CIE colorimetry
The colour equation
Condition 1: 2° bipartite visual field, central
fixation and dark surround.
Matching (reference, primary) stimuli: Red
(R): 700 nm, Green (G): 546,1 nm and Blue
(B): 435,8 nm
C  R (R ) + G ( G ) + B (B )
Colour matching experiment
CIE colorimetry
The colour equation
Condition 2: Magnitude of the Matching
Stimuli: The units of the three primaries
provide a colour match with an equienergetic
white test stimulus:
L u m in a n ce o f th e R , G , B m a tch in g stim u li:
re d :
g re e n :
b lu e :
1 ,0 0 0 0
4 ,5 9 0 7
0 ,0 6 0 1
cd /m 2 = 1 n e w R u n it
cd /m 2 = 1 n e w G u n it
cd /m 2 = 1 n e w B u n it
The colour equation
C  R (R ) + G ( G ) + B (B )
But
C ( 520 nm )  R ( R )  G ( G ) + B ( B )
i.e.:
C   R (R ) + G (G ) + B (B )
Practical realization of
negative matching stimulus
Tristimulus values and colour
matching functions
r (  ), g (  ) and b (  )
re l.
se n s.
r2
g2
b2
400
500
600
w a ve le n g th, nm
700
Colour matches are additive
If
C (  1 )  r 1( R ) + g 1( G ) + b 1( B )
and
C ( 2)  r 2(R ) + g2(G ) + b 2(B )
th e n :
C (  1) + C (  2 )  ( r 1  r 2 ) ( R ) + ( g1 + g 2 )( G ) + (b 1 + b 2 )( B )
Additivity: Complex spectrum
780 nm
R  k
 P ()
r (  ) 
380 nm
780 nm
G  k
 P ()
g (  ) 
380 nm
780 nm
B  k
 P ()
380 nm
b (  ) 
Additivity: Complex spectrum
or as integrals
780 nm
 P ( )r ( )d ,
R k
380 nm
780 nm
B k
 P (  )b (  )d 
380 nm
780 nm
G k
 P ( ) g ( )d ,
380 nm
X,Y,Z colour space
CIE 1931 Standard Colorimetric Observer
1 . th e tristim u lu s v a lu e s o f th e co lo u r stim u lu s o f th e
e q u ie n e rg e tic sp e ctru m sh o u ld a g a in b e e q u a l;
2 . a ll th e p h o to m e tric in fo rm a tio n (lu m in a n ce , if th e
stim u lu s is m e a su re d in ra d ia n ce u n its) sh o u ld b e
in a sin g le v a lu e , i.e . o n e o f th e co lo u r m a tch in g
fu n ctio n s sh o u ld b e e q u a l w ith th e V (  )-fu n ctio n ;
3 . th e tristim u lu s v a lu e s o f a ll re a l co lo u rs sh o u ld b e
p o sitiv e a n d th e v o lu m e o f th e te tra h e d ro n sh o u ld
b e a s sm a ll a s p o ssib le .
RGB - XYZ matrix transformation
X
2 , 76888
1, 75175
1,13016
R
Y
 1, 00000
4 ,59070
0 , 06010
 G
Z
0 , 00000
0 , 05651
5 ,59427
B
T h e in v e rse tra n sfo rm a tio n :
0 , 41846
-0 , 15866
-0 , 08283
-0 , 09117
0 , 25243
0 , 01571
0 , 00092
-0 , 00255
0 , 17860
The colour matching
functions
1,80
1,60
1,40
x 2(lam bda)
rel. sen s.
1,20
1,00
y2(lam bda)
0,80
z2(lam bda)
0,60
0,40
0,20
0,00
350
400
450
500
550
600
650
w avelength, nm
700
750
800
850
The tristimulus values
T h e X , Y , Z tristim u lu s v a lu e s o f a co lo u r stim u lu s
(S (  )):
780 nm
X  k
780 nm
 S  (  ) x (  )d  ,
Y  k
380 nm
 S  (  ) y (  )d  ,
380 nm
780 nm
Z  k
 S  (  ) z (  )d 
380 nm
w ith k = 6 8 3 lm /W fo r p h o to m e tric q u a n titie s.
Chromaticity co-ordinates
x
X
X Y  Z
,
y
Y
X Y  Z
where, as x + y + z = 1
, z
Z
X Y  Z
Chromaticity diagram
0,9
0,8
540
G
0,7
560
0,6
500
0,5
580
y2
E: equienergy
chromaticity
R, G, B:
chromaticity
of real
primaries
520
0,4
600
E
620
0,3
R
0,2
0,1 480
0
460
0
B
0,2
0,4
0,6
0,8
x2
Mixing and visualising colours in
the chromaticity diagram
achromatic (N for neutral) "white point”
dominant (complementary) wavelength
(D), correlate of hue
excitation purity, correlate of saturation
Excitation purity
0,9
For chromaticity
point C
520
0,8
540
CW
0,7
p e = (y C - y N )/(y D W - y N ) o r
0,6
p e = (x C - x N )/(x D W - x N )
0,5
560
500
y
580
0,4
600
C
620
N
0,3
C'
DW
700
0,2
0,1
P
480
0
0
460
380
0,2
0,4
0,6
0,8
Description of a colour stimulus
Tristimulus values, X, Y, Z.
Chromaticity and luminance:
Y (or L), x, y.
Further descriptors:
Luminance: L,
dominant (or complementary) wavelength:D
excitation purity: pe
Additive mixture of two stimuli
X = aRXR + aGXG ;
Y = aRYR + aGYG ;
Z = aRZR + aGZG
. x 
y 
aRXR + aGXG
aR ( XR + YR  ZR )  aG ( XG + YG  ZG )
aRYR + aGYG
aR ( XR + YR  ZR )  aG ( XG + YG  ZG )
CIE 1964 Standard Colorimetric
Observer
Macula lutea or yellow spot
10° filed of vision
780 nm
.
780 nm
 S ( ) x
X 10  k
10
( )d ,
 S ( ) y
Y10  k
380 nm
10
( )d ,
380 nm
780 nm
Z 10  k
.
 S ( ) z
10
( )d
k = Y 10
380 nm
and
x
10
X
10

X
10
Y  Z
10
10
,
y
10
Y
10

X
10
Y  Z
10
10
, z
10
Z
10

X
10
Y  Z
10
10
CIE 1931 and 1964 Standard
Colorimetric Observers
MacAdam ellipses
The CIE x,y
diagram
with ellipses
representing
small colour
differences
The CIE system of colorimetry
CIE 1976 uniform chromaticity diagram
colour temperature, Tc & correlated Tc, TCC
Colorimetry of surface colours
CIE standard illuminants and sources
CIE colour spaces
CIELUV space
CIELAB space
CIE 1994 colour difference
Brightness - luminance ratio
Uniform colour scales
u' = 4X / (X+15Y+3Z) = 4x / (-2x+12y+3)
v' = 9Y / (X+15Y+3Z) = 9y / (-2x+12y+3)
u = u' , v = (2/3)v'
CIE 1976 u,v hue angle:
huv = arctg[(v' - v'n) / (u' - u'n)] = v* / u*
The CIE 1976 u,v saturation:
suv = 13[(u' - u'n)2 + (v' - v'n)2]1/2
u’,v’ chromaticity diagram
550
0 ,6
600
650
0 ,5
500
700
huv
Sn
v'
0 ,4
0 ,3
C
0 ,2
0 ,1
450
400
0
0
0 ,1
0 ,2
0 ,3
0 ,4
0 ,5
u'
0 ,6
0 ,7
0 ,8
0 ,9
1
Colour temperature - 1
The spectral power distribution of a full
radiator can be calculated using Planck's
formula:
Me = c1-5[exp(c2/T)-1]-1
c2 = 1,4388x10-2 mK
Colour temperature - 2
Colorimetry of surface colours
radiance factor b()
tristimulus values:
780 nm
X k
780 nm
 S ( )  b ( )  x ( )d ,
Y k
380 nm
 S ( )  b ( )  y ( )d ,
380 nm
780 nm
Z k
 S ( )  b ( )  z ( )d
380 nm
k 
1
 S ( ) y ( )d
CIE Standard sources and
illuminants - 1
CIE Standard Illuminant A: An illuminant
having the same relative spectral power
distribution as a Planckian radiator at a
temperature of 2856 K
CIE Standard Illuminant C: An illuminant
representing average daylight with a
correlated colour temperature of about
6800 K. (This illuminant is now obsolete.)
CIE Standard sources and illuminants - 2,
daylight illuminants
for correlated colour temperatures from
approximately 4000 K to 7000K:
x D   4 , 6070
10
T
9
3
c
 2 ,9678
10
T
6
2
c
 0 , 09911
y D = -3,000x D 2 + 2,870x D - 0,275
10
Tc
3
 0 , 244063
CIE Standard sources and illuminants 3, daylight illuminants
for correlated colour temperatures from
7000K to approximately 25 000 K
x D   2 , 0064
10
T
9
3
c
1,9018
10
T
6
2
c
 0 , 24748
y D = -3,000x D 2 + 2,870x D - 0,275
10
Tc
3
 0 , 237040
CIE Standard sources and illuminants 4, daylight illuminants
S() = S0() + M1S1() + M2S2()
M 1
M 2
 1, 3515 1, 7703 x D  5 , 9114 y D
0,0241 + 0,2562 x D  0 , 7341 y D
0 , 0300  31 , 4424 x D  30 , 0717 y D
0,0241 + 0,2562 x D  0 , 7341 y D
CIE Standard sources and illuminants 5, daylight illuminants
CIE Standard Illuminant D65: An
illuminant representing a phase of daylight
with a correlated colour temperature of
approximately 6500 K
CIE Illuminants: Fluorescent lamps
R e la t iv e s pe c t ra l pow e r dis t rib ut io n
CIE Standard Illuminants
300
250
200
Ill.A
150
Ill.D 65
100
50
0
300 350 400 450 500 550 600 650 700 750 800 850
W av eleg th , n m
CIE D65 simulator
450
400
F L R 4 0 S D E D L D 6 5 /M
D65
350
300
Re
l
po
we
r
250
200
150
100
50
0
350 400 450 500 550 600 650 700 750 800
W a v e le n g th , n m
Correlated colour temperature
Iso-temperature lines (in u,v-diagram)
Different temperature
concepts
Real temperature
Radiant temperature
Distribution temperature
Colour temperature
Correlated colour temperature
Further recommendations on
surface colour measurement
 Standard of reflectance factor:
perfect reflecting diffuser
secondary reference reflectance factor
pressed barium sulphate plate
“ halon" white standards
 Standard measuring geometry
45°/normal reflectance factor
diffuse/normal, specular included/excluded:
reflectance factor
normal/diffuse, specular included/excluded:
reflectance
CIE 1976 (L*a*b*) colour space,
CIELAB colour space

L* 116(Y/Yn)1/3 - 16

a* 500 ( X/Xn)1/3 - (Y/Yn)1/3 

b* 200 (Y/Yn)1/3 - (Z/Zn)1/3
for
X/Xn > 0,008856

Y/Yn > 0,008856

Z/Zn > 0,008856
CIE 1976 a,b colour difference
and CIELAB components
Colour difference:
Eab   (L*)2 + (a*)2  (b*)21/2
CIE1976 a,b chroma:
 Cab*  (a*2 + b*2)1/2
CIE 1976 a,b hue-angle:
 ha  arctan (b*/a*)
CIE 1976 a,b hue-difference:
 Hab*  (Eab*)2 - (L*)2 - (Cab*)21/2
CIE 1994 colour difference
E
*
94
2

*
*

 L 
 C ab
 
  
 k L S L 
 kC SC





2
 H 


 kH SH 
*
ab
2




1/ 2
k parametric factors, industry dependent
S weighting functions, depend on location
in colour space:
S L = 1 ; S C = 1 + 0 ,0 4 5 C * ab ; S H = 1 + 0 ,0 1 5 C * a b
2.2 Reference conditions
Reference conditions describe a set of experimental and
material variables that are typical of
the conditions used in developing visual colour-difference
data sets for object colours. The
reference conditions may not have been universally
employed in all data sets used by CIE
TC1-47 in developing and testing the recommended model
but they represent common levels
of the experimental variables. The reference conditions are:
CIE 2000 colour difference
equation
2.2 Reference conditions
Reference conditions describe a set of experimental and
material variables that are typical of
the conditions used in developing visual colour-difference
data sets for object colours. The
reference conditions may not have been universally
employed in all data sets used by CIE
TC1-47 in developing and testing the recommended model
but they represent common levels
of the experimental variables. The reference conditions are:
Reference conditions
Illumination: source simulating the spectral relative irradiance of CIE
Standard Illuminant D65.
Illuminance: 1000 lx.
Observer: normal colour vision.
Background field: uniform, neutral gray with L* = 50.
Viewing mode: object.
Sample size: greater than 4 degrees subtended visual angle.
Sample separation: minimum sample separation achieved by placing the
sample pair in direct edge contact.
Sample colour-difference magnitude: 0 to 5 CIELAB units.
Sample structure: homogeneous colour without visually apparent pattern or
non-uniformity.
Notes
Deviations from the reference conditions can affect the
performance of the colour-difference model.
-Changes in viewing and illuminating conditions affect the validity
of CIELAB as a colour space and further necessitate the definition
of parametric factors.
- Changes in the source correlated colour temperature from 6500
K affect the accuracy of the chromatic adaptation transformation
embedded in CIELAB, i. e. X/Xn, Y/Yn, and Z/Zn.
- Illuminance levels much lower than 1000 lux result in reduced
discrimination. With an increase in the angle subtended by the
colour-difference pair, the influence of background lightness on
colour discrimination decreases.
Modification of the a* (redgreen opponent) axis
The CIE 1976 (L*a*b*) colour space (CIE, 1986) is retained as
an approximate uniform colour space representing perceptual
colour magnitudes in terms of opponent colour scales with a
localized modification to the a* (red-green opponent) axis. This
modification was made to improve agreement with visual colourdifference-perception for neutral colours. The modification
increases the magnitudes of a’ values compared to a* values for
colours at low chroma. At higher chroma the modified a’ value
approaches the conventional a* value. Quantities L’ and b’ are
defined as equal to L* and b* respectively. Primed quantities in
this report refer to quantities derived from L’, a’, b’ coordinates.
Modification of the a* (redgreen opponent) axis
 L’=L*
 a’ = a*(1 + G)
 b’ = b*
where G depends on mean C* value of the two
samples
Modified chroma and hue angle are calculated
using the a’, b’ coordinates, but should not be
used in colour space calculaqtions
Total colour-difference
A perceived visual colour-difference
magnitude, DeltaV, is related to the total
colour difference, DeltaE00, through an
overall sensitivity factor, kE.
Delta V = kE-1Delta E00
Total colour difference
The total colour-difference between two
colour samples with lightness, chroma and
hue differences, with weighting functions,
SL, SC, SH, parametric factors, kL, kC, kH
and rotation function is determined similarly
as CIE94 including this rotation factor
Rotation function
Visual colour-difference perception data show an
interaction between chroma difference and hue
difference in the blue region. The interaction results in a
significant tilt of the major axis of the colour-difference
ellipse. The ellipse tilt is in the counter-clockwise
direction and away from the direction of constant hue
angle. To account for this effect, a rotation function is
applied to weighted hue and chroma differences.
The rotation function has a significant effect only for
the blue high chroma region of the a’, b’ plane.
Parametric factors
Parametric factors, kL, kC, kH, are
correction terms for variation in perceived
colour-difference component sensitivity with
variation in experimental conditions. Under
the reference conditions the parametric
factors have assigned values of unity and do
not affect the total colour difference.
In the textile industry it is common practice to set
the lightness parametric factor to 2.
Metamerism
 Different
spectra,
identical
tristimulus
values
 Metamerism
indices:
Illuminant
Observer
0.9
0.8
S am ple
1
0.7
R ad i- 0.6
an c e
fact o r 0.5
S am ple
2
0.4
0.3
0.2
0.1
0
40 0
45 0
50 0
55 0
W av elen g th ,
nm
60 0
65 0
70 0
CIE Whiteness formulae
Whiteness:
W  Y + 800(xn-x) + 1700(yn - y)
Tint:
TW  1000 (xn-x) + 650(yn - y)
Advanced colorimetry
Colour appearance models
chromatic adaptation
vonKries transformation
CIE (Nayatani) proposal
Bradford transformation
Hunt model
CIECAM97s model
Colour management
Brightness/Luminance
Chromatic versus achromatic signal
brightness
Ware-Covan correction
L** = log(L) +C
C=0.256 - 0.184y - 2.527 xy +
+4.656x3y + 4.657xy4
Contour lines of equiluminous
lights of equal brightness
CIECAM97s model
Comprehensive
Wide range of stimuli: dark to bright
Wide range of adapting intensities and
viewing conditions, degree of adaptation
Based on x,y,z functions
Predictions: hue-angle, -quadrature,
brightness, lightness, saturation, chroma,
colourfulness
Reverse mode
Simplified and complete model
Version for unrelated colours
CIECAM97s model
Input data
Adapting field luminance, LA
Tristim.values of sample in source condition
Source white in source condition
Rel.lum. Of source background in s.cond.,Yb
Inpact of surround, chromatic induction,
lightness contrast factor
Viewing condition
CIECAM97s model
Chromatic adaptation
spectrally sharpened cone responses
modified vonKries: degree of adapt.
Induction factor calculations
Non-linear response compression
Appearance correlates
red-green, yellow-blue - hue angle & quadr.
Lightness, brightness
colourfulness, chroma, saturation
Signal colours
Colorimetry of materials
Fluorescing materials
photo-fluorescence
luminophores - phosphors
optical brighteners
Measurement
reflected radiance factor
emitted radiance factor
total radiance factor
Spectral radiance factor
Two monochromator method for
measuring total radiance factor
CIE standards and
recommendations
ISO/CIE 10526-1991: Colorimetric illuminants
ISO/CIE 10526-1991: Colorimetric observers
CIE 13.3-1988: Colour rendering
CIE 15.2-1986: Colorimetry
CIE 17.4: International lighting vocabulary
CIE 51-1981: Quality of daylight simulators
CIE TCs working on colorimetry
CIECAM colour appearance models
VDU - Reflective media comparison
Chromaticity diagram with physiologically
significant axes
Geometric tolerances in colorimetry
Updating the colorimetry and colour
rendering documents