3.12 c hromaticity diagram

CHROMATICITY DIAGRAMSTo represent the other two dimensions of colour it is usual to first define Chromaticity coordinates (x, y and z) and then plot y against x (Eqn 3.19):

CHROMATICITY DIAGRAM

From Eqn 3.19 it follows that x + y + z = 1 for all colours;

it is therefore only necessary to quote two of the chromaticity coordinates,

and these can of course be plotted on a normaltwo-dimensional graph.

It can also be shown that X and Z can easily be calculatedfrom x, y and Y; hence the latter set is an acceptable form of specification, and consideration of Y values and plots of y against x should cover all possible colours. A plot of yagainst x is called a chromaticity diagram. Such a plot is shown in Figure 3.7, in which thespectrum colours are plotted.

From Eqn 3.19 it follows that

x + y + z = 1 for all colours;

A plot of y against x is called a chromaticity diagram.

Such a plot is shown in Figure 3.7, in which the

spectrum colours are plotted.

From Eqn 3.19 it follows that x + y + z = 1 for all colours;

The line joining the spectrum colours is known as the

Spectrum Locus.

The x and y values for each wavelength were obtained from the correspondingdistribution coefficients (1931 standard observer in this case) (Eqn 3.20):

where pure colours fall on the chromaticity diagram. Wavelengths around 480 nm look blue, wavelengths around 520 nm look green, while wavelengths from 630 nm to the end of the spectrum look red.

Colours with x and y values close to the spectrum locus will be very saturated colours with hues close to those of the corresponding spectrum colours. For other colours the problem is more difficult.

Consequently. in attempting to predict colour appearance from

chromaticity coordinates or tristimulus values

we must be careful to ascertain which illuminant has been used.

Strictly speaking, in any applicationwe should also be careful to ascertain which standard observer and which set of observing and viewing conditions are appropriate, but these are not normally as important as the illuminant.

If we now consider colours relative only to illuminant C (surface colours illuminated by illuminant C

and coloured lights with the eye adapted to illuminant C),

the positions for other colours can be deduced from a simple property of the chromaticity diagram.

two points on the chromaticity diagram,

If two coloured lights are represented by two points on the chromaticity diagram,

then any additive mixture of the two will correspond to a point on the straight linejoining the two points.

Since the spectrum locus is always concave, it follows that all real colours (each of which must correspond to one or more wavelengths additively mixed) must fall within the area bounded by the spectrum locus and joining the ends.Mixing white light (illuminant C) with monochromatic light of wavelength 520 nm will give points exactly on the line CG in Figure 3.7.


Since light of 520 nm looks green, the mixtures will appear various shades of green, from white through pale greensto the saturated green of the spectrum colour.

(The points will fall exactly on the line;the colours seen will not necessarily look exactly the same hue.

What is seen depends on many factors, but generally mixing white light and a spectrum colour will produce aslight but significant change in hue.)


All colours lying on the line CG may be described

as colours having a dominant wavelength of 520 nm.

Similarly mixing white light and light of wavelength 700 nm (red) will produce a range of pinks and reds.

In general, the more the colour resembles the spectrum colour,

the closer will the point be to the spectrum locus,

while near-neutral colours will correspond to points close to C.


For colour F in Figure 3.7 this attribute is defined by the ratio CF : CG, known as the

excitation purity of colour F. As the excitation purity increases the colour will look lesslike a neutral colour and more like the corresponding spectrum colour.

Samples with excitation purity as low as 0.1 (or 10%) will look distinctly different from neutral. Even very saturated-looking samples, particularly greens, will have excitation purities far from 1 (or 100%).

As the excitation purity increases the colour will look lesslike a neutral colour and more like the corresponding spectrum colour.


For the sample used as an example for the calculation of tristimulus values X = 38, Y = 45 and Z = 21, hence x = 0.365 and y = 0.433. Remembering that the tristimulus values were calculated for illuminant A,

we can see that the dominantwavelength is about 500 nm and hence the sample is a green-blue



For the sample used as an example for the calculation of tristimulus values X = 38, Y = 45 and Z = 21, hence x = 0.365 and y = 0.433.

If, however, the illuminant was mistakenly taken to be C the dominant wavelength would have been estimated to be about 580 nm and the colour judged to be yellow!


Chromaticity diagramIt was stated in section 3.11 that the Y scale is far from

uniform. The same applies tothe xy diagram; equal distances in the diagram do not

correspond to equal visual differences.

For a fixed difference in x and y the difference seen would be much smallerfor a pair of green samples than for pairs of blue or grey samples.

It has been emphasised that colour is three-dimensional. Thus no two-dimensional plot can represent colour

completely.

In the case of the chromaticity diagram it is simplestto regard the missing factor as the Y tristimulus value.

two points on the chromaticity diagram,Consider a sample where R = 10% at all

wavelengths.

If the sample is illuminated by illuminant C the tristimulus values are simply one-tenth of the corresponding values for the

sample described in Appendix 3 (where R = 100% at all wavelengths) and the chromaticity coordinatesare the same:

x = 0.310 and y = 0.316.

Both samples are neutral and the differencebetween the two is indicated by the Y tristimulus values. A neutral sample with a Y value of 100 would be white, while one with a Y value of 10 would be a darkish grey.



All other samples with similar chromaticity coordinates would look neutral,

but could be white, black or any intermediate shade of grey.

(All samples with constant R valueswill look neutral, but the converse does not hold; many neutral-looking samples have R values that vary considerably with wavelength.) Similarly a colour fairly close to neutral but with a dominant wavelength of 650 nm would look a pale pink if the Y value was very high (the colour was very light), but a reddish grey if the Y value was low (the sample was dark).

two points on the chromaticity diagram,In general, any one point on the chromaticity diagram

corresponds to a range of colours differing in lightness, and this should always be kept in mind when trying to visualise the colours corresponding to particular chromaticity coordinates. The relationships between x, y and Y values on the one hand and the visual appearance on the other could be developed much further, but it is recommended that, if possible, students should measure their own samples. With modern instruments a student can measure dozens of samples in an hour, and compare the readings obtained with the visual appearance of the samples.

This is far better than relying on the vague terms such as grey, red, pink and so forth that have to be used in a textbook. Particular attention should be paid to colours such as browns, fawns and purples.

After a little practice it is instructive, for each new sample, to estimate the dominant wavelength, excitation purity, x, y and Y before making measurements.

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3.12 c hromaticity diagram