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Basic concepts of colour measurement

Colours in our Daily Life

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People involved with colour and colour reproduction needed a unique and unambiguous specification of colour, leading to colours being expressed in numeric codes, which is explained in detail in this article like the perception of colours, the representation of colours, and other interesting semantics of it.

Uniform Colour Scales

CIE tri­stimulus values or chro­maticity coordinates are not very convenient for identifying the colour of the objects, because these were designed for colour stimuli of different modes. None of the values is directly correlated with any visual attributes of colo­ur. Only Y value has a high correlation with luminance and object lightness. The spacing of colours in the chromaticity diagram is not visible uniform. A number of uniform colour scales are, therefore, developed which can represent colours with equal visual spacing and are directly related to meaningful attributes of colour appearance.

In 1976 CIE recommended CIELUV and CIELAB uniform colour spaces. Colourant industries were in favour of a formula similar to Adam-Nickerson (AN40) formula, popular at that time. The CIELAB formula was acceptable as colour-difference values were about 1.1 times those produced by AN40 formula. On the other hand, television industries preferred a colour space (CIELUV) associated with a chromaticity diagram because of its simple way of presentation of the additive mixture which also occurs in televi­sion and other display devices. No simple relation exists between the two colour scales.

Both CIELUV and CIELAB formulae are plotted on rectangular coordi­nat­es. Lightness L* function is the same for both colour spaces and is represented by the formula,  L* = 116(Y/Yn)1/3 – 16    if Y/Y= 0.008856

For CIELAB Colour Space,        Red-green attribute,      a* = 500[f(X/Xn) – f(Y/Yn)]

Yellow-blue attribute,     b* = 200[f(Y/Yn) – f(Z/Zn)]

Subscript n represent nominally white object colour stimulus given by a perfect reflecting diffuser as reference surface illuminated by standard illuminant. For standard daylight illuminant D65, the values are: Xn = 95.047, Yn = 100.000, Zn =108.883.  The white object has been taken into account because we perceive colours in relation to surrounding colours.

In recent years efforts have been made to define CIE correlates for perceptual attributes like lightness, chroma and hue.  Hence, two new attributes corresponding to visual attributes have been derived from a* and b* values namely:

Metric chroma, C*ab = [(a*)2 + (b*)2] 1/2

Hue angle, h = tan -1 (b*/a*).

CIELAB colour space is shown in Figure 5. Lightness L* is represented in vertical axis with white (L* = 100) at the top and black (L* = 0) at the bottom. Chromatic colours are represented by two opponent a* and b* axes. Red and green are represented by a* axis – the positive values are for red and negative for green. Similarly, positive b* values are for yellow and negative b* values are blue.

Figure 5. CIELAB 1976 Uniform colour space.

Colour Difference

Measurement of difference in colour between two objects is one of the most complicated aspects of colour vision. The colour discrimination may be general/overall or of a specific psychophysical attribute like hue, chroma or lightness. For colourant users like textile, leather, paper or paint industries, the difference in colour of two specimens namely a standard and a sample or of different portions of a coloured specimen may be more important than the measurement of absolute colour (Luo, 1986). The prime difficulty is that the perception of colour-difference by an individual is not a precise phenomenon and may vary on successive assessment (Zeller and Hemmendinger, 1978). Colour-difference perception and evaluation may also vary widely among individuals.

The colour-difference evaluation is necessary for day to day colour control and for colour matching in colouration industries like textile, paint etc. Colour-difference formulae have accelerated the instrumental pass-fail device a success.

The colour differences are calculated by subtracting values of the standard from the respective values of the sample.

The total colour-difference (ΔE) is intended to be single number metric for pass/fail decisions and in the CIELAB system ΔE is given by the following equation:

ΔE = [ (ΔL*)² + (Δa*)² + (Δb*)² ]1/2

In addition to the overall colour difference (ΔE), the difference in individual parameters of the standard and a sample are also estimated e.g. ΔL = L (sample) – L (standard).

These may indicate some specific visual difference such as

if ΔL < 0 or > 0, the sample is darker or lighter respectively,

if Δa* < 0 or > 0, the sample is greener or redder respectively,

if Δb* < 0 or > 0, the sample is bluer or yellower respectively.

ΔE (CIELAB) values are not always reliable in predicting perceptible differences between object colours, especially when the variations are in different visual attributes. This is due to the fact that the visual spacing along L, a* and b* axes are unequal.

The formulae based on surface-mode colour discrimination data mainly aimed at single number shade-passing. Much of the available visual data related to physical samples are supplied by the textile and dye industries, where prime criteria are whether the colours will be acceptable against the respective standards.

The main reason for poor correlation with visual data of the earlier formulae was an equal weighting of the colour parameters. The weighted values of lightness, chroma and hue showed significant improvement in the performance of colour-difference equations. The weights can be determined by empirical fitting to experimental data-sets. These formulae are optimized by visual acceptability/ perceptibility scaling. They represent most closely the average visual results of judgments of the colour difference of textile and other physical samples under normal evaluation conditions (Kuehni, 1984)

A few colour-difference formulae based on surface-mode colour discrimination data are:

  • JPC79 colour-difference Formula
  • CMC (l:c) colour-difference Formula
  • BFD (l:c) colour-difference Formula
  • CIE 94 colour-difference Formula
  • CIE 2000 colour-difference Formula

However, none of the above formulae is completely satisfactory and acceptability of a particular formula is decided mutually by producers and users/sellers.

Colourimetry is the science of quantitative measurement of colour. Even though study on colour science started as far back as the Newtonian age, research continues even today. Colour Science is a vast field. Hunt (1977) identified three phases of development of colourimetry – colour matching, colour difference evaluation and lastly, prediction of colour appearance. It is now possible to predict the colour appearance of an object under a test illuminant from the colour appearance data under a reference illuminant with the help of complex mathematical transformations.


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  • Kuehni  R. G. (1984). Colour Technology in the Textile Industry, AATCC, U.S.A., pp.123.
  • Kuehni R. G. (2005), Colour: an introduction to practice and principles, New Jersey, Wiley-Interscience.
  • Leblon C. Jacob (1756). Coloritto or the harmony of colouring in painting, English and French
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  • Luo M.R.  (1986). New Colour Difference Formula for Surface Colours, Ph.D Thesis, University of
  • Bradford, Bradford, U.K.
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  • Optical society of America (OSA) (1953). The science of color,   Committee on Colorimetry, Thomas Y. Cromwell, New York.
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  • Roy Choudhury A.K. (2010). Chapter 2. Scales for communicating colour in Colour Measurement: Principles, advances and industrial applications. Edited by M L Gulrajani, Woodhead Publishing Series in Textiles No. 103, ISBN 1 84569 559 3.
  • Wyszecki G (1986), Colour Appearance, Chapter 9 in Handbook of Perception and Human Performance, New York, Wiley.
  • Zeller R.C. and Hemmendinger H. (1978). Evaluation of Color-difference equations: a new approach, AIC Color 77, Bristol: Adam Hilger.
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