Ocean Optics OOIColor - Manual (Page 13)

10
The tristimulus values (X, Y and Z) are computed by the following equations. It is important to
note that by convention, these calculations are scaled so that the Y value for all illuminants is
100.00:
X
x
x
x
y
Y
y
y
y
y
Z
z
z
z
y
sam
ref
ref
ref
sam
ref
ref
ref
sam
ref
ref
ref
=
L
NMM
O
QPP
=
L
NMM
O
QPP
=
L
NMM
O
QPP
100
100
100
All other color space values are derived from these fundamental tristimulus values:
x
X
X Y Z
y
Y
X Y Z
z
Z
X Y Z
=
+ +
=
+ +
=
+ +
′ =
+ +
′ =
+ +
′ =
− + +
+ +
u
X
X Y Z
v
Y
X Y Z
w
X Y Z
X Y Z
4
15 3
9
15 3
3 6 3
15 3
u v
v v
u u
u v
u u
v v
, atan
,
hue angle
Saturation
Illuminant
Illuminant
Illuminant
Illuminant
=
′ − ′
′ − ′
=
′ − ′
′ − ′
13
2
2
a f
a f
The derivation of other color space values can be found in references on measuring color. The
reference used for all of the coordinates and equations was R.W.G Hunt, Measuring Colour, 2 nd
Edition, Ellis Horwood, 1991.