phy1020.DVI

Appendix S

CIE Chromaticity Coordinates

In this appendix, we’ll look at some of the details of the CIE chromaticity diagram (Fig. 56.4) and how
coordinates on the diagram are computed. The mathematics involves the integral calculus, so is outside the
usual scope of this course.
Suppose we have a colored object, and we wish to find its coordinates.x;y/on the CIE chromaticity
diagram. We begin by measuring thespectral power distributionI./of the object: this is the fractionIof
light reflected from the object at each wavelength ( ), under some standard illumination conditions. We also
need a set of “weighting” functions called theCIE color matching functions.x;y; ́/; these are defined as
shown in Figure S.1. Then thetristimulus values.X;Y;Z/are given by

XD

Z 1

0

I./x./d (S.1)

YD

Z 1

0

I./y./d (S.2)

ZD

Z 1

0

I./ ́./d (S.3)

Roughly speaking,Xmeasures the “redness” of the object,Y its “brightness” (orluminance), andZ
its “blueness.” Normalizing these tristimulus values gives us the coordinates.x;y; ́/on the chromaticity
diagram:

xD

X

XCYCZ

(S.4)

yD

Y

XCYCZ

(S.5)

́D

Z

XCYCZ

D 1 xy (S.6)

(S.7)

Because of the normalization condition, knowingxandyautomatically gives ́D 1 xy; therefore only
xandyare needed as the chromaticity coordinates.