Instrument based methods of judging the colour appearance measure the colour co-ordinates of the test and of the standard panel and then determine the total colour difference dE*, and the component differences dL* (lightness) dC* (intensity of colour) and dH* (hue).

CIE L*a*b* Colour difference

Determination of dE*

This means that if a large number of people were asked to judge two samples with dE* = 1, about 50% of observers would say that there was a difference in colour, the other 50% would say the two colours matched.  An example calculation is given later.

Interpretation of dE*

The following is a guide to the interpretation of CIE L* a* b* colour difference values.

In practice a customer and a supplier would include a dE* limit as part of the colour specification of the object.  The limit could be larger than 1.0 or smaller than 1.0, depending on the type of product and the importance of obtaining an accurate colour match to the standard.

Reliability of a dE* < 1 pass/fail limit

The correct answer as to whether a trial colour matches that of the standard is the majority decision of a group of colourists.  An instrumental assessment based on the condition that dE* must be less than 1 for a match, will disagree with the majority about 19% of the time.  Instrumental judgements made this way are no more reliable, on average, than judgements made by a colourist.

The instrumental method has the advantage of being repeatable, most instruments and sample pairs can be measured with a repeatability of dE* to better than ±0.20.

Colour difference splitting dL*, dC* dH*

Calculation

Subtracting the contributions of the lightness (dL*) and chroma (dC*) differences from the total colour difference (dE*) leaves the hue difference (dH*).

The hue difference equation cannot provide a sign for the value of dH*.  The convention is that it takes the same sign (±) as the difference between the hue angles of the trial and standard.

Interpretation

dL*, lightness difference

dC*, chroma difference

dH*, hue difference

Hue difference description

The hue difference is described using one or more of the primary hue names yellower, greener, redder or bluer.  For example if an orange coloured standard is considered then the trial will be described as either yellower or redder than the standard.

The CIE L*a*b* system provides a method of obtaining the hue difference description from the positions of the trial and standard on the a* b* plane.  An arc is imagined drawn from the position of the standard to the trial and then continued on around the hue circle.  The hue associated with the first axis crossed by the arc is quoted followed, enclosed in brackets, by the hue of the second axis crossed.  This is illustrated in Figure 3 and Figure 4.

The appropriate hue difference terms are those neighbouring the standard in the hue circle, as shown in Table 1.

Table 1: Hue difference terms

Example colour difference calculation

Setting pass/fail tolerance values

A reliable method of assessment of colour difference is important for both scientific and economic reasons.  The incorrect rejection of a batch of material has the consequence of extra cost and time in unnecessary colour correction.  Costs are also incurred if a batch is incorrectly accepted at an early stage in a process and then found unacceptable after further steps in manufacture have been carried out.

Consider the case of a manufacturer making repeated batches of a product based on matching to the same standard colour.  The small variations in the manufacturing process will produce batches whose colour co-ordinates in L* a* b* space will lie in a small volume surrounding the standard.  Some of these batches will have been judged visually as an acceptable match to the standard colour and others rejected.

It is possible to imagine drawing a smooth, three-dimensional surface around the standard such that the majority of points representing accepted batches lie within the volume enclosed by the surface.  This is known as an acceptance ellipsoid since, on average, the shape of the volume is ellipsoidal.  Extensive investigation has shown that the shape, size and orientation of the acceptance ellipsoid in CIE L* a* b* space varies with the colour of the standard.

The CIE L*a*b* colour difference equation assumes, irrespective of the colour of the standard, the acceptance volume is a sphere of radius 1 unit.  Unfortunately pass/fail decisions based on the CIE L*a*b* (1976) equation with a limit of dE* = 1 are, on average, less reliable than visual judgements made by a single colourist.  The simplest method of improvement is to assign individual tolerances either to dL*, da* and db* or to dL*, dC* and dH*.

dL* da* db* acceptance limits

The colour of the standard is measured and plotted in colour space as shown in Figure 5.  In this case the standard is a medium lightness, intense, cyan blue colour.

Figure 7 illustrates this process by considering just the hue plane, a* b*.  In this plane the true acceptance regions are ellipsoid shaped areas roughly oriented towards the neutral point (0, 0).  The tolerance limits, da* and db*, define a rectangular area that encloses the area of true acceptance and also a significant region in which colours should be rejected.  The reliability of instrumental pass/fail judgements based on setting individual tolerances for dL*, da* db* is better than CIE dE* judgements, but by no means the best that can be obtained.

dL* dC* dH* acceptance limits

The system where individual limits to dL*, dC* and dH* are set is shown in Figure 8.  The acceptance volume is similar in shape to that shown in Figure 6, but has a different orientation.  The orientation of the dL* dC* dH* acceptance volume relative to the L* a* and b* axis changes as the standard moves in colour space, as illustrated in Figure 9.

It is clear from Figure 9 that the tolerance area defined by limits dC* and dH* will still include an area in which colours should be rejected.  However, the size of this "incorrect decision" area is less than that when tolerances are based on da* db*, (illustrated in Figure 7).  The change in orientation of the dL* dC* dH* tolerance volume with position of the standard is similar to the change in orientation of the acceptance ellipsoid.  Therefore pass/fail judgements based on dL*, dC* and dH* tolerance limits are significantly more reliable than those based on dL*, da* and db*.

Colourist terms versus colorimetric terms

The terms used routinely by people working in the colour using industries are often different from the set defined by the CIE.  Typically the Lighter-Darker judgement is retained, a second adjective pair is used to describe a coloration strength difference and a third pair is used to describe a difference in the purity of the colour.

It is often possible to associate the use of these terms with particular directions of colour difference on a plot of dC* versus dL*.  The position of the standard is at the origin and the trial is represented by the point  dC*, dL*.  This is illustrated for the paint and the textile industry in Figure 10 and Figure 11 respectively.

The use of the word pair stronger/weaker often leads to confusion.  Colourists in the paint and ink industries use the pair to describe an excess or deficit of colorant in the trial compared to the standard, whereas the CIE use the pair to describe a higher or lower chroma of the trial compared to the standard.  In some trial-standard comparisons the two judgements would agree while in others they would not.

In case 2, the colourist would still describe the trial as stronger than the standard, however in terms of the numerical chroma difference (dC* < 0 ), the trial is judged less intense (weaker) than the standard.