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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;

Y = K P(λ). (λ)dλ;

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 K_m 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

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°

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)		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 D_T 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

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