CIE ΔE* (Color Difference) Equations
Pictured above is a combination handheld spectrophotometer and densitometer, the SpectroDens 4. The intent of using deltaE (ΔE) is to describe the distance between two colors. The Just Noticeable Difference (JND) of deltaE is usually 1. In other words, if two colors have a deltaE less than 1 it is imperceptible and larger than 1 is perceivable. Unfortunately, due to the nature of human color perception (our eyes), the visual perception of colors is different. In general, our eyes are more sensitive to changes in Chroma than lightness. That means, the same deltaE between two yellows and two greens will very likely look different in our eyes. With that in mind, newer deltaE equations have been developed over the years and below is a list of 4 major formulas we might encounter in the color reproduction field.
Note: it is inadvisable to change from the default coefficient unless specified in the Print Quality Requirement from the print buyer
Picture 1. TECHKON SpectroDens deltaE equation settings
We have noticed an obvious tendency that more and more people are switching from ΔEab (ΔE76, dEab or dE76) to the ΔE2000 (ΔE00, dE2000, CIEDE2000 or dE00). If you are thinking about switching, or just curious about seeing the deltaE values from different equations, we have a free app to help. You can download and give it a try via the link here: download the deltaE calculator
Picture 2. TECHKON deltaE equation calculator

 ΔEab (aka. ΔE76, dEab or dE76) The CIEL*a*b* and ΔEab was introduced by the International Commission on Illumination (CIE) in 1976. Given two colors in the CIEL*a*b* color space, (L_{1}, a_{1}, b_{1}) and (L_{2}, a_{2}, b_{2}), the ΔEab formula is defined as: _{dEab equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html} Where, L_{1 }– the CIE L* value of reference color a_{1 }– the CIE a* value of reference color b_{1 }– the CIE b* value of reference color L_{2 }– the CIE L* value of sample color a_{2 }– the CIE a* value of sample color b_{2 }– the CIE b* value of sample colorThe ΔEab has been succeeded by other formulas that are discussed below, while it still bears useful information about the linear distance between two colors.

 ΔE_{CMC}(aka. dE_{CMC}, CMC l:c) The CIE is not the only party that defined color differencing equations. The Colour Measurement Committee of the Society of Dyers and Colourists (CMC) defined a new color difference method in 1984, named after the developing committee, CMC l:c. _{dECMC equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html}This equation takes the complexity of human color sensitivity/perception into consideration based on CIEL*C*h* – notation of colors. There are a few variations in the formula since it allows the user to assign different weights to its lightness (l) and chroma (c) factors. The CMC l:c was developed based on the visual evaluation of textile samples and human vision sensitivity levels in the lightness (l) and the chrome (c), the default ratio of l: c is 2:1, which doubles the tolerance of variation for lightness then that for chroma. The other common ratio of l:c is 1:1. Please consult with your supplier/buyer on which ratio to use if CMC l:c is selected for your production. Different ratios will result in varying sizes of tolerance ellipses, in other words, acceptability of color match.

 ΔE_{94 }(aka. dE94)> In 1995, the CIE revised the formula by introducing ΔE_{94} to address the color nonlinearity nature under ΔEab. Like CMC l:c method, ΔE_{94 }also uses CIEL*C*h* for calculating color differences. _{dE94 equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html}The ΔE_{94 }formula provides two coefficients, k and S, which are mostly based on tolerance data from RIT/Dupont from automotive paint research. The kcoefficients are known as parametric factors and refer to effects including colordifference judgement. The Scoefficients account for CIEL*a*b*’s lack of visual uniformity (Billmeyer, 2000). Most of the time, those two types of coefficients are preselected by the software developer based on either textile or graphic arts industry users. While, due to the limitation of the ΔE_{94 }that lacking accuracy in the blueviolet region of the color space, which eventually leads to the release of ΔE_{2000 }(Habekost, 2013)_{.}
 ΔE_{2000 }(aka. ΔE_{00}, dE2000, CIEDE2000 or dE00) The ΔE_{2000 }was first proposed by CIE TC147 in CIE Publ.142 in 2001 and standardized in 2013. You might find an old ISO white paper or IDEAlliance G7 Specification that still use ΔEab as the dominant color difference formula along with ΔE_{2000 }for information purposes only. Since 2013, both ISO and IDEAlliance has adopted ΔE_{2000} as the new industry standard for calculating color differences. _{dECMC equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html}
 Select a single method of calculation and use it consistently.
 Always specify exactly how the calculations are made.
 Never attempt to convert between two color differences calculated by different equations through the use of averaging factors.
 Use calculated color differences only as a first approximation in setting tolerance, until they can be confirmed by visual judgments – in other words, verify all calculation visually.
 Always remember that nobody accepts or rejects color because of numbers – it’s the way that it looks that counts.
kL  kC  kH  
ΔEab  N/A  N/A  N/A 
ΔE_{CMC}  2  1  N/A 
ΔE_{94}  1  1  1 
ΔE_{2000}  1  1  1 
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References Bruce Lindbloom, varies screenshots of different color differencing formula, April, 2017 (http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html) CIE TC 155 committee, Recommended Method For Evaluating The Performance of ColourDifference Formulae, CIE217:2016 (http://www.cie.co.at/publications/recommendedmethodevaluatingperformancecolourdifferenceformulae) Martin Habekost, Which color differencing equation should be used, International Circular of Graphic Education and Research, No. 6, 2013 (https://www.hdmstuttgart.de/international_circle/circular/issues/13_01/ICJ_06_2013_02_069.pdf) Billmeyer, S. (2000): ”Principles of Color Technology”, 3rd ed. New York: Wiley & Sons.