour Space) is ±0.001. In other words, if we view two LEDs with a CCT difference of more than 60K, the chances are that we will see a color difference. The table below relates the number of SDCM ellipse steps to the range of CCT and chromaticity coordinates for a 3000K color temperature light source.

SDCM CCT @ 3000K ΔUV
1x ±30K ±0.0007
2x ±60K ±0.0010
4x ±100K ±0.0020
7-8x ±175K ±0.0060

Within the lighting industry, reference is often made to the standard IES LM-79-08 “Approved Method of Electrical & Photometric Measurements of Solid-State Lighting Products" published by the Illuminating Engineering Society of North America (IESNA). This, in turn, references the American standard ANSI C78.377-2008 “Specification for the Chromaticity of Solid State Lighting Products” which places white light LEDs used for illumination into standard color groups which all have the same “nominal” correlated color temperatures (CCTs). The size of the ANSI C78.377 nominal CCT quadrangle is a 7-step MacAdam ellipse. A 7 to 8-step SDCM is currently representative of the variation in chromaticity of high brightness white LEDs used for illumination.