1. 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

2. Colour matching experiment

3. 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:

4. The colour equation
But
i.e.:

5. Practical realization of negative matching stimulus

6. Tristimulus values and colour matching functions

7. Colour matches are additive

8. Additivity: Complex spectrum

9. Additivity: Complex spectrum
or as integrals

10. X,Y,Z colour space
CIE 1931 Standard Colorimetric Observer

11. RGB - XYZ matrix transformation

12. The colour matching functions

13. The tristimulus values

14. Chromaticity co-ordinates

15. Chromaticity diagram E: equi-energy chromaticity
R, G, B: chromaticity of real primaries

16. Mixing and visualising colours in the chromaticity diagram
achromatic (N for neutral) "white point”
dominant (complementary) wavelength (lD), correlate of hue
excitation purity, correlate of saturation

17. Excitation purity
For chromaticity point C

18. 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:lD
excitation purity: pe

19. Additive mixture of two stimuli
X = aRXR + aGXG ;
Y = aRYR + aGYG ;
Z = aRZR + aGZG .

20. CIE 1964 Standard Colorimetric Observer
Macula lutea or yellow spot
10° filed of vision .

21. CIE 1931 and 1964 Standard Colorimetric Observers

22. MacAdam ellipses
The CIE x,y diagram with ellipses representing small colour differences

23. 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

24. 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

25. u’,v’ chromaticity diagram

26. 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

27. Colour temperature - 2

28. Colorimetry of surface colours
radiance factor b(l)
tristimulus values:

29. 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.)

30. CIE Standard sources and illuminants - 2, daylight illuminants
for correlated colour temperatures from approximately 4000 K to 7000K:

31. CIE Standard sources and illuminants - 3, daylight illuminants
for correlated colour temperatures from 7000K to approximately K

32. CIE Standard sources and illuminants - 4, daylight illuminants
S(l) = S0(l) + M1S1(l) + M2S2(l)

33. 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

34. CIE Standard Illuminants

35. CIE D65 simulator

36. Correlated colour temperature
Iso-temperature lines (in u,v-diagram)

37. Different temperature concepts
Real temperature
Radiant temperature
Distribution temperature
Colour temperature
Correlated colour temperature

38. 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

39. 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

40. CIE 1976 a,b colour difference and CIELAB components
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

41. CIE 1994 colour difference k parametric factors, industry dependent
S weighting functions, depend on location in colour space:

42. 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:

43. 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:

44. 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.

45. 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.

46. 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.

47. 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

48. 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

49. 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

50. 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.

51. 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.

52. Metamerism Different spectra, identical tristimulus values
Metamerism indices:
Illuminant
Observer

53. CIE Whiteness formulae
Whiteness: W  Y + 800(xn-x) (yn - y)
Tint:
TW  1000 (xn-x) + 650(yn - y)

54. Advanced colorimetry Colour appearance models chromatic adaptation
vonKries transformation
CIE (Nayatani) proposal
Bradford transformation
Hunt model
CIECAM97s model
Colour management

55. Brightness/Luminance
Chromatic versus achromatic signal brightness
Ware-Covan correction
C= y xy x3y xy4

56. Contour lines of equiluminous lights of equal brightness

57. 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

58. 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

59. CIECAM97s model Chromatic adaptation Induction factor calculations
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

60. Signal colours

61. Colorimetry of materials
Fluorescing materials
photo-fluorescence
luminophores - phosphors
optical brighteners
Measurement
reflected radiance factor
emitted radiance factor
total radiance factor

62. Spectral radiance factor

63. Two monochromator method for measuring total radiance factor

64. CIE standards and recommendations
ISO/CIE : Colorimetric illuminants
ISO/CIE : Colorimetric observers
CIE : Colour rendering
CIE : Colorimetry
CIE 17.4: International lighting vocabulary
CIE : Quality of daylight simulators

65. 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