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# 3.12 c hromaticity diagram

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### 3.12 c hromaticity diagram

1. 1. To represent the other two dimensions of colour it is usual to firstdefineChromaticity coordinates (x, y and z)and then plot y against x(Eqn 3.19):
2. 2. CHROMATICITY DIAGRAM
3. 3. From Eqn 3.19 it follows thatx + y + z = 1 for all colours; it is therefore only necessary to quote two of the chromaticitycoordinates,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 ofspecification, and consideration of Y values and plots of yagainst x should cover all possible colours. A plot of yagainst x is called a chromaticity diagram. Such a plot isshown in Figure 3.7, in which thespectrum colours are plotted.
4. 4. From Eqn 3.19 it followsthatx + y + z = 1 for allcolours;A plot of y against x iscalled a chromaticitydiagram.Such a plot is shown inFigure 3.7, in which thespectrum colours areplotted.
5. 5. From Eqn 3.19 it follows thatx + y + z = 1 for all colours;The line joining the spectrumcolours is known as theSpectrum Locus.The x and y values for eachwavelength were obtained fromthe correspondingdistribution coefficients (1931standard observer in this case)(Eqn 3.20):
6. 6. 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.
7. 7. Consequently. in attempting to predict colour appearance from chromaticity coordinates or tristimulus valueswe must be careful to ascertainwhich illuminant has been used.Strictly speaking, in any applicationwe should also be careful to ascertainwhich standard observerand which set of observing and viewing conditions areappropriate,but these are not normally as important as the illuminant.
8. 8. If we now consider colours relative only to illuminant C (surface colours illuminated by illuminant Cand coloured lights with the eye adapted to illuminant C), the positions for other colours can be deduced from a simple property of thechromaticity diagram.
9. 9. two points on the chromaticity diagram,If two coloured lights are represented bytwo 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 realcolours (each of which must correspond to one or more wavelengthsadditively mixed)must fall within the area bounded by the spectrum locus and joiningthe ends.Mixing white light (illuminant C) with monochromatic light ofwavelength 520 nm will give points exactly on the line CG in Figure3.7.
10. 10. two points on the chromaticity diagram,Since light of 520 nm looks green, the mixtures will appear variousshades 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 lightand a spectrum colour will produce aslight but significant change in hue.)
11. 11. two points on the chromaticity diagram,All colours lying on the line CGmay be describedas colours having a dominantwavelength of 520 nm.Similarly mixing white light andlight of wavelength 700 nm (red) willproduce a range of pinks and reds.In general, the more the colourresembles the spectrum colour,the closer will the point be to thespectrum locus,while near-neutral colours willcorrespond to points close to C.
12. 12. two points on the chromaticity diagram,For colour F in Figure 3.7 this attribute As the excitationis defined by purity increases the colour will the ratio CF : CG, known as the look less like a neutral colour and moreexcitation purity of colour F. like the correspondingAs the excitation purity increases the spectrum colour.colour will look lesslike a neutral colour and more likethe corresponding spectrum colour.Samples with excitation purity aslow as 0.1 (or 10%) will lookdistinctly different from neutral.Even very saturated-lookingsamples, particularly greens, will haveexcitation purities far from 1 (or
13. 13. two points on the chromaticity diagram,For the sample used as an example for As the excitationthe calculation of tristimulus values purity increases the colour willX = 38, look less like a neutralY = 45 and colour and moreZ = 21, like the correspondinghence x = 0.365 and y = 0.433. spectrum colour.Remembering that the tristimulusvalues were calculated for illuminantA,we can see that the dominantwavelength is about 500 nm andhence the sample is a green-blue
14. 14. two points on the chromaticity diagram,For the sample used as an example for As the excitationthe calculation of tristimulus values purity increases the colour willX = 38, look less like a neutralY = 45 and colour and moreZ = 21, like the correspondinghence x = 0.365 and y = 0.433. spectrum colour.If, however, the illuminant wasmistakenly taken to be C thedominant wavelength would havebeen estimated to be about 580 nmand the colour judged to be yellow!
15. 15. 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.
16. 16. two points on the chromaticity diagram,Consider a sample where R = 10% at allwavelengths. As the excitation purity increases the colour will look lessIf the sample is illuminated by illuminant C the like a neutral colour and moretristimulus values are simply like theone-tenth of the corresponding values for the corresponding spectrumsample described in Appendix 3 colour. (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 tristimulusvalues. A neutral sample with a Y value of 100would be white, while one with a Y value of 10would be a darkish grey.
17. 17. two points on the chromaticity diagram,All other samples with similar chromaticity coordinates would lookneutral,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 considerablywith wavelength.)Similarly a colour fairly close to neutral but with a dominantwavelength of 650 nm would looka 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).
18. 18. 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 mindwhen trying to visualise the colours corresponding to particular chromaticitycoordinates.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 ownsamples.With modern instruments a student can measure dozens of samples in an hour, andcompare 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 forththat have to be used in a textbook. Particular attention should be paid to colourssuch as browns, fawns and purples.After a little practice it is instructive, for each new sample, to estimate thedominant wavelength, excitation purity, x, y and Y before making measurements.