Measuring colours

By the kind permission of the Italian Ceramic Society in the person of the Chairman P. Zannini

Any body struck by a light source has the properties for absorbing the components of specific wavelengths and for reflecting and diffusing the others.  These are captured by a sense organ like the human eye, giving rise to a colour perception. Man is sensitive to wavelengths between 380 and 780 nm alone and if an object reflects all incident light, it appears white to the observer, whereas, if it absorbs it completely, it appears black. On the other hand, a body with the characteristic of absorbing some wavelengths differentially and reflecting others causes a precise colour sensation. Absorbing electromagnetic radiations, and thus the colour of a body, is closely connected to the atomic or molecular structure. In the region of the visible and in the ultraviolet this phenomenon is caused by interactions between incident radiation and the electronic layers outside the elements being examined. In the field of inorganic colouring agents, often associated with ceramic materials (although with due distinctions), compounds containing transition metals play a significantly important role. These elements are characterised by partially occupied d type orbitals and easily undergo electronic transitions when they are energised by energy sources like light. Indeed colour and intensity depend on the oxidation of the ion, on the surroundings and on the coordination geometry.

The human eye is capable of perceiving small colour differences thanks to the sensitivity of the retina. In standard lighting conditions, the eye has an excellent capacity for observing a particular object and for comparing the tone and intensity with a series of standards.   From an application viewpoint, the visual examination for measuring the colour, which remains qualitatively the most sensitive system, has several disadvantages:

The visual impression is difficult to express verbally and cannot give those numerical indications which are essential in industrial and commercial situations:  it is, therefore necessary to adopt an appropriately standardised instrumental measuring system to employ colour measurements that are accurate, repeatable and can be expressed in a numerical manner.

Apart from depending on the sensitivity of the human eye, as mentioned, colour also depends on the light source and on the colour nature of the surface to be investigated. Of these three variables the important one for a comparative analysis will obviously be the last one. Therefore, the other two variables will have to be established to know this. In other words a standardisation of both the energy distribution of the light and of the response of the average observer's eye at the various wavelengths is performed.  In this way the colour of the sample examined (or more correctly the colour sensation) depends exclusively on the nature of the sample.
It is, therefore, possible to objectify the vision of the colour by means of three attributes:   tone, saturation and luminance. The tone depends on the wavelength of the diffused light and makes the objects appear variously coloured. The saturation defines the intensity of a colour because it indicates how much it has been diluted with white light. Luminance, finally represents the total quantity of light which reaches the eye from the object without being absorbed. These three variables can be used in different ways to measure and define the colour, once the lighting conditions are also established. It has been observed that in the retina, to perceive the colour, there are three different centres of stimulus whose maximum spectral sensitivity is situated in red, in green and in blue.
Thanks to these observations the basic chromatic values of X (red), Y (green) and Z (blue) have been defined, which strongly indicate how much the three centres of stimulus are stressed by the chromatic impulse reaching the eye. The simplest system of measurement is based on the operation of the human eye and is made up of an instrument with three filters (tristimulus) through which the light reflected by the sample passes so that it can be measured; the spectral transmission of the three filters corresponds to the standard spectral values (tristimulus values) illustrated in fig.1.

Fig.1: tristimulus values

A widely known measuring method has been devised by the CIE (Commission Internationale d’Eclairage) and represents the fractions of red, green and blue with the symbols X,Y,Z respectively.
Since a colour cannot be easily recognised through the tristimulus values, a new system of description has been created which uses the letters x, y and z, which are connected to X,Y and Z according to the following relations:

                   X                                                  Y                
 x  =                                               y  =                                          z  =  1-x-y 
               X+Y+Z                                       X+Y+Z 

the values x, y and z are the chromatic coordinates in the CIE diagram fig. 2

  

Fig.2 : CIE chromaticity diagram

This diagram consists of a bell-shaped spectral curve and all the colours are located inside this line. At the centre of the bell, there is a point C which represents the chromatic tone of white; all the segments which reach this point with the curve, indicate the position of the colour of the same dominating wavelength. In practice the CIE diagram can be used, but some colours in it are much closer to one another (violet, blue) than others (green) and this uneven spacing represents a problem. Other methods were adopted to transform the tristimulus values: the most common ones include HUNTERLAB and CIELAB.

The HUNTERLAB system. The instruments developed by Hunter, which is widespread in the USA and Europe, adopt a system based on the coordinates L, a and b derived as follows:

                                 Fig. 3 : The system L. a and b.

In three-dimensional space:

With this method, according to the standards, it is possible to indicate the quantity, defined as a quadratic mean of the deviations and between sample and reference:
 

The CIELAB system. Since 1976 CIELAB has developed a new system of colour which redefines L, a and b and introduces another two polar coordinates H (hue) and C (chroma), which respective represent the hue and colour saturation.

with e regarding absolute white.
In this system it is then possible to define comparative measurements:

where P stands for test and R for reference.

   Fig. 4:The system L, a, b, H and C.

From the previously reported equations, it is obvious how the CIELAB and HUNTERLAB systems use the same symbols L, a and b, referring to measurement calculated in different ways from the tristimulus values. Moreover, the type of visualisation is extended by the rectangular coordinates a and b to the polar ones H and C.   As shown in the figure, this allows a better localisation of the colour on the plane, while the axis L continues to define the luminosity.

The characterisation of a colour will thus be defined by a COLORIMETRIC INSTRUMENT capable of attributing numerical parameters to:
:
L  which measures the luminosity and which varies from 0 (black) to 100 (white)
a  chromatic component which varies from red (+) to green (-)
b  chromatic component which varies from yellow (+) to blue (-)
H  represents the hue
C  the saturation