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: Luminance of the R, G, B matching stimuli: red: 1,0000 cd/m2 = 1 new R unit green: 4,5907 cd/m2 = 1 new G unit blue: 0,0601 cd/m2 = 1 new B unit
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 ( λ ), g ( λ ) and b ( λ ) rel. sens. r2 g2 b2
400
500
600
wavelength, nm
700
Colour matches are additive If
C ( λ 1) ≡ r 1( R ) + g1( G ) + b 1( B ) and
C ( λ 2 ) ≡ r 2( R ) + g2( G ) + b 2( B ) then:
C( λ1) + C( λ2) ≡ (r 1 + r 2)(R) +(g1+g2)( G) +(b1+b2)(B)
Additivity: Complex spectrum 780 nm
R=k
∑ P ( λ ) r ( λ ) Δλ
380 nm 780 nm
G=k
∑ P ( λ ) g ( λ ) Δλ
380 nm 780 nm
B=k
∑ P ( λ ) b ( λ ) Δλ
380 nm
Additivity: Complex spectrum or as integrals 780 nm
R=k
∫ P ( λ ) r ( λ ) dλ ,
380 nm
780 nm
B=k
∫ P(λ )b (λ )dλ
380 nm
780 nm
G=k
∫ P ( λ ) g ( λ ) dλ ,
380 nm
X,Y,Z colour space CIE 1931 Standard Colorimetric Observer 1.the tristimulus values of the colour stimulus of the equienergetic spectrum should again be equal; 2.all the photometric information (luminance, if the stimulus is measured in radiance units) should be in a single value, i.e. one of the colour matching functions should be equal with the V(λ)-function; 3.the tristimulus values of all real colours should be positive and the volume of the tetrahedron should be as small as possible.
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
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 1,80 1,60
rel. sens.
1,40 x2(lambda)
1,20 1,00
y2(lambda)
0,80 z2(lambda)
0,60 0,40 0,20 0,00 350
400
450
500
550
600
650
wavelength, nm
700
750
800
850
The tristimulus values The X, Y, Z tristimulus values of a colour stimulus (S(λ)): X =k
780 nm
∫ Sλ( λ )x ( λ )dλ ,
Y =k
380 nm
Z =k
780 nm
∫ Sλ( λ ) y ( λ )dλ ,
380 nm 780 nm
∫ Sλ( λ )z ( λ )dλ
380 nm
with k = 683 lm/W for photometric quantities.
Chromaticity co-ordinates x=
X , X +Y + Z
y=
Z Y , z= X +Y + Z X +Y + Z
where, as x + y + z = 1
Chromaticity diagram 0,9 0,8
540 G
0,7
560
0,6 y2
E: equienergy chromaticity R, G, B: chromaticity of real primaries
520
500
0,5
580
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 (λD), correlate of hue excitation purity, correlate of saturation
Excitation purity 0,9
For chromaticity point C
520
0,8
540 CW
0,7
pe=(yC - yN)/(yDW - yN) or 0,6 pe=(xC - xN)/(xDW - xN) 0,5
560 500
y
580
0,4
600
C
620
N
0,3
C'
DW
700
0,2 P
0,1 480 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:λD excitation purity: pe
Additive mixture of two stimuli X = aRXR + aGXG ; Y = aRYR + aGYG ; Z = aRZR + aGZG .
a RX R + a G X G x= aR( XR + YR + ZR ) + aG( XG + YG + ZG ) a RY R + a G Y G y= aR( XR + YR + ZR ) + aG( XG + YG + ZG )
CIE 1964 Standard Colorimetric Observer Macula lutea or yellow spot 10° filed of vision 780 nm
.
X 10 = k
∫ S (λ ) x
10
(λ )dλ , Y10 = k
380 nm
.
and
x10 =
∫ S (λ ) y
10
(λ )dλ ,
380 nm
780 nm
Z10 = k
780 nm
∫ S (λ ) z
10
( λ ) dλ
k = Y10
380 nm
X10 X10 +Y10 + Z10
, y10 =
Y10 X10 +Y10 + Z10
, z10 =
Z10 X10 +Y10 +
CIE 1931 and 1964 Standard Colorimetric Observers 2 ,5 0 E + 0 0
2 ,0 0 E + 0 0
1 ,5 0 E + 0 0
1 ,0 0 E + 0 0
5 ,0 0 E - 0 1
0 ,0 0 E + 0 0 350
400
450
500
550
600
650
w a v e l e n g th , n m
700
750
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
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 0,9 0,8 550
0,7 0,6 500 0,5
2856K
0,4
4000K 6500K E 10.000K
0,3 0,2
600 650 2000K
100.000K 480
0,1 0 0
0,2
0,4
0,6
0,8 x
Colorimetry of surface colours radiance factor β(λ) tristimulus values: 780 nm
X =k
∫ S (λ ) ⋅ β (λ ) ⋅ x (λ )dλ ,
780 nm
Y =k
380 nm
780 nm
Z =k
380 nm
∫ S (λ ) ⋅ β (λ ) ⋅ z (λ )dλ
380 nm
k=
∫ S ( λ ) ⋅ β ( λ ) ⋅ y ( λ ) dλ ,
1
∫ S ( λ ) y ( λ ) dλ
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: 109 106 103 xD =− 4,6070 3 +2,9678 2 +0,09911 +0,244063 Tc Tc Tc 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 9
6
3
10 10 10 xD =− 2,0064 3 +1,9018 2 +0,24748 +0,237040 Tc Tc Tc yD = -3,000xD2 + 2,870xD - 0,275
CIE Standard sources and illuminants 4, daylight illuminants S(λ) = S0(λ) + M1S1(λ) + M2S2(λ) − 1,3515−1,7703xD +5,9114 yD M1= 0,0241+0,2562xD −0,7341yD 0,0300−31,4424xD +30,0717 yD M2= 0,0241+0,2562xD −0,7341yD
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
Relative spectral power distribution
CIE Standard Illuminants 300 250 200 Ill.A 150
Ill.D65
100 50 0 300 350 400 450 500 550 600 650 700 750 800 850 Wavelegth, nm
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)
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: ΔEab = [ (ΔL*)2 + (Δa*)2 + (Δβ∗)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: ΔHab* = [(ΔEab*)2 - (ΔL*)2 - (ΔCab*)2]1/2
CIE 1994 colour difference * ΔE 94
2 ⎡⎛ * * ⎛ ⎞ Δ C Δ L ab ⎜ + = ⎢⎜ ⎟ ⎜k S ⎢⎝ k L S L ⎠ ⎝ C C ⎣
⎞ ⎛ ΔH ⎞ ⎤ ⎥ ⎟ ⎜ ⎟ ⎟ ⎝k S ⎠ ⎥ ⎠ H H ⎦ 2
* ab
2
1/ 2
k parametric factors, industry dependent S weighting functions, depend on location
in colour space: SL = 1; SC = 1 + 0,045 C *ab; S H = 1 + 0,015 C *ab
Metamerism Different spectra, identical tristimulus values Metamerism indices: Illuminant Observer
0.9 0.8
Sample
0.7 Radi- 0.6 ance factor 0.5
Sample
0.4 0.3 0.2 0.1 0 400
450
500
550
Wavelength,
600
650
700
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
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
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 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
