Delta E blues

Visual colour difference formulae

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Colour is a stimuli sensation in the human visual system. It is perceived when the retina detects mixtures of incoming light waves and forwards the data to the brain where it is analysed and distinguished as colours. The instrument that best emulates the human eye’s ability to measure the appearance of light and colour is the spectrophotometer. This device also analyses the spectral components of light in a way similar to that of the human brain.
Prior to the introduction of the spectrophotometer in graphic arts production, it was the densitometer that helped us control colour on press. But the densitometer is actually colour blind, and it assumes that the incoming light is either filtered through a thin ink film which may consist of either cyan print, or yellow, magenta or black. If those inks called cyan, magenta, yellow and black really do comprise the correct and assumed colours, the densitometer can’t tell. The print will be expected to look good, assuming that we print with the correct target ink densities, and also assuming that the ink manufacturer has delivered ink with the correct colour appearance, and that the paper supplier has provided paper of good quality and whiteness. But if it is exact colours that we want, we can’t know just by relying on a densitometer.

Well then, if a spectrophotometer mimics the human colour perception system, a spectrophotometer should do the trick admirably. A spectrophotometer detects all the wavelengths that are visible for the human eye, which is roughly between 385nm (nanometer) to 720nm. But the problem is that most colours are made up of a mixture of light waves at different frequencies, and we need to choose a formula to describe a certain colour with a single set of precise numbers. One such popular formula is CIELab –- a three-dimensional colour model which defines colours numerically according to their degrees of blueness to yellowness along the a axis, and redness to greenness along the b axis and their degrees of luminance along the, er, L axis (it’s colour science remember) which is a lightness to darkness vertical measure.

So when printing according to SWOP or ISO 12647, you can check if your cyan ink, for example, conforms to the colour defined in those standards. If it doesn’t, you can detect the colour difference using a spectrophotometer and report the colour deviation between measured colour and expected colour as a Delta E value (see illustration 2). Traditionally, a Delta E value (often written ΔE) of one or lower is considered to be undetectable by human vision, while ΔE values of 2-4 are just noticeable. For people with normal colour discrimination capacity colour differences of ΔE 5 and just above are easy to detect, and at around ΔE 10 and above you start suggesting that it’s actually not the same colour anymore, because it doesn’t match at all.

So far, we have used the term ΔE as if there is only one formula to use when calculating a colour difference. But, in fact, colour scientists have come up with a series of alternative formulae over the years, so today we should actually specify what formula we use when calculating ΔE. In the above example, we referred to the formula from 1976 using quite straightforward CIELab values. But, in the same year, it was also suggested we use CIELuv, a perceptually uniform colour space, when calculating the ΔE. So, that is a second way to calculate colour difference.

But a third formula came about in 1984 when the Colour Measurement Committee of the Society of Dyes and Colourists of Great Britain presented a formula that should correspond closer to the eye’s sensitivity to hue, chroma and lightness. This formula is called the ΔE CMC, but it is a little tricky to refer to, since you have the ability to weight the ratio between lightness and chroma. The default ratio is 2:1, but you may use 1:1 as well. A variation of the CMC formula came about in 1994, and is referred to as CIE 94, or ΔE94. This also has different weighting functions for lightness and chroma.

The CIE 94 in turn was revised in the year 2000, and the ΔE formula of 2000, often written ΔE00, varies the lightness settings depending on the actual colour. For example the spot colour Pantone Reflex Blue has its maximum chroma at a low value of L (it’s a dark colour), while the process colour yellow has its maximum chroma at a high value for L (it’s a light colour).

While the ΔE00 formula perhaps is the least used of the above mentioned, it’s been adopted for use within the graphic arts by IFRA, the organisation for newspaper publishing, technology and newsprint. Newspaper publishers who want to make sure they print according the ISO standard 12647-3, can enrol in the IFRA Color Club quality control program. Measurements made in this procedure are calculated according the∆ΔE00 formula in regard to colour deviation.

When switching between different formulas for ΔE, you soon notice that when using the older formula from 1976, the value for  E is normally significantly higher than when using newer formulas. This is because the newer formulas try to better simulate the actual appearance over the whole gamut. So we need to interpret what a certain value really means, when deciding on tolerances. It’s not much use in selecting, for example, ΔECMC just because it seems to give lower values than when using the formula for ΔE76.

So what formula should one use and does it really matter? Well, if you ask colour scientists, it does matter, but the reasons for why it matters vary and the explanations are quite difficult to understand for a lay person. We asked Robin Myers at RM Imaging, a well-known and respected colour ‘guru’, which ΔE formula he would recommend? He told us: “It is still not clear to me which is best. There is a group of people trying to get ΔE 2000 accepted by everyone, but when the difference exceeds 5 ΔE some studies have shown it is no better than the CIE 1976 Lab ΔE for predicting perceived colour differences. Also, the CIE 1994 ΔE has a similar problem of being useful below 5 ΔE units but not as useful for larger differences.

“There is also a problem with any metric where values can be changed by the user which affect the result. For instance, the weighting factors in ΔE94, ΔECMC, and ΔE00. Often in use people will quote the ΔE value, but fail to mention the weighting factor values, with the result that the people involved are comparing different things without knowing it. For instance, some people will quote a CMC ΔE without mentioning whether they are using (2:1) or (1:1) for the weighting factors. Since many industries have problems getting their processes controlled to get down to a 5 ΔE difference, it is hard to definitively state which one is the best to use”.

We asked Dr Philip Urban at the Munsell Color Science Laboratory at RIT, the same question – which formula for calculating colour difference would he suggest? He answered: “The CMC colour difference equation corrects the major deficiency in CIELAB (so it is better than the ΔE76 formula) but the large number of constants suggests a level of precision and accuracy that cannot be supported on statistical grounds. A mathematical drawback is that the formula is not symmetric, but depends on a standard and a test colour. Switching standard and test colour changes the difference. The CIE ΔE00 formula is symmetric but it has some (small) discontinuities. The complexity of the formula cannot be justified statistically as well. On the other hand the formula accounts for the non-hue-linearity of the CIELAB space in the blue area (around hue angle 270 degree) by using a rotational term.

“The CIE ΔE00 formula outperforms the CMC formula in terms of fitting accuracy to various visual datasets. The main problem is that the observer variability is so high that it is possible that single observers prefer the CMC formula. However, the CIE ΔE00 should perform better in general.”

The conclusion for us is that for most designers, publishers and printers, the classical ΔE formula from 1976 will work well when defining colour tolerances for proofs and print. The important thing is to familiarise yourself with how to use a spectrophotometer and correctly interpret the results. After a while, you will develop a feel for what a certain value of ΔE means in terms of visual colour difference, depending on which formula you use. But make sure you communicate which formula you use when executing this quality control for printing!

Paul Lindstrom lectures at the Department of Media Production, Malmo University, Sweden, is the technical editor of Spindrift and a regular contributor to Indian Printer and Publisher and Packaging South Asia.