World of colour emotion: fundamentals of colorimetry

Colour Appearance Attributes

The three colour appearance attributes Every colour has three basic characteristics: hue, lightness and chroma (see the diagram on the right). These are sometimes referred to as the three colour appearance attributes. There are also other attributes used to describe colour appearance, such as brightness, colourfulness and saturation, and some of them are more useful than these three basic attributes in certain circumstances. For instance, in scaling colour appearance, colourfulness is preferred to chroma as a measure of chromatic property for colour stimuli. The CIE International Lighting Vocabulary has defined these attributes as shown in the following:-

Hue

Attribute of a visual sensation according to which an area appears to be similar to one, or to proportions of two, of the perceived colours, red, yellow, green and blue.

Brightness

Attribute of a visual sensation according to which an area appears to exhibit more or less light.

Lightness

The brightness of an area judged relative to the brightness of a similarly illuminated area that appears to be white or highly transmitting (i.e. reference white).

Colourfulness

Attribute of a visual sensation according to which an area appears to exhibit more or less of its hue.

Chroma

The colourfulness of an area judged in proportion to the brightness of a similarly illuminated area that appears to be white or highly transmitting (i.e. reference white).

Saturation

Colourfulness of an area judged in proportion to its brightness.

Note that brightness and colourfulness represent absolute strength of the perception, whereas lightness and chroma represent relative strength, i.e. relative to brightness of the reference white, which is normally the brightest colour in the visual field. All of these attributes can be used to describe related colours (those perceived in relation to other colours). The absolute attributes (i.e. brightness and colourfulness) can be used to describe unrelated colours (those perceived in isolation).

CIE Colorimetry - Key Elements of Colour Perception

The CIE is an international commission of illumination and is responsible for international standards of photometry and colorimetry. The CIE system provides methods for specifying colour stimuli under controlled viewing conditions.

The CIE system standardises three key elements of colour perception, namely light source, geometry of illumination and viewing, and standard colorimetric observers. This section describes how these elements are quantified and how they can be combined to produce colorimetric data.

Light Source

Light is the most essential element of colour perception. Hunt wrote, “without light there is no colour.” (1998) The most important light source is daylight. In 1931, the CIE recommended the use of three standard illuminants, known as A, B and C, representing incandescent light, direct sunlight and average daylight, at the colour temperatures of about 2856, 4874 and 6774 K, respectively. In 1963, the CIE recommended a series of D illuminants to meet the need of measuring colours that contain the ultra-violet region. The most widely used D illuminants are D65 for surface colour industries and D50 for graphic arts industry.

A light source can be quantified by measuring its spectral power distribution (SPD), a function of wavelength across the visible spectrum. A spectroradiometer is commonly used for measuring the SPD of a light source.

Geometry of Illumination and Viewing

The second element of colour perception is concerned with reflectance or transmittance of light measured from an object. The reflectance or transmittance of an object is not merely a function of wavelength, but also of the geometry of illumination and viewing. The CIE has recommended four types of illumination and viewing geometries for reflectance measurement: normal/diffuse (0/d), diffuse/normal (d/0), 45º/normal (45/0) and normal/45º (0/45), as illustrated in the diagram below (a) to (d), respectively. These geometries have been widely used in colour industries.

Geometry of illumination and viewing In the 0/d geometry, measured colour sample is illuminated from an angle near the normal and the reflected energy is collected from all angles using an integrating sphere (a hollow sphere which is painted white inside). In the d/0 geometry, the sample is illuminated from all angles using an integrating sphere and viewed at an angle near the normal to the surface. These two geometries are optical reverses of each other and therefore produce the same measurement results, assuming all other instrumental variables are constant.

In the 45/0 geometry, the sample is illuminated with one or more beams of light, incident at an angle of about 45º and measurements are made along the normal. In the 0/45 geometry, the sample is illuminated normal to its surface and measurements are made using one or more beams at about 45º. The 45/0 and 0/45 geometries both ensure all components of gloss to be excluded from measurements.

Standard Colorimetric Observers

In 1931, the CIE recommended a set of standard colour-matching functions based on colour-matching properties obtained from 17 observers. These properties are called the CIE 1931 Standard Colorimetric Observer, often referred to as the 2º Observer, which serves for visual field size of 1º to 4º. Colour-matching functions define how human eyes match a colour stimulus with an additive mixture of three primaries, the monochromatic red, green and blue lights.

A different set of colour-matching functions were recommended in 1964 by the CIE for samples with the field size greater than 4º. These functions solve the problem that a colour match made with 2º field size does not remain a match if the field size is changed into greater than 4º. This problem is due to non-uniformity of the distribution of photoreceptors across the retina. These new functions define the CIE 1964 Supplementary Standard Colorimetric Observer, often referred to as the 10º Observer.

Tristimulus Values

Colours on an object's surface (called surface colours) can be represented by three values X, Y and Z, called tristimulus values, calculated by integrating the SPD of the light source [], the spectral reflectance [] and the CIE colour-matching functions [, and ], as illustrated in the following equations:

where k is a constant and is the wavelength (in unit of nm).

If the 10º Observer is used, the colour-matching functions, , and , should be replaced by , and .

For measuring self-luminous colours such as those on a Cathode Ray Tube (CRT) display, a television or a light source, the term should be replaced by , the spectral radiance of the colour stimulus. The tristimulus values are then determined by

Chromaticity

CIE chromaticity diagram A convenient way of visually representing tristimulus values is the use of chromaticity co-ordinates, which map all colours into a two-dimensional space, called chromaticity diagram (see the diagram on the right). This space has two axes x and y, determined by

The CIE chromaticity diagram provides a colour map on which the chromaticities of all colours are plotted, as shown in the diagram on the right. The curved line in this diagram shows where the colours of the spectrum lie, called spectral locus; the wavelengths are indicated in nanometres along the curve. The straight line connects the chromaticity co-ordinates of extreme red and blue, called purple boundary. The area enclosed by the spectrum locus and the purple boundary cover the domain of all visible colours, since all perceivable colours existing in nature can be represented by combinations of spectral colours and that any mixture of two spectral colours in this system is located on the line joining the two points that represent the two original spectral colours.

Uniform Colour Spaces

Although the CIE chromaticity diagram has been widely used, it has a serious disadvantage – the non-uniformity of colour distribution in its space, i.e. equal distances in various parts of the colour space represent different perceptual colour differences.

The CIELAB and CIELUV systems are currently the most widely used approximately uniform colour spaces both in colour research and in colour industries. Both systems were recommended by the CIE in 1976.

CIELAB colour space The CIELAB system (see the diagram on the right) is constituted by three orthogonal dimensions L*, a* and b*. The vertical dimension L* represents the lightness; the two horizontal dimensions a* and b* represent the redness-greenness and yellowness-blueness perceptions of colours. These dimensions are determined by the following:

where X, Y, Z and , , are tristimulus values for the stimulus and for the reference white, respectively.

This system predicts chroma and hue angle by the following formulae:

The CIELUV system also has three orthogonal dimensions. The vertical dimension L* represents the lightness; the two horizontal dimensions u* and v* represent the redness-greenness and yellowness-blueness perceptions of colours.

for

where and are the chromaticity co-ordinates for the sample and for the reference white, respectively, determined by

The CIELUV system predicts chroma , saturation and hue angle by the following formulae:

Another well-known approximately uniform colour space is Munsell system, which was originated by the artist A. H. Munsell in 1905. In this system, a correlate of lightness, Munsell Value, is considered as a vertical axis; Munsell Hue consists of five main segments, denoted Red, Yellow, Green, Blue and Purple; Munsell Chroma, a correlate of perceived chroma, is represented by the distance of a sample from the vertical axis.

Colour Difference Formulae

A colour difference formula predicts perceived colour difference between a pair of coloured stimuli. The simplest form of colour difference considers the distance between co-ordinates of two stimuli in a colour space to be their colour difference, such as . Due to non-uniformity of existing colour spaces (neither CIELAB nor CIELUV is perfectly uniform), more advanced colour difference formulae have been developed, such as CMC (l:c), CIE94 [whose structure is similar to CMC (l:c) formula but whose weighting functions are largely based on the RIT/DuPont tolerance data derived from experiments with automotive paints] and CIEDE2000 [which was developed on the basis of experimental data accumulated through a number of different studies and whose structure is similar to BFD (l:c) formula]. Today the work of achieving more precise prediction for colour difference still continues.

The CIELAB system can be represented either in terms of the three orthogonal co-ordinates L*, a* and b* or of the cylindrical co-ordinates L*, and . The CIELAB colour difference is accordingly determined in two methods, both by means of the Euclidean distance between two colours in the CIELAB colour space, as follows: