CIE colorimetryThe 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 G B ( ) + ( ) + ( )R G 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:
Luminance of the R, G, B matching stimuli:
red: 1,0000 cd/m2 = 1 new R unitgreen: 4,5907 cd/m2 = 1 new G unitblue: 0,0601 cd/m2 = 1 new B unit
The colour equation
But
i.e.:
C R G B ( ) + ( ) + ( )R G B
C R G B(520 nm) ( ) ( ) + ( ) R G B
C R G B ( ) + ( ) + ( )R G B
Practical realization of negative matching stimulus
Tristimulus values and colour matching functions
r g b( ), ( ) ( ) and
wavelength, nm
rel.sens.
400 500 600 700
r2
g2
b2
Colour matches are additive
I f
C r( 1 1) ( ) + g ( ) + b ( )1 1 R G Ba n d
C r( 2 2) ( ) + g ( ) + b ( )2 2 R G Bt h e n :
C C r r( ( ( ) 1 2 1 2) + ) ( ) + ( g + g ) ( ) + ( b + b ) ( )1 2 1 2 R G B
Additivity: Complex spectrum
R k P r
G k P g
B k P b
( ) ( )
( ) ( )
( ) ( )
380 nm
780 nm
380 nm
780 nm
380 nm
780 nm
Additivity: Complex spectrum
or as integrals
nm 780
nm 380
nm 780
nm 380
nm 780
nm 380
d)()(
,d)()( ,d)()(
bPkB
gPkGrPkR
X,Y,Z colour space
CIE 1931 Standard Colorimetric Observer1.the tristimulus values of the colour stimulus of the
equienergetic spectrum should again be equal;
2.all the photometric information (luminance, if thestimulus is measured in radiance units) should bein a single value, i.e. one of the colour matchingfunctions should be equal with the V()-function;
3.the tristimulus values of all real colours should bepositive and the volume of the tetrahedron shouldbe as small as possible.
RGB - XYZ matrix transformation
B
G
R
Z
Y
X
59427,505651,000000,0
06010,059070,400000,1
13016,175175,176888,2
The inverse transformation:
0,41846 -0,15866 -0,08283
-0,09117 0,25243 0,01571
0,00092 -0,00255 0,17860
The colour matching functions
wavelength, nm
rel.
sen
s.
0,00
0,20
0,40
0,60
0,80
1,00
1,20
1,40
1,60
1,80
350 400 450 500 550 600 650 700 750 800 850
x2(lambda)
y2(lambda)
z2(lambda)
The tristimulus values
T h e X , Y , Z t r is t im u lu s v a lu e s o f a c o lo u r s t im u lu s
(S ( ) ) :
X k S x Y k S y
Z k S z
( ) ( ) , ( ) ( ) ,
( ) ( )
d d
d
3 8 0 n m
7 8 0 n m
3 8 0 n m
7 8 0 n m
3 8 0 n m
7 8 0 n m
w ith k = 6 8 3 lm /W fo r p h o to m e tr ic q u a n t i t ie s .
Chromaticity co-ordinates
ZYX
Zz
ZYX
Yy
ZYX
Xx
, ,
where, as x + y + z = 1
Chromaticity diagram
E: equi-energy chromaticity
R, G, B: chromaticity of real primaries
x2
y2
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8
G
R
B
500
480
520
540
560
580
600620
460
E
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
For chromaticity point Cpe=(yC - yN)/(yDW - yN) or
pe=(xC - xN)/(xDW - xN)
x
y
0
0 , 1
0 , 2
0 , 3
0 , 4
0 , 5
0 , 6
0 , 7
0 , 8
0 , 9
0 0 , 2 0 , 4 0 , 6 0 , 8 1 1 , 2 1 , 4 1 , 6 1 , 8
5 0 0
4 8 0
5 2 0
5 4 0
5 6 0
5 8 0
6 0 06 2 0
4 6 0
NC
D W
C W
7 0 0
3 8 0
C '
P
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
a X a X
a X Y Z a X Y Z
ya Y a Y
a X Y Z a X Y Z
R R G G
R( R R R G( G G G
R R G G
R( R R R G( G G G
+
+ +
+
+ +
) )
) )
CIE 1964 Standard Colorimetric Observer
Macula lutea or yellow spot10° filed of vision
.
.
nm 780
nm 380
1010
nm 780
nm 380
1010
nm 780
nm 380
1010
d)()(
,d)()( ,d)()(
zSkZ
ySkYxSkX
k = Y10
a n d
xX
X Y Zy
Y
X Y Zz
Z
X Y Z1010
10 10 1010
10
10 10 1010
10
10 10 10
, ,
CIE 1931 and 1964 Standard Colorimetric Observers
wavelength, nm
0,00E +00
5,00E -01
1,00E +00
1,50E +00
2,00E +00
2,50E +00
350 400 450 500 550 600 650 700 750 800 850
x10
y10
z10
x2
y2
z2
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,
TCCColorimetry of surface colours
CIE standard illuminants and sourcesCIE 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
u '
v'
0
0 ,1
0 ,2
0 ,3
0 ,4
0 ,5
0 ,6
0 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7 0 ,8 0 ,9 1
S n
C
h u v
4 0 0
4 5 0
5 0 0
5 5 06 0 0
6 5 0
7 0 0
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
x
0
0 ,1
0 ,2
0 ,3
0 ,4
0 ,5
0 ,6
0 ,7
0 ,8
0 ,9
0 0 ,2 0 ,4 0 ,6 0 ,8 1 1 ,2 1 ,4 1 ,6 1 ,8
6 5 0
6 0 0
5 5 0
5 0 0
4 8 0
1 0 0 .0 0 0 K
1 0 .0 0 0 K
6 5 0 0 KE
4 0 0 0 K2 8 5 6 K
2 0 0 0 K
Colorimetry of surface colours
radiance factor tristimulus values:
nm 780
nm 380
nm 780
nm 380
nm 780
nm 380
d)()()(
,d)()()( ,d)()()(
zSkZ
ySkYxSkX
d)()(
1
ySk
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:
244063,010
09911,010
9678,210
6070,4c
3
2c
6
3c
9
D TTT
x
yD = -3,000xD2 + 2,870xD - 0,275
CIE Standard sources and illuminants - 3, daylight illuminants
for correlated colour temperatures from 7000K to approximately 25 000 K
237040,010
24748,010
9018,110
0064,2c
3
2c
6
3c
9
D TTT
x
yD = -3,000xD2 + 2,870xD - 0,275
CIE Standard sources and illuminants - 4, daylight illuminants
S = S0() + M1S1 + M2S2
DD
DD2
DD
DD1
7341,00,2562+0,0241
0717,304424,310300,0
7341,00,2562+0,0241
9114,57703,13515,1
yx
yxM
yx
yxM
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
CIE Standard Illuminants
0
50
100
150
200
250
300
300 350 400 450 500 550 600 650 700 750 800 850
Wavelegth, nm
Rel
ativ
e sp
ectr
al p
ow
er d
istr
ibu
tio
n
Ill.A
Ill.D65
CIE D65 simulator
Correlated colour temperature
Iso-temperature lines (in u,v-diagram)
Different temperature concepts
Real temperatureRadiant temperatureDistribution temperatureColour 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
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*)
21/2
CIE 1994 colour difference
k parametric factors, industry dependentS weighting functions, depend on
location in colour space:
EL
k S
C
k S
H
k S94
2 2 21 2
**
/
L L
ab*
C C
ab*
H H
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 conditionsIllumination: 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* (red-green 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 colour-difference-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* (red-green 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
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 transformationCIE (Nayatani) proposalBradford 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
ComprehensiveWide range of stimuli: dark to brightWide range of adapting intensities and
viewing conditions, degree of adaptationBased on x,y,z functionsPredictions: hue-angle, -quadrature,
brightness, lightness, saturation, chroma, colourfulness
Reverse modeSimplified and complete modelVersion 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 calculationsNon-linear response compressionAppearance 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 observersCIE 13.3-1988: Colour renderingCIE 15.2-1986: ColorimetryCIE 17.4: International lighting vocabularyCIE 51-1981: Quality of daylight simulators
CIE TCs working on colorimetry
CIECAM colour appearance modelsVDU - Reflective media comparisonChromaticity diagram with
physiologically significant axesGeometric tolerances in colorimetryUpdating the colorimetry and colour
rendering documents