The MacAdam ellipse is a Standard Deviation Color Matching (SDCM) protocol for describing visibility of human observers of differences of sources, by how far they deviate from a reference color. Each ellipse represents a standard deviation from the reference (center) source. It is generally accepted that within 3 MacAdam ellipses, most observers cannot discern a difference between two sources. At 4 steps, a significant sampling of observers would see a color difference. At 7, virtually everyone will see a difference. For a more complete background, there are numerous sources describing these details, such as https://en.wikipedia.org/wiki/MacAdam_ellipse. The shape of the ellipses varies by color, as human visual differentiation changes in both spectral sensitivity as well as range between sources.
With this, it would seem pretty straightforward that when someone claims their product, LED, or light sources fall within 2 or 3 steps, that it can be assumed that the difference between two sources from that provider will be unseen. Unfortunately, a common miss-interpretation and incorrect application of the MacAdam ellipse protocol creates an actual deviation that can be as much as double that stated. The illustration below shows how this happens.
A large number of providers of sources and luminaires are using the reference of MacAdam ellipse, while ignoring that the entire system is based on a center reference point. The center of the ellipse to its edge are the parameters of deviation described, not edge to edge. The center can be either an industry standard, a specified x-y value, the center of a bin cluster, or any other reference the involved producers decide. However, the assumption made by too many is that any source that falls inside the total ellipse’s perimeter is within the range described for a particular step. For example, looking at the illustration, sources A and A are assumed to be only two steps apart, as thet fall inside the ellipse boundary. This is not correct. In fact, points A and A, both 2 steps from the center reference, are actually 4 steps apart, not two. To be clear, both are 2 steps from the center reference, not from one another. At 4 steps, a significant number of observers will see the color difference between A and A.
Points B and B are not 4 steps apart, even though they are both 4 steps from the center reference – making the two 8 steps apart. The same applies to points C and C, with 7 and 14 steps distance.
This is why, regardless of specifying the tightest bins available, LEDs and luminaires produce undesirable color differences that should not be visible at all. LED manufacturers and distributors compound this by binning products by quadrants around a reference center, claiming that all of the LEDs in all quadrants fall within the ellipse, thus are of that ellipses deviation range. This is incorrect by a factor of two as can be seen in the illustration below.
In the illustration above, the manufacturer will claim that all 4 sources, 1B, 2B, 3B and 4B fall inside the 4 step ellipse, thus are binned to within 4 step deviation. In real terms, the only thing that can be accurately said is that all 4 LEDs fall within 4 steps of the center reference. If 1B and 3B are compared, they will be visibly different, as they are actually 8 steps apart.
How this works in comparing one source to another directly, is that one of the two sources takes place of the “Center” reference, with the second deviating from that reference as center. If one looks at three sources side by side, a curious thing happens. While in isolation 1B and 3B will be close to the reference center, and thus somewhat un-discernible (4 step), the difference between 1B and 3B will actually be seen by the majority of observers (8 steps).
As it is with most metrics used to describe qualitative visual responses to light, stating a value without including its reference center point, produces inaccurate results. MacAdam ellipse values are meaningless unless the reference center is also stated. Further, all sources within the stated ellipse must occupy points that fall within the stated ellipse from one another, not simply from the reference center itself.
To make matters worse, when clusters of sources are described around either a standard center, a quadrant, or within the inscribed statistical area, differences between sources can become evident to observers, as they fall both outside the limits of deviations from one another, but cross the black body locus, to be seen different by shifting between magenta and green. Other factors include color shift effects from optic components, temperature, voltage and current effects, even circuit designs… all can have a significant impact on uniformity of color from LED to LED. Further, subtle changes in binning specifications between orders placed at different times, can create visible differences due to movement of the effective reference center, and comparisons between the clustering of bins from production run to production run. In other words, unless you have very specific data showing how a product (LED or luminaire) performs, it falls on trusting manufacturers themselves to take all of this into consideration to deploy products with solid color consistency, within products, and between products.