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Chapter: 2 General physics
    Section: 2.5 Radiation and optics
        SubSection: 2.5.4 Colorimetry

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2.5.4 Colorimetry

Evaluation of colour

The trichromatic system of colorimetry recommended by the CIE in 1931 is used internationally for specifying the colour of light or of illuminated objects. The colour of any radiation is specified by three tristimulus values X, Y, Z which represent the amounts of three standard reference stimuli (X), (Y), (Z) which if mixed together by optical superposition would produce the same sensation of light and colour for an observer with normal colour vision. The tristimulus values for radiation of spectral power distribution P(λ) are given by the formulae:

   X = K

P(λ).

(λ)dλ;

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Y = K

P(λ).

(λ)dλ;   

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Z = K

P(λ).

(λ)dλ   

where K is a scaling constant and (λ), (λ) and (λ) are known as spectral tristimulus values, i.e. the tristimulus values of unit powers of monochromatic radiation as given in the table below. The ‘colour quality’ of the radiation, as distinct from its amount, is expressed in terms of the chromaticity co-ordinates x, y, z, given by:

   x = X/(X + Y + Z);     y = Y/(X + Y + Z);     z = Z/(X + Y + Z).

Of the three tristimulus values, Y represents the luminosity of a colour, and if Km is used for the constant K above, then Y becomes the photometric flux, since the function (λ) is identical to V(λ). (See section 2.5.3.)

The colour of a reflecting surface is specified in terms of the tristimulus values X, Y, Z of the radiation reflected when the surface is illuminated with radiation of specified spectral power distribution P(λ). Here the absolute values of X, Y, Z are usually just as important as the chromaticity co-ordinates x, y, z, and they are defined as


   

X =

P(λ).(λ).ρ(λ) dλ

P(λ).(λ) dλ


   

Y =

P(λ).(λ).ρ(λ) dλ

P(λ).(λ) dλ


   

Z =

P(λ).(λ).ρ(λ) dλ

P(λ).(λ) dλ


where ρ(λ) is the reflectance expressed as a percentage. These definitions give Y the value 100 for a perfect reflector, or more generally Y equals the luminous reflectance (the photometric value); in addition the chromaticity co-ordinates x, y, z for a spectrally non-selective reflector will be those of the illuminant. Similar expressions hold for a transmitting object, with the spectral transmittance τ(λ) replacing ρ(λ) above.

The table of spectral tristimulus values given below allows the chromaticity co-ordinates x(λ), y(λ), z(λ) of the spectral radiations to be calculated immediately since

   x(λ) = (λ)/((λ) + (λ) + (λ)), etc.

The table is normalized so that the chromaticity co-ordinates of the equi-energy white radiation are each equal to 0.3333. In many cases adequate accuracy can be obtained by computation at 10 nm intervals from 380 nm provided that the tristimulus values X, Y, Z so obtained are multiplied by 1.0002, 1.0000 and 1.0008 respectively; this has the effect of renormalizing the shortened table for 10 nm intervals to give the same chromaticity co-ordinates for equi-energy white, and hence to minimize spectral sampling errors on average.

The (X, Y, Z) colour space is subjectively rather non-uniform as far as perceived colour differences are concerned. In 1976 the CIE recommended for use two possible non-linear transformations of (X, Y, Z), namely (L*, U*, V*) and (L*, a*, b*), which are more nearly uniform for colour differences. Of these (L*, a*, b*) has proved more suitable for the colour manufacturing industries (textiles, plastics, paints, ceramics, paper, etc.) while (L*, U*, V*) has been used in television and photography. However, under the aegis of the Society of Dyers and Colourists a system known as CMC (l:c) based on the (L*, a*, b*) colour space but with local modulations of colour tolerance specified by supplementary equations, is being widely used by the colour manufacturing industries. This achieves a better correlation with visual judgement and is the basis of BS 6923: 1988 and industry standards in the USA.

The CIE (X, Y, Z) system of 1931 is valid for observations with uniform areas subtending up to 4°; for uniform areas subtending larger angles there is an alternative (X10, Y10, Z10) system recommended by CIE in 1964, based on observations with a 10° field. This latter is widely used for textiles, plastics, paints and ceramics, whereas the CIE 1931 system is more appropriate for television, photography and light sources.



1931 CIE colorimetric Standard Observer for subtenses 0.5° to 4°

λ/nm

Spectral tristimulus values

λ/nm

Spectral tristimulus values

(λ)

(λ)

(λ)

(λ)

(λ)

(λ)

 

 

 

 

 

 

 

 

 380

0.0014

0.0000

0.0065

580

0.9163

0.8700

0.0017

 385

0.0022

0.0001

0.0105

585

0.9786

0.8163

0.0014

 390

0.0042

0.0001

0.0201

590

1.0263

0.7570

0.0011

 395

0.0076

0.0002

0.0362

595

1.0567

0.6949

0.0010

 400

0.0143

0.0004

0.0679

600

1.0622

0.6310

0.0008

 

 

 

 

 

 

 

 

 405

0.0232

0.0006

0.1102

605

1.0456

0.5668

0.0006

 410

0.0435

0.0012

0.2074

610

1.0026

0.5030

0.0003

 415

0.0776

0.0022

0.3713

615

0.9384

0.4412

0.0002

 420

0.1344

0.0040

0.6456

620

0.8544

0.3810

0.0002

 425

0.2148

0.0073

1.0391

625

0.7514

0.3210

0.0001

 

 

 

 

 

 

 

 

 430

0.2839

0.0116

1.3856

630

0.6424

0.2650

0.0000

 435

0.3285

0.0168

1.6230

635

0.5419

0.2170

0.0000

 440

0.3483

0.0230

1.7471

640

0.4479

0.1750

0.0000

 445

0.3481

0.0298

1.7826

645

0.3608

0.1382

0.0000

 450

0.3362

0.0380

1.7721

650

0.2835

0.1070

0.0000

 

 

 

 

 

 

 

 

 455

0.3187

0.0480

1.7441

655

0.2187

0.0816

0.0000

 460

0.2908

0.0600

1.6692

660

0.1649

0.0610

0.0000

 465

0.2511

0.0739

1.5281

665

0.1212

0.0446

0.0000

 470

0.1954

0.0910

1.2876

670

0.0874

0.0320

0.0000

 475

0.1421

0.1126

1.0419

675

0.0636

0.0232

0.0000

 

 

 

 

 

 

 

 

 480

0.0956

0.1390

0.8130

680

0.0468

0.0170

0.0000

 485

0.0580

0.1693

0.6162

685

0.0329

0.0119

0.0000

 490

0.0320

0.2080

0.4652

690

0.0227

0.0082

0.0000

 495

0.0147

0.2586

0.3533

695

0.0158

0.0057

0.0000

 500

0.0049

0.3230

0.2720

700

0.0114

0.0041

0.0000

 

 

 

 

 

 

 

 

 505

0.0024

0.4073

0.2123

705

0.0081

0.0029

0.0000

 510

0.0093

0.5030

0.1582

710

0.0058

0.0021

0.0000

 515

0.0291

0.6082

0.1117

715

0.0041

0.0015

0.0000

 520

0.0633

0.7100

0.0782

720

0.0029

0.0010

0.0000

 525

0.1096

0.7932

0.0573

725

0.0020

0.0007

0.0000

 

 

 

 

 

 

 

 

 530

0.1655

0.8620

0.0422

730

0.0014

0.0005

0.0000

 535

0.2257

0.9149

0.0298

735

0.0010

0.0004

0.0000

 540

0.2904

0.9540

0.0203

740

0.0007

0.0002

0.0000

 545

0.3597

0.9803

0.0134

745

0.0005

0.0002

0.0000

 550

0.4334

0.9950

0.0087

750

0.0003

0.0001

0.0000

 

 

 

 

 

 

 

 

 555

0.5121

1.0000

0.0057

755

0.0002

0.0001

0.0000

 560

0.5945

0.9950

0.0039

760

0.0002

0.0001

0.0000

 565

0.6784

0.9786

0.0027

765

0.0001

0.0000

0.0000

 570

0.7621

0.9520

0.0021

770

0.0001

0.0000

0.0000

 575

0.8425

0.9154

0.0018

775

0.0001

0.0000

0.0000

 

 

 

 

780

0.0000

0.0000

0.0000




Standard illuminants for colorimetry

In 1931 the CIE recommended three standard illuminants for the colorimetry of materials. Illuminant A was intended to represent the illumination from incandescent lamps used in general lighting and in projectors. Illuminant B was intended to represent direct sunlight with no sky component, while Illuminant C was intended to represent overcast skylight. Of these, Illuminant B has fallen largely into disuse and is therefore omitted from the specifications below. However in 1964 the CIE introduced Illuminant D65 based on the measured spectral power distribution of average overcast skylight and of sunlight mixed with total skylight.

Illuminant A.  Black-body radiation corresponding to a value of c2/T (see section 2.5.2) of (1.4350 × 10−2/2848)m, or on ITS-90, to a temperature of approximately 2856 K. The chromaticity co-ordinates of Illuminant A are (x = 0.4776, y = 0.4074).

Illuminant A is realized in the laboratory by Source A, the radiation from a gas-filled tungsten-filament lamp of the same correlated colour temperature.

Illuminant C. The radiation from Illuminant A after selective attenuation in accordance with the published CIE data on the transmittance of the filter described below. The chromaticity co-ordinates of Illuminant C are (x = 0.3101, y = 0.3162) and its correlated colour temperature is 6774 K (ITS-90).

Illuminant C is realized in the laboratory by Source A combined with a colour filter consisting of a layer 10 mm thick of each of two solutions C1 and C2, contained in a double cell made of colourless optical glass.

Solution C1

     
  Copper sulphate (CuSO4. 5H2O)   3.412 g
  Mannite (C6H8(OH)6)   3.412 g
  Pyridine (C5H5N)   30.0 ml
  Distilled water, to make 1 litre.    
       

Solution C2

     
  Cobalt ammonium sulphate (CoSO4. (NH4)2SO4. 6H2O) spacer 30.58 g
  Copper sulphate (CuSO4.5H2O)   22.52 g
  Sulphuric acid (density 1.835 g ml−1)   10.0 ml
  Distilled water, to make 1 litre.    

Illuminant D65. A relative spectral power distribution defined and recommended by CIE as representing a phase of daylight with a correlated colour temperature of approximately 6504 K (IPTS-68). This is a much better representation of an average overcast sky than Illuminant C. The chromaticity co-ordinates of Illuminant D65 are (x = 0.3127, y = 0.3290). At present Illuminant D65 cannot be realized with enough accuracy for many applications, and there is no recommended source specification as yet.

Methods of specifying standard illuminants DT of different correlated colour-temperatures T have been published by the CIE: these are spectral power distributions which represent different phases of daylight.

A table of relative spectral power distributions of CIE standard illuminants is given below.




References

BS 6923:1988 British Standard Method for Calculation of small colour differences, British Standards Institution, London.
CIE Publication No. 15.2 (1986) Colorimetry, 2nd edn, CIE, A-1033 Vienna, PO Box 169.
CIE Publication No. S001 (1986) Colorimetric Illuminants, CIE, A-1033 Vienna, PO Box 169.
CIE Publication No. S002 (1986) Colorimetric Observers, CIE, A-1033 Vienna, PO Box 169.

F.J.J.Clarke

Relative spectral power distributions of CIE standard illuminants

λ/nm

(A)
P(λ)

(C)
P(λ)

(D65)
P(λ)

λ/nm

(A)
P(λ)

(C)
P(λ)

(D65)
P(λ)  

375

  8.77

27.50

  51.0

575

110.80

100.15  

96.1  

380

  9.80

33.00

  50.0

580

114.44

97.80

95.8  

385

10.90

39.92

  52.3

585

118.08

95.43

92.2  

390

12.09

47.40

  54.6

590

121.73

93.20

88.7  

395

13.35

55.17

  68.7

595

125.39

91.22

89.3  

 

 

 

 

 

 

 

 

400

14.71

63.30

82.8

600

129.04

89.70

90.0 

405

16.15

71.81

87.1

605

132.70

88.83

89.8

410

17.68

80.60

91.5

610

136.35

88.40

89.6

415

19.29

89.53

92.5

615

139.99

88.19

88.6

420

20.99

98.10

93.4

620

143.62

88.10

87.7

 

 

 

 

 

 

 

 

425

22.79

105.80  

90.1

625

147.24

88.06

85.5

430

24.67

112.40  

86.7

630

150.84

88.00

83.3

435

26.64

117.75  

95.8

635

154.42

87.86

83.5

440

28.70

121.50  

104.9  

640

157.98

87.80

83.7

445

30.85

123.45  

110.9  

645

161.52

87.99

81.9

 

 

 

 

 

 

 

 

450

33.09

124.00  

117.0  

650

165.03

88.20

80.0

455

35.41

123.60  

117.4  

655

168.51

88.20

80.1

460

37.81

123.10  

117.8  

660

171.96

87.90

80.2

465

40.30

123.30  

116.3  

665

175.38

87.22

81.2

470

42.87

123.80  

114.9  

670

178.77

86.30

82.3

 

 

 

 

 

 

 

 

475

45.52

124.09  

115.4  

675

182.12

85.30

80.3

480

48.24

123.90  

115.9  

680

185.43

84.00

78.3

485

51.04

122.92  

112.4  

685

188.70

82.21

74.0

490

53.91

120.70  

108.8  

690

191.93

80.20

69.7

495

56.85

116.90  

109.1  

695

195.12

78.24

70.7

 

 

 

 

 

 

 

 

500

59.86

112.10  

109.4  

700

198.26

76.30

71.6

505

62.93

106.98  

108.6  

705

201.36

74.36

73.0

510

66.06

102.30  

107.8  

710

204.41

72.40

74.3

515

69.25

98.81

106.3  

715

207.40

70.40

68.0

520

72.50

96.90

104.8  

720

210.36

68.30

61.6

 

 

 

 

 

 

 

 

525

75.79

96.78

106.2  

725

213.27

66.30

65.7

530

79.13

98.00

107.7  

730

216.12

64.40

69.9

535

82.52

99.94

106.0  

735

218.92

62.80

72.5

540

85.95

102.10  

104.4  

740

221.67

61.50

75.1

545

89.41

103.95  

104.2  

745

224.36

60.20

69.3

 

 

 

 

 

 

 

 

550

92.91

105.20  

104.0  

750

227.00

59.20

63.6

555

96.44

105.67  

102.0  

755

229.59

58.50

55.0

560

100.00  

105.30  

100.0  

760

232.12

58.10

46.4

565

103.58  

104.11  

98.2

765

234.59

58.00

56.6

570

107.18  

102.30  

96.3

770

237.01

58.20

66.8

 

 

 

 

 

 

 

 

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