What is difference between SDCM & MacAdam Ellipses


In the study of color vision, a MacAdam ellipse is a region on a chromaticity diagram which contains all colors which are indistinguishable, to the average human eye, from the color at the center of the ellipse. The contour of the ellipse therefore represents the just noticeable differences of chromaticity. Standard Deviation Color Matching in LED lighting uses deviations relative to MacAdam ellipses to describe color precision of a light source.

MacAdam ellipses for one of MacAdam's test participants, Perley G. Nutting (observer "PGN"), plotted on the CIE 1931 xy chromaticity diagram. The ellipses are ten times their actual size, as depicted in MacAdam's paper.


Talking Photometry: LED Colour Difference Metrics: SDCM & MacAdam Ellipses

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) colour space within which the human eye cannot discern colour difference. Most LEDs are binned at the 4-7 step level, in other words you certainly can see colour differences in LEDs that are ostensibly the same colour.

Due to the variable nature of the colour produced by white light LEDs, a convenient metric for expressing the extent of the colour difference within a batch (or bin) or LEDs is the number of SDCM (MacAdam) ellipses steps in the CIE colour 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 colour. If the colour 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 colour 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 colour space diagram at a ten times magnification (see image to above, 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 vision system is very good at discriminating colour 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 colour 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 colour difference. The table below relates the number of SDCM ellipse steps to the range of CCT and chromaticity coordinates for a 3000K colour temperature light source.

SDCM    CCT @ 3000K    ΔUV
1x           ±30K                     ±0.0007

2x           ±60K                     ±0.0010
4x           ±100K                   ±0.0020
7-8x       ±175K                   ±0.0060


White light surrounds us, and if we pause to look, we will see that the color of white light varies dramatically from warm reddish yellows to cool blue bright whites. While we can all “feel” the quality and nature of white light, it’s typically described with two numbers: Correlated Color Temperature (CCT) and Color Rendering Index (CRI).

The black body locus defines white light within the CIE color space.

CCT is a statement of how warm or cool the light looks. The lower the number, the more yellowish and warm it seems to us. The higher the number, the brighter and cooler it seems. A typical halogen bulb has a CCT of about 3000K (K = Kelvin), and moonlight is approximately 4100K. Xicato tunes its modules to provide light output measured as 2700K, 3000K, 3500K and 4000K.

Color rendering is a measure of how accurately colored objects are rendered when lit with a particular light source.

If we look at the CIE color space often used to define and describe white light, we can see a black line running through the center; this is called the black body locus. As long as the light stays on or about the line, our eyes perceive it as white. If the white light shifts above the line, it will tend to display a green tint; if it shifts below the line, it will display a pink tint. The measurement of visible difference is described as a MacAdam Ellipse.

The measurement of visible difference in color shift within the CIE color space is typically described as a MacAdam Ellipse.


The smaller the shift along the MacAdam Ellipse, the less noticeable the color shift will be to the human eye.


In general, a shift of 1 MacAdam Ellipse (1 step, or 1 SDCM) will not be noticeable to the human eye, and if the shift is along the black body locus, it’s generally not noticeable for 2 steps, or 2 MacAdam Ellipses. Once the white color has shifted 3 steps, the change can be detected by the human eye.

In 1931 the CIE (Commission Internationale de l’Eclairage) published its famous Chromaticity graph. It meant that every colour that could be created by a mixture of red-green-blue could be given a unique number on the graph. That graph, and its successors, have been the mainstay of light-colour science ever since.

In 1942, David MacAdam, a physicist and colour scientist working with Kodak, posed the question: does every point on the CIE graph really represent a different colour ? 

He ran a series of tests and demonstrated that, rather than a single colour being indicated by a point on a graph, it could be represented by an ellipse surrounding that point. Within the ellipse there would be no discernible difference in colour from the reference point at its centre.

And that was the birth of the MacAdam Ellipse.

The 1931 Chromaticity graph


Why is it important?

Until the introduction of the LED there was very little practical use for the MacAdam ellipse. Light sources were mass-produced and colour tolerances were sufficiently controlled that very few people complained about colour inconsistencies between two lamps.

However, with the introduction of the LED module, the method of light production changed. The manufacturing process is such that millions of LED chips are produced from an assembly line every day and it’s inevitable that there will be colour inconsistencies between individual chips and the modules built from them.

In the early days of LED production, quality of product was determined by the accuracy of the binning process of chips. This was the way that LEDs were separated into separate bins according to their colour output. It was an expensive and time consuming process. Improvements in LED module design have brought the Macadam Ellipse to the forefront of the colour checking process.

A perfect LED module assembly line will produce batches of modules operating within a once MacAdam Ellipse. There will be no discernible difference between any of the module outputs. LED modules produced at this level are used where colour performance and accuracy between fixtures is vitally important. Typically, good LED modules are produced within a two to three MacAdam ellipse range, here will be a visual difference if you look for it, but it is minor and generally considered to be acceptable in commercial usage.

Cheaper products will often use LED modules that have a range of MacAdam Ellipses beyond four, some going as high as eight. Fixtures using such modules need to be used with care. There may be general commercial of industrial areas where they are acceptable, but any requirement for colour sensitivity would rule them out.


Every led manufacturer believes that with better light, shoppers will buy more, diners will order more and guests will be happier and feel more comfortable. In turn, for owners, operators and managers of environments, better lighting will contribute to higher sales, margins and brand perception. The true value of Xicato light lies in delivering on the aesthetic and economic potential of LEDs: the quality of light, its efficacy and ownership cost for retail stores, hotels, restaurants and bars, architectural environments and more.

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