pre-congress seminar: INTRODUCTION TO COLOUR MEASUREMENT by Prof. Lindsay MacDonald
pre-congress seminar: INTRODUCTION TO COLOUR MEASUREMENT (the seminar is taught in English)
by Prof. Lindsay MacDonald Place: ADUM (Agremiación Docente Universitaria Marplatense): Address: Guido 3256, between San Lorenzo and Roca, Mar del Plata (close to the University)
PROGRAMA
Tuesday 12 October 2010, from 15:30 to 18:00 It is often said that “if you can’t measure it you can’t manage it”. This is just as true for colour as for other quantities. But how do we measure what is essentially a visual experience? This tutorial course will provide an introduction to measuri ng colour, by considering the spectral characteristics of light sources and of light as it is reflected by surfaces and of human visual response. The CIE system of colorimetry will be reviewed, including standard illuminants, the standard observer, and colour matching functions. It will become clear how spectral measurement data is transformed into CIE tristimulus values and chromaticity coordinates, and hence to the uniform colour space CIELAB. This provides the basis of colour difference assessment in industrial applications such as textile dyeing and printing. Related topics such as metamerism, colour rendering of light sources, and repeatability of instruments will be demonstrated.
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AIC 2010, Congreso Interino de la Asociaci贸n Internacional del Color Mar del Plata, Argentina, 12-15 octubre 2010
Curriculum Lindsay MacDonald is Professor of Digital Media at London College of Communication. He has been deeply involved in all aspects of colour for 25 years, in industrial research and development projects, academic research and teaching. His research interest is in the colour appearance of 3D surfaces with gloss characteristics. He has edited eight books on colour in image science and engineering and he is a Fellow of five societies, including the US-based Society for Imaging Science and Technology (IS&T). He was Chairman of The Colour Group (Great Britain) 2007-09 and is currently a member of the Executive Committee of AIC with responsibility for editing the annual newsletter.
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TUTORIAL NOTES – AIC CONFERENCE – MAR DEL PLATA, ARGENTINA – OCTOBER 2010
An Introduction to Colour Measurement Lindsay MacDonald London college of Communication
1. Introduction It is often said that “if you can’t measure it you can’t manage it”. This is just as true for colour as for other quantities. But how do we measure what is essentially a visual experience? There is a duality about colour. On the one hand, it depends on physical phenomena, especially illumination and the interaction of light with materials. On the other hand, colour is perceptual, because it depends on an observer’s judgement, memory and responses. Thus the measurement of colour can be conducted in either domain: (a) by measuring the wavelengths and power of the radiation and the reflectance or transmittance of the material; or (b) by quantifying what a human observer would see under standard viewing conditions. This tutorial aims to give an introduction to the various aspects of colour measurement, through a combination of theory and practical demonstrations. The following topics are covered: Spectral power distribution of light sources; CIE standard illuminants; Reflectance and transmittance of materials; Human visual response and colour matching; CIE standard observer; Calculating tristimulus, chromaticity and CIELAB values; Metamerism; Colour rendering index; Measuring instruments, accuracy and repeatability.
2. Light Sources Light is electromagnetic radiation in the region of the spectrum visible to the human eye, nominally in the wavelength range 380 to 760 nanometres (nm), corresponding to a frequency range of 790 to 395 terahertz (a single octave). Light is characterised by its intensity, wavelength (preferred to frequency), phase and polarisation. The first two quantities are related through the spectral power distribution (SPD), namely the power per unit wavelength throughout the spectrum. The SPD is typically specified at intervals of 5 nm or 10 nm, and hence for the wavelength range 380‐760 nm can be represented as a vector of 77 or 39 elements respectively. Figure 1 (left) Spectral power distribution of Planckian radiators at different temperatures (Hunt 1998, p.85); (right) Relative power of Planckian radiators at 2856K, 5000K, 10,000K, normalised at 560 nm (Berns 2000, p.4) Lindsay MacDonald, London College of Communication
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A common source of light is blackbody radiation, more properly called Planckian radiation, produced by thermal energy in heated metals. Planck’s Law, proposed in 1900, states that the radiant emittance per wavelength interval is: 1
(1)
A family of curves for Planckian radiators of increasing temperature T (expressed in degrees Kelvin) is shown in Fig. 1 left, and the inverse relationship between T and λ is clear as the function peaks at: λ = hc/ 4.97kT
(2)
This peak wavelength is in the infra‐red region for T<3000 and in the ultraviolet for T>6000. The slope of the curve within the visible spectrum changes from positive for low T to negative for high T. It is approximately level at T=5000 (Fig. 1 right). Planckian radiators of temperature less than 5000K therefore have more power at longer wavelengths and appear reddish, whereas those of temperature greater than 5000K have more power at shorter wavelengths and appear bluish. As Planckian radiators are heated their colour changes in a predictable sequence from dull red through orange and yellow to white and bluish white. The clear functional relationship between temperature and colour leads to the convenient concept of correlated colour temperature (CCT), defined as: “The temperature of a Planckian radiator whose perceived colour most closely resembles that of the stimulus seen at the same brightness” (Hunt, 1998). The procedure finds the temperature of the Planckian radiator nearest to the chromaticity coordinates of the light source (Fig. 2 left). Numerous attempts have been made to develop a formula for colour temperature as a function of chromaticity coordinates. Robertson (1968) proposed a CCT algorithm using a technique for numerical interpolation between 31 isotemperature lines. He tested the accuracy of his algorithm versus the known CCT’s of 1800 daylight chromaticity coordinates, and showed that the errors of his algorithm were quite small, reaching a maximum of 5.4K in the range 2000K to 14,000K. McCamy (1992) noted that the isotemperature lines generally converge toward the bottom of the CIE 1931 chromaticity diagram. He defined an epicentre of convergence, about which CCT would be a single‐ valued function of angle, by the parameter: n = (x-xe) / (y-ye)
(3)
The coordinates of the epicentre, found by successive trials to minimise the errors, were xe = 0.3320, ye = 0.1858. McCamy then calculated the CCT by the polynomial function: T = -449 n3 + 3525 n2 - 6823.3 n + 5520.33
(4)
The approximation is valid in the range 2500K to 8000K with errors limited to ±2K.
Figure 2. (left) Lines of constant correlated colour temperature (isotherms) in the x‐y chromaticity diagram; (right) Spectrum of solar radiation in space (dotted line) and normally incident solar spectrum (solid line).
Lindsay MacDonald, London College of Communication
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The predominant source of light on earth is daylight, which is a mixture of direct sunlight and reflected skylight. The balance between these at the earth’s surface varies according to the latitude, time of day and weather conditions. The spectrum of solar radiation in space (above the Earth's atmosphere) is specified in standard ASTM E490 (2000). It peaks at 451 nm and resembles the distribution of a blackbody radiator of 5525K. At ground level the solar spectrum (Fig. 2 right) is modified by absorption and scattering in the atmosphere, specified in standard ISO 9845‐1 (1992). Short wavelengths in the UV region are attenuated by ozone, and at longer wavelengths in the IR region absorption bands are caused by water vapour, oxygen and carbon dioxide. Rayleigh scattering accounts for a reduction of about 25% in radiant power in the visible region, particularly at shorter (blue) wavelengths. The distribution of daylight can be approximated well by a mean and two principal components, as shown by Judd et al (1964). Spectral distributions of daylight were measured in USA, England and Canada and dataset of 622 spectra was analysed by computing the covariance matrix and solving for characteristic vectors. The first component (Fig. 3 left) represents the blue‐yellow axis of variation, and hence the balance between reflected skylight (bluish) and direct sunlight (yellowish). The second component represents a magenta‐green axis, and is lower in amplitude because its variance in the dataset is less. Reconstructed spectra of daylight (Fig. 3 right) normalised at 560 nm show that the basic shape of the spectrum is maintained while the balance of power shifts from long wavelengths (red) to short wavelengths (blue) as the CCT increases. Figure 3. (left) First two principal components derived from analysis of 622 daylight spectra; (right) SPDs of typical daylight at various temperatures reconstructed from the mean and first two principal components, normalised at 560 nm (from Judd et al, 1964).
An illuminant is an idealised source defined by an SPD, which may not be achievable by a real source. The CIE (2004) recommends the use of two standard illuminants (Fig. 4 left), one representing a phase of daylight with a CCT of 6500K, known as D65, and a second representing incandescent illumination (SA) with a CCT of 2856K. They are presented as data tables at 1 nm and 5 nm intervals. ISO 7589 (2002) recommended an SPD to represent ‘photographic daylight’ with a CCT of 5500K (designated as D55) for the sensitometry of ‘daylight balanced’ colour films. This approximates the prevailing condition in temperate zones during the daylight hours recommended for colour photography. Real light sources may be characterised in terms of the spectral power distribution as either ‘smooth’ or ‘spiky’. The fluorescent lamp falls into the latter category, because the phosphors, when excited by the UV light from the internal arc discharge, radiate strongly at particular wavelengths, tending toward a line spectrum. Fig. 4 (right) for a ‘daylight’ fluorescent lamp exhibits spikes in the spectrum more pronounced than in natural daylight. Lindsay MacDonald, London College of Communication
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250
Relative spectral power
SA 200
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Figure 4. (left) Relative spectral power distributions of CIE standard illuminants D65 and A; (right) Spectral power distribution of a white fluorescent lamp.
3. Surface Reflectance When light encounters the surface of an object four different interactions may occur (Fig. 5): 1. Specular reflection from the first surface (associated with gloss); 2. Scattering within the material (associated with diffuse reflection/transmission); 3. Absorption within the material (associated with colour); 4. Regular transmission through the object (associated with clarity).
Incident light
SURFACE
Specular reflection Diffuse reflection
Yellow pigment
Figure 5. Microscopic view of light striking a yellow plastic box (Hunter and Harold, 1987, p.30). Transmission
The light reflected directly from the surface is the specular component and has the spectral composition, and therefore the colour, of the incident light. The light that enters the body of the material is refracted at the boundary according to the refractive index of the material, described by Snell’s Law. It then undergoes a series of interactions with a series of pigment particles, at each of which some wavelength‐selective absorption occurs. The rays of light that finally emerge from the surface as the diffuse component carry the colour of the material. The gloss component can be seen only from a single angle if the surface is smooth, or a small range of angles if it is textured, whereas the body colour can be seen from all angles. In photometry and heat transfer, reflectivity ρ is the fraction of incident radiation reflected by a surface (Eq. 5). Reflectivity measures the fractional amplitude of the reflected electromagnetic field intensity G, while reflectance refers to the fraction of incident electromagnetic power I reflected at an interface. The reflectance is thus the square of the magnitude of the reflectivity. The reflectivity can be expressed as a complex number, determined by the Fresnel equations for a single layer, whereas the reflectance is always a positive real number. Lindsay MacDonald, London College of Communication
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When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. Reflectivity is the limiting value of reflectance as the surface becomes thick; it is the intrinsic reflectance of the surface, independent of other parameters such as reflectance of the rear surface.
(5)
Reflectance factor R is the ratio at each wavelength between the reflected and incident power. More specifically, it is defined as ‘the ratio of the radiant or luminous flux reflected in a given cone, whose apex is on the surface considered, to that reflected in the same directions by the perfect diffuser identically irradiated’ (Hunt, 1998). The perfect diffuser is further defined as ‘an ideal isotropic diffuser with a reflectance (or transmittance) equal to unity’. The albedo α of an object is the extent to which it diffusely reflects light from sources such as the sun. It is therefore a more specific form of reflectivity, and is widely used in astronomy and remote sensing. Albedo is defined as the ratio of diffusely reflected to incident electromagnetic radiation. For a transmissive material the non‐specular component of the incident light passes through the body of the material and emerges out of the other side, carrying the colour of the material. For a transparent material there is no scattering, only wavelength‐dependent absorption. The density of the material is determined by its thickness and the colorant concentration, described by the Beer‐ Lambert Law (Fig. 6). For a translucent material there is Figure 6. Absorption of light passing through also scattering of light by opaque particles, and the optical a homogeneous material. The intensity of behaviour of such materials may be characterised by transmitted light is related to the intensity of incident light by I = I010-bc. Kubelka‐Munk analysis (Yang et al, 2009). The transmittance factor T is a characteristic of a transmissive material, and is defined as the ratio at each wavelength between the transmitted and incident power. Absorbance A, which in photography is also called optical density D, is the logarithm of transmittance factor: log
log
(6)
The relationship between the physical structure of a material and its optical radiation properties (scattering, reflection, etc) is complex. For example, selective absorption, which is largely responsible for the colour of a material, takes place during the passage of light through the material. Scattering occurs where light encounters interfaces between pigments and resin, fibre, air, etc. Normally, when particle sizes are made smaller, less light is absorbed during the passage through each particle resulting in less colour being apparent. At the same time, the total particle surface becomes greater, leading to an increase in light scattering, or diffusion, since reflection occurs at the particle surfaces. 4. Gloss Usually the appearance of coloured samples varies with the direction of the illumination and viewing because most surfaces exhibit gloss, which results in some of the incident light being reflected directly from the top surface without passing through the material body (Fig. 5). This is called the specular component and, for a smooth and uniform surface, is usually maximum when the angle of reflection is equal to the angle of incidence. In the case of a perfect mirror surface all of the incident ray of light would be reflected at this single angle. Conversely, an idealised perfectly matte surface with no gloss, known as a Lambertian surface, would reflect equally at all angles. Harrison (1945) recognised that all real materials reflect both specular and diffuse components, and that the intensity is distributed over a range of angles of reflection. He used polar plots to show the intensity of the reflected radiation at all angles in the half‐plane above the surface containing the Lindsay MacDonald, London College of Communication
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incident and reflected rays (Fig. 7). The more glossy the surface, the more sharply defined is the specular ‘spike’ in the distribution around the primary reflection angle. A well‐rounded curve indicates a generally diffuse reflection, which in the case of a perfect Lambertian surface would be a circle. The complexity of gloss as a visual phenomenon is revealed by the many definitions in use: A surface shine or lustre; a smooth finish; a deceptively attractive appearance. (OCED, 1996) Angular selectivity of reflectance, involving surface reflected light, responsible for the degree to which reflected highlights or images of objects may be seen as superimposed on a surface. (ASTM, 2002) A measure of the relative amounts of diffuse reflectance to specular reflectance. (Tilley, 1999) Ability or capacity of a surface to direct reflected light. (Trezza & Krochta, 2001) The power of a surface to reflect light specularly. (Silvennoinen et al, 2008)
Figure 7. Polar reflection curves for two types of paper (from Harrison, 1945)
Specular gloss I
Sheen I
S
I G S/I G S/I Absence-of-bloom gloss D B I S G (B-D)/I
Contrast gloss or lustre D
S
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G D/S Distinctness-of-image gloss S
I
G dS/d
Figure 8. Hunter’s five types of gloss (Hunter and Harold, 1987).
There are two reasons for this diversity of definition. The first is that gloss, like colour, is a physical process that produces a perceptual response in an observer. Therefore the difference in approach between measurement of patterns of radiation and psychophysical experiment into how it appears in a given viewing environment. Second that gloss is not a single attribute but a family of related appearance characteristics. Hunter and Judd (1939) recognised that the perception of gloss involves more than just specular reflection, and so in addition to specular gloss they defined (Fig. 8): a) sheen as gloss at grazing angles of incidence and viewing; b) contrast gloss or lustre as the ratio of the specularly reflected light and that diffusely reflected normal to the surface; c) absence‐of‐bloom as a measure of the absence of haze or a milky appearance adjacent to the specularly reflected light; d) distinctness‐of‐image as the sharpness of specularly reflected light.
Lindsay MacDonald, London College of Communication
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5. Colorimetry Three elements are needed to specify the colour of an object: the source of illumination, the reflection/transmission properties of the surface, and the sensitivity of the observer (Fig. 9). In 1931 the CIE (Commission Internationale de l’Éclairage) standardised a method for colour specification, including standard light sources and a standard observer. This has become the basis of all colour measurement (CIE, 2004).
Radiated
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Reflected
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Figure 9. The three elements of colour specification: a light source, an object with a selectively reflecting or transmitting surface, and an observer.
All three elements (illumination, object and observer) must be characterised in spectral terms, i.e. their behaviour defined at each wavelength throughout the visible spectrum from 380 to 760 nm. For a source of illumination, this means specifying the power of the radiation incident on the surface as a function of wavelength through the spectral power distribution. Reflection from a surface is characterised by the reflectance factor, i.e. the ratio of reflected to incident power, as a function of wavelength. For the great majority of real‐world and synthetic colorants, the spectral reflectance distribution is smooth and well‐behaved (Fig. 10 left). 1.00
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Figure 10. (left) Reflectance factor of the orange patch in the Macbeth ColorChecker chart, at 10 nm intervals; (right) Spectral luminous efficiency functions for photopic and scotopic vision. http://webvision.med.utah.edu/
The perception of brightness as a function of wavelength is specified by the spectral luminous efficiency function, which was standardised by CIE in 1924. For daylight (photopic) vision, the function is denoted V(λ) and peaks at λ=555 nm, whereas for night (scotopic) vision the alternative V’(λ) peaks at λ=507 nm (Fig. 10 right). A separate function V10(λ) is used for large (nominally 10°) visual fields. A revised luminosity function V*(λ) has recently been proposed (Sharpe et al, 2005) to Lindsay MacDonald, London College of Communication
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correct for the known deficiency in the original V(λ) curve for wavelengths less than 480nm. Photopic luminance Lv is related to radiance L by: 683
.
(7)
and has units lm.m‐2.sr‐1 = cd.m‐2. The factor 683 arises from the definition of the lumen as an SI unit, and the assignation of 683 lumens/watt for the spectral luminous efficiency (Km) of monochromatic radiation having a wavelength of 555 nm. For scotopic luminance L’v the above formula uses V’(λ) and normalising constant Km = 1700. The CIE Standard Observer Central to the CIE system of colorimetry is the specification of the responsivity functions of a ‘standard observer’, derived from the responses of only 17 observers in the classic colour matching experiments by Wright (1929) and Guild (1931). The curves (Fig. 11 left) represent the intensity value selected by the observer for each of three primary lights (red, green and blue) in a mixture to obtain a visual match with a monochromatic test light at each wavelength throughout the visible spectrum (Fairman et al, 1997). The transformed curves (Fig. 11 right) are non‐negative functions where is equal to . These curves represent the mean visual sensitivity over the population of non‐ deficient observers, and are known collectively as the CIE Standard Observer. For most imaging applications the data for the so‐called 2‐degree observer is used, because it represents the foveal response of the eye to small‐area stimuli in a scene. For applications in architecture and interior design the data for the 10‐degree Supplementary Observer is used (Judd, 1968), particularly because of the greater sensitivity to blue in the peripheral retinal field.
Figure 11. (left) Colour matching functions of RGB intensities required to match monochromatic test light; (right) Colour‐matching functions for the CIE 2‐degree 1931 Standard Colorimetric Observer.
Calculating Tristimulus Values The colour stimulus is quantified by multiplying together the power of the source by the reflectance of the object by the sensitivity of the observer at each wavelength and integrating over the visible spectrum. More formally, if the illumination source power is represented by S(), the reflectance of the surface by R(), and the observer’s colour matching functions by x ( ), y( ), z ( ) for each wavelength , then the visual stimulus of a colour is obtained by computing:
X k S ( )R( ) x ( )d
Y k S ( )R( ) y( )d Z k S ( )R( ) z ( )d
where k 100 / S ( ) y ( )d
Lindsay MacDonald, London College of Communication
(8)
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The three numbers defined by Eq. (8), known as tristimulus values X,Y,Z, uniquely define the perceived colour as viewed in the given environment. Because the y ( ) colour matching function is identical to the photopic spectral luminous efficiency function V ( ) , the Y tristimulus value is equal to the luminance of the stimulus. The scaling factor k is chosen so that Y=100 for a perfectly reflecting diffuser. The X and Z tristimulus values give an indication of the relative intensities of long (red) and short (blue) wavelengths in the stimulus, but have no perceptual correlates. For many purposes it is useful to calculate the chromaticity coordinates, which normalise the tristimulus values with respect to the total power of the stimulus:
x X /( X Y Z ) y Y /( X Y Z )
(9)
The original CIE 1931 x,y chromaticity diagram provided a convenient way of mapping coloured samples relative to the ‘white’ light used to illuminate them. The boundary of this diagram, the spectrum locus, represents the chromaticity coordinates of monochromatic stimuli throughout the spectrum (Fig. 12). The chromaticity diagram is actually quite non‐uniform perceptually, because the sensitivity of the eye to colour differences varies in different regions, particularly in the green where quite large coordinate changes are not very obvious visually. To correct this, the diagram can be altered in shape so that equal distances more nearly represent equal perceptual steps. This led to the further recommendation of the CIE 1976 u’,v’ diagram as a more uniform chromaticity representation. Figure 12. CIE x, y chromaticity diagram, showing the spectral locus with associated wavelengths (outer boundary) and the locus of blackbody radiators with temperatures in Kelvin (centre). www.lighttestlabs.com/index_files/color.htm
Uniform Colour Spaces Colour is trichromatic because there are three classes of photoreceptor in the retina. Two‐ dimensional chromaticity diagrams are only strictly applicable to colours having the same luminance. In general, colour stimuli vary in both chromaticity and luminance, and some method of specifying the colours in a three‐dimensional space is required. To meet this need, the CIE recommended in 1976 the use of two alternative uniform colour spaces, designated CIELUV and CIELAB, and the latter has found general favour for reflective surface colours. L* = 116 f(Y/Yn) - 16 a* = 500 [f(X/Xn) - f(Y/Yn)] b* = 200 [f(Y/Yn) - f(Z/Zn)] where: f(x) = (x)1/3 f(x) = (841/108)(x) + 16/116 Lindsay MacDonald, London College of Communication
(10) x > (24/116)3 x <= (24/116)3
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Correlates of the perceptual quantities chroma C*ab and hue hab can be derived as polar coordinates from the Cartesian a* and b*. Together with L*, these form a cylindrical 3D colour space (Fig. 13).
C*ab = (a*2 + b*2)1/2
(11)
hab = arctan (b*/a*)
(12)
Figure 13. (left) Three dimensions of the CIELAB colour space: light‐to‐dark, red‐to‐green and yellow‐to‐blue; (right) the a*‐b* plane, with achromatic grey at the centre.
Limitations of the CIE System Although CIE colorimetry has been remarkably successful as a basis for industrial colour measurement and specification, it assumes the very simple scenario of an observer performing a colour matching experiment under carefully controlled (and rather artificial) viewing conditions. The numerous inherent assumptions of the CIE system limit its applicability: There is a single source of illumination, uniform across the visual field; Tristimulus values are always referred to the light source. Sources with different SPDs may produce different tristimuli from the same patch (the phenomenon of metamerism); There is no fluorescence, i.e. contribution to reflected power from stimulation of the object by wavelengths outside the visible spectrum; The observer is fully adapted to the viewing conditions and is not colour deficient; Illumination levels are above the upper mesopic threshold, i.e. there is no response from the rod cells in the retina of the observer; Individual variations between observers, leading to observer metamerism, are ignored; Colour patches subtend a visual angle of between 1 and 4 degrees – outside this range the standard 2‐degree colour matching functions do not apply; Although the tristimulus values X,Y,Z may be absolute, their normalisation in the chromaticity and CIELAB formulae yield relative values from which it is not possible to deduce luminance; Background and surround effects are ignored, and the coloured patch is assumed to be viewed against a uniform achromatic field of similar luminance (avoiding simultaneous contrast); A unique white exists in the scene, or can be inferred, which is taken as the anchor point for vision and the reference value for computation; The stimuli are stationary and steady‐state, so that temporal effects do not affect perception; Viewing geometry, including the distance and relative angles of the light source and observer to the sample, is controlled. Lindsay MacDonald, London College of Communication
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6. Colour Rendering Colour rendering index 50 The ability of a light source to render the colours of V* Reference 40 an object in a natural way is specified by the CIE Test source General Colour Rendering Index Ra in the range 0‐ 30 100 (CIE, 1988). Sources with continuous spectra, 20 such as daylight and tungsten, have high values of 10 U* Ra approaching 100, whereas sources with spiky or 0 discontinuous spectra have lower values. A laser -40 -20 20 40 60 -10 0 scanner with three monochromatic lasers is an -20 extreme form of a tri‐band source, such as -30 fluorescent lamp or light‐emitting diode (LED). The -40 method for calculating Ra uses eight Munsell test -50 colours distributed around the hue circle, and takes the averages of their differences in U*,V*,W* space Figure 14. Coordinates in U*V* of 8 test colours when rendered by the test source and a reference under reference D65 daylight and the RGB lasers. source correlated to daylight. Computation for an equi‐energy RGB laser source vs daylight correlated to 8092K showed substantial differences in the U* axis (red‐green direction), especially for the ‘light reddish purple’ test colour (Fig. 14). The low overall value of Ra = 51.9 is similar to white fluorescent lamps, and is considered ‘appreciably deficient in some respects’ (Hunt, 1998: 95‐97). Berns and Haddock (2010) have recently proposed a new colour target for evaluating the colour rendering of light sources in museum applications, which consists of 24 colour samples, with 12 high‐chroma colours arranged at 30° hue intervals, four greys and four metameric pairs.
Metamerism Calculation of the tristimulus values (Eq. 8) combines three elements (Fig. 9), namely the illumination, object and observer. Thus three multi‐dimensional vector spaces are multiplied to give three scalar values. So it is possible for different spectral characteristics in any of the three elements to produce the same values, which leads to the phenomenon of metamerism. The most common form is where two surfaces with different reflection spectra look the same under one source of illumination but different under another. An example is the ‘jacket and trousers’ problem where one matches two garments under the store lighting then finds outside in daylight that they do not match because of different dye spectra (Fig. 15).
Figure 15. Reflectance spectra of two metameric woollen fabrics (Berns 2000).
Figure 16. Three sectional 3D views of the vectors of colours of 100 art pigments in CIELAB space from D65 (o) to A illuminant (x): (left) a*‐b* plane; (centre) a*‐L* plane; (right) b*‐L* plane. Lindsay MacDonald, London College of Communication
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7. Colour Measurement Geometry The CIE has recommended two basic systems of geometry for measuring instruments (CIE, 2004). The first is a bidirectional geometry for reflectance measurement, which requires the specimen to be illuminated at an angle of 455 from the normal and viewed in the direction normal to the surface (Fig. 17 left). This is known as 45:0 geometry and is the standard configuration for print viewing cabinets (Johnson and Scott‐Taggart, 1993). The converse 0:45 geometry is also permitted, on the assumption that physical reflection of the light rays is identical in both directions.
Figure 17. The configuration of standard illuminating/viewing geometries for colour measurement of reflective and transmissive materials (from Rich, 2002).
In the second configuration the sample is illuminated diffusely by an integrating sphere and then viewed along a line at approximately 8 to the normal to the surface; this configuration, known as d:8 geometry, gives a good indication of diffuse reflectance while avoiding the direct specular component. The converse geometry, 8:d, illuminates the sample with a beam and uses an integrating sphere to collect reflected rays at all angles. By control of a port in the sphere at the specular angle, the specular component (the ‘gloss ray’) may be either included or excluded from the measurement, with corresponding nomenclature di:8 and de:8. Analogous geometries t:0 and t:8 are defined for transmissive materials (Fig. 17 right). Colorimetry Colour is specified in terms of the perception of a human observer, and is standardised through the CIE tristimulus functions x ( ), y ( ), z ( ) . The colorimeter simulates the response of the eye with three channels having the sensitivities of the tristimulus functions. For each colour sample measured, the colorimeter generates three numbers for the tristimulus values X,Y,Z. Filter‐ based colorimeters have a source of light, a set of primary filters and a detector, and they compare the light reflected from the test colour with the light Figure 18. Schematic diagram of a tristimulus reflected from the reference colour (Fig. 18). Colour colorimeter (from Rich, 2002) separation is most simply achieved by three filters, with the short wavelength ‘bump’ in x ( ) (Fig. 11 right) approximated by a fraction of the blue filter. Better accuracy can be achieved by adding a separate indigo filter, thus forming a four‐filter colorimeter, or by constructing mosaic arrays of small slivers of different coloured filters (Rich, 2002). A sophisticated method of fabricating filters involves thin‐film deposition to form an interference stack with a precisely defined passband (Engelhardt and Seitz, 1993).
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Spectrophotometry Photometry is the measurement of visible light, and is a subset of radiometry, the measurement of radiant power. The power captured by a photosensor is the product at each wavelength of the power of the incident illumination by the sensitivity of the sensor, summed over the wavelength range. By using a suitable filter to match the sensitivity of the instrument to the V(λ) function a direct reading of luminance can be obtained. A spectrophotometer can be constructed by replacing the broadband coloured filters with a sequential series of narrowband interference filters. For example with 10 filters of width 30 nm covering the spectrum 400‐700 nm, the signals derived from each can be summed to approximate tristimulus values. Use of a monochromator to disperse the wavelengths of the reflected beam enables a sampling slit to be scanned across the wavelength range, to take a measurement of the power in each wavelength interval. Instruments may divide the spectrum Figure 19. Schematic diagram of a spectrophotometer into intervals of 20 nm, producing 20 values over the range 380 to 760 nm, or 10 nm (39 values), 5 nm (77 values) or 1 nm (361 values). Instead of a scanning technique, most current spectrophotometers disperse the incoming light by means of a diffraction grating onto a fixed linear array of photo‐detectors (Fig. 19). The geometry of the detector array determines the wavelength interval of each signal. When configured for surface colour measurement the instrument may be called a spectro‐ colorimeter. A measurement is taken of the reflectance of the internal light source from a white calibration tile, and then the reflectance factor of the test sample can be determined by dividing the power reflected at each wavelength by the corresponding power from the white tile. Using stored data tables for standard illuminants and observers at corresponding wavelength intervals, the tristimulus values are computed, enabling more accurate determination of the colour and colour‐ difference of metameric pairs. If the internal light source emits sufficient UV power, the influence of fluorescence may be assessed, which almost all papers and textiles possess (Bristow, 1994). When configured without an internal light source, and with a telescope to collect radiation from a small area in the field of view (typically a solid angle of diameter one degree), the instrument becomes a telespectroradiometer. It can be used to make direct measurements of the SPD of light emission from a source, or of the light reflected from a surface. Such instruments are invaluable for non‐contact measurement of lamps and displays, and, if portable, for measurements of environmental sources such as exterior shop lighting, street lights, and the sky. Goniophotometry In the standard measurement geometries (Fig. 14) the angles of both illumination and collection of the light are considered together. But there are many surfaces that cannot be adequately measured using such limited conditions, such as gonio‐apparent colours (Johnston and Stanziola, 1969). A popular example is the coloured metallic finish applied to car bodies which changes its appearance according to the angles of illumination and viewing. For complete characterisation, the colour of such a surface should be measured at more than one illumination/viewing angle combination (McCamy, 1996). To use an integrating sphere is a compromise because it captures the average reflectance of the sample but not the detailed variation with angle. This limitation has been partly overcome by multi‐angle spectrophotometers (Alman, 1987), which measure reflectance at three to five fixed angles (Fig. 20), as used in the automotive paint industry.
Lindsay MacDonald, London College of Communication
Tutorial Notes – An Introduction to Colour Measurement
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45 degrees 75 degrees Illumination
25 degrees
15 degrees
Specular angle
110 degrees
Figure 20. Multi‐angle spectrophotometry (viewing angles are specified with respect to the specular angle).
These instruments use the concept of aspecular angle, i.e. difference of angle from the specular direction, rather than designating the angles from the normal (90) to the sample surface (Rössler, 1990). It should be noted that aspecular angles may be negative, indicating a detection angle further away from the normal than the specular angle.
8. Metrology The conformance of a filter colorimeter to visual colour perception can be assessed by measuring a series of standard colours for which the tristimulus values (or a derivative such as CIE L*a*b*) under a standard illumination source are known. Typical test objects are ceramic tiles, or chips from a colour atlas such as the Munsell Atlas or the Swedish Natural Color System. Care is required in the intercomparison of values, because most colour order systems are specified by measurement with integrating sphere instruments (d:8 geometry), whereas most filter colorimeters are bi‐directional instruments (45:0 geometry). Measurements are not transferable between the two geometries. For a spectrophotometer the main operating parameters are the wavelength scale, radiometric scale (irradiance or radiance), spectral sampling interval and spectral pass band. There are accepted, international standards for each of these scales. The instrument manufacturer will generally supply a realisation one or more of these scales but it is the responsibility of the user to develop procedures to verify the scale realisation and to confirm the short‐term and long‐term repeatability. For verifying the scale of transmittance, a series of neutral density filters is available from standards laboratories, such as the National Physical Laboratory (NPL), and from filter glass suppliers. These filters will test both the scale of transmittance and the linearity of the system. For verifying the scale of reflectance or reflectance factor, there is a set of ceramic tiles (Fig. 21), which test the scale of reflectance factor, the linearity of the detector/amplifier/ digitiser system and the optical zero of the scale. This latter parameter is usually not an issue in transmittance readings, but reflection optics often produce homochromatic (similar wavelength) stray light that must be measured and subtracted from all subsequent readings. This correction should always be done at the time Figure 21. BCRA Series II colour tiles for the white tile is used to standardise (‘calibrate’) the checking the accuracy and consistency of colour‐measuring instruments. radiometric scale of the instrument (Clarke, 2006). The key performance parameters for colour measuring instruments are:
Repeatability, both short‐term (within a minute) and long‐term (typically an 8‐hour period); Reproducibility, or inter‐instrument agreement; Accuracy, the conformance to the correct or accepted value of test parameter.
All three parameters are frequently stated in terms of a colour difference between two instruments, or between a test instrument and a master instrument, or the average of a group of production Lindsay MacDonald, London College of Communication
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instruments (often called the production aim point). The colour difference may be reported as a mean or median, as a maximum, as an RMS value, as a Coefficient of Variation (CV), and at times as the Mean Colour Difference from the Mean (MCDM). Sometimes the colour differences are plotted to show relationships versus lightness, hue or chroma (Wyble and Rich, 2007). A key requirement is traceability, defined as ‘a property of a measurement result relating the result to a stated metrological reference through an unbroken chain of calibrations of a measuring system or comparisons, each contributing to the stated measurement uncertainty’ (Gardner, 2006). In practice this means that it should be possible to relate any measurement back to a primary national standard, for example at NPL or NIST, via one or more artefacts as secondary (transfer) standards. Testing a spectrophotometer The X‐rite eye‐one spectrophotometer (Fig. 22), is an economical and convenient instrument for measurement of surface reflectance. This hand‐held instrument was designed for surface colour measurement in the graphic arts, and has an internal gas‐filled tungsten source, ring illumination optics, 45°:0° geometry, 5.5 mm aperture, holographic diffraction grating and linear 128‐pixel diode array detector. It reports reflectance values from 380 to 730 nm at 10 nm wavelength intervals. The instrument relies on inbuilt factory data for calibration to its own reference white, using the spectralon target built into the baseplate supplied by the manufacturer GretagMacbeth (now owned by X‐rite), who give the following specifications:
Figure 22. X‐rite eye‐one spectrophotometer.
Inter‐instrument agreement: Average ΔE*94 = 0.4, max. ΔE*94 = 1.0 (Deviation from standard at 23°C for single measurement mode on 12 BCRA tiles, D50, 2°). Short‐term repeatability: ΔE*94 ≤ 0.1 (D50, 2°) (With respect to the mean CIE L*a*b* value of 10 measurements every 3 seconds on white). Repeatability One ceramic tile from the BCRA set (Fig. 18) – No. 2 Mid Grey E – was chosen for investigating the short‐term repeatability of the eye‐one spectrophotometer. The instrument was calibrated to white, and then the tile was measured 100 times at approximately constant time intervals, at a fixed position in the centre of the tile. The results showed very good agreement (Fig. 23 left) of the dataset at each wavelength. The mean of the 100 sets of reflectance data was calculated, and the difference from mean at 550 nm plotted (Fig. 23 right). This shows a systematic trend with earlier measurements being greater than the mean and the later measurements less than the mean, possibly caused by heating of the instrument held in the hand over a period of several minutes while the measurements were being taken. The swing in values of ±1.7% was relatively minor. 0.25 0.23 0.22
0.0005
0.21
0.20 0.19
0.0004
Difference from mean
Reflectance factor
0.24
0.18
0.17 0.16
0.15 350
400
450
500
550
600
650
700
750
0.0003 0.0002 0.0001 0.0000 -0.0001 0
10 20 30 40 50 60 70 80 90 100
-0.0002 -0.0003 -0.0004 -0.0005 -0.0006
Wavelength (nm) Measurement number Figure 23. (left) Reflectance factor vs wavelength for 100 successive measurements of a grey tile; (right) Difference from mean of successive values of reflectance factor at 550 nm. Lindsay MacDonald, London College of Communication
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The differences from the mean were plotted against wavelength (Fig. 24 left) and show clearly that the scatter was much greater for shorter than longer wavelengths. The standard deviation dropped from 0.0008 down to a minimum of 0.00007 (Fig. 24 right), corresponding to a range of CV (coefficient of variation = 100*stdev/mean) values from 0.46% at 380 nm to 0.043% at 730 nm. The equivalent signal‐to‐noise ratio (SNR = mean/stdev) therefore increased from 220 at 380 nm to 2330 at 730 nm. This could be attributed mainly to the SPD of the internal tungsten light source, which has much less power at short wavelengths (see Fig. 4 left). The spectral reflectance data were converted to X,Y,Z and thence into L*, a*, b* values using the D50 illuminant and 2° observer. The mean colour difference ΔE*ab over the set of 100 measurements was 0.026 with a maximum error of 0.06. The instrument therefore conforms to the manufacturer’s specification for repeatability. 0.0025
0.0008
0.0015
0.0007
Standard deviation
Difference from mean
0.0009
0.0020 0.0010
0.0005 0.0000
-0.0005 -0.0010
-0.0015
0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0.0000
-0.0020 350
400
450
500 550 600 Wavelength (nm)
650
700
350 400 450 500 550 600 650 700 750 Wavelength (nm)
750
Figure 24. (left) Difference of reflectance factor from mean vs wavelength for all 100 measurements; (right) Standard deviation of reflectance factor vs wavelength.
Accuracy Each of the 12 gloss BCRA tiles (Fig. 18) was measured five times and the mean reflectance factor of each tile was used to calculate X,Y,Z and hence L*,a*,b* values referred to a D50 illuminant. The accuracy was evaluated by comparing the measured data with the reference data provided by the tile manufacturer (Ceram). For seven of the tiles the average ΔE*ab colour differences were less than 1.0, and the overall average was 0.97 with a maximum of 2.42 (Table 1). These figures were not within the manufacturer’s specification of average 0.4 and maximum 1.0, but nevertheless indicate a reasonable level of accuracy in colour measurement. Pale grey L* a* b* ΔL* Δa* Δb* ΔE*
Mid grey
Diff grey
81.41
82.51
57.11
57.47
57.51
55.65
‐0.35
‐0.62
‐0.16
‐0.33
‐2.07
‐2.32
0.54
0.50
0.42
0.54
2.38
2.49
Deep grey 26.11
Deep pink
Red
26.53
40.71
40.91
38.33
38.31
0.14
0.01
30.87
30.87
55.26
53.80
1.37
1.33
6.67
6.53
38.82
37.94
1.09
0.36
1.87
0.42
0.20
0.03
0.27
0.17
0.25
0.13
0.00
1.47
0.04
0.12
0.11
0.04
0.14
0.88
1.13
0.42
1.89
0.44
0.24
1.71
Orange
Bright yellow
Green
Diff green
Cyan
Deep blue
65.95 65.38 45.90 43.32 65.88 63.14 0.57 1.58 1.74
82.94 82.77 1.45 1.20 83.10 81.44 0.17 0.25 1.66
52.13 52.58 ‐33.30 ‐32.90 15.24 15.02 0.45 0.40 0.22
2.42
1.69
0.64
L* a* b* ΔL* Δa* Δb* ΔE*
52.62 52.95 49.62 49.92 ‐32.97 ‐32.58 ‐19.33 ‐19.52 18.27 18.11 ‐35.09 ‐35.10 0.33 0.30 0.39 0.18 0.16 0.01
0.54
0.35
10.12 10.10 15.83 15.89 ‐31.00 ‐31.17 0.02 0.06 0.18
0.19
Table 1. Values of L*,a*,b* specified for the BCRA ceramic tiles (left column) vs average of five measurements by the eye‐one spectrophotometer (right column) and their differences. Lindsay MacDonald, London College of Communication
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Colour test charts Figure 25. Three test targets designed for characterisation of digital cameras: (left) Macbeth ColorChecker; (centre) GretagMacbeth ColorChecker DC; (right) GretagMacbeth ColorChecker SG.
For digital cameras three colour test targets are commonly used, with colorants typical of natural scenes. The traditional target is the Macbeth ColorChecker, originally developed for film cameras and television cameras (McCamy et al, 1976). It has 24 patches in a 3:2 aspect ratio, including a 6‐ step grey scale. For digital cameras the more recent Gretag Macbeth DC and SG charts were developed (Fig. 25), with 12x20=240 and 10x14=140 colour patches respectively. The patches in the original ColorChecker and the DC chart are matte, whereas the SG chart is semi‐gloss. The SG chart includes the same 24 colours of the original ColorChecker plus 16 skin tones, making it good for characterising cameras for portrait photography. A miniature version of the Macbeth ColorChecker chart is also available, having credit‐card‐size dimensions of 82x57 mm, with each patch being 9x9 mm. The reflectance spectra of the 24 patches (Fig. 26) were measured three times with the eye‐one spectrophotometer, with data imported via the Key Wizard software utility directly into an Excel spreadsheet. Reflectance data were recorded from 380 to 760 nm at intervals of 10 nm. The corresponding colorimetric data for the CIE tristimulus values X,Y,Z, chromaticity values x,y and uniform colour coordinates L*,a*,b* were calculated using the D50 illuminant and 2‐degree standard observer. The colour accuracy of the mean of the three sets of measured data was assessed against the standard data provided by X‐rite (Pascale, 2005), and showed an average error (ΔE*ab) of 1.06, with the worst colours being purple (ΔE*ab =3.86) and blue (ΔE*ab =2.45).
Figure 26. Reflectance spectra of 24 patches in MiniMacbeth colour chart, measured by eye‐one.
Lindsay MacDonald, London College of Communication
Tutorial Notes – An Introduction to Colour Measurement
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Bibliography Berns R (2000) Billmeyer & Saltzmann’s Principles of Color Technology, 3rd Ed., New York: John Wiley. Harrison VGW (1945) The Definition and Measurement of Gloss, London: The Printing and Allied Trades Research Association. Hunt RWG (1998) Measuring Colour, 3rd Ed., Kingston‐upon‐Thames: Fountain Press. Hunter RS and Harold RW (1987) The Measurement of Appearance, 2nd Ed., New York: John Wiley. Johnson AJ and Scott‐Taggart M (1993) Guidelines for choosing the correct viewing conditions for colour publishing, Leatherhead: PIRA International. McCluney R (1994) Introduction to Radiometry and Photometry, Norwood MA: Artech House. OCED (1996) Oxford Compact English Dictionary, Oxford University Press. Tilley RD (1999) Colour and the Optical Properties of Materials, New York: John Wiley Silvennoinen R, Peiponen K‐E and Myller K (2008) Specular Gloss, Amsterdam: Elsevier. Wright WD (1969) The Measurement of Colour, 4th Ed., New York: Van Nostrand Reinhold.
Standards ASTM (2000) E490, Standard extraterrestrial spectrum reference, West Conshohocken, PA: American Society for Testing and Materials. ASTM (2002) E284, Standard terminology of appearance, West Conshohocken, PA: American Society for Testing and Materials. ASTM (2004) E1767, Standard Practice for Specifying the Geometry of Observations and Measurements to Characterize the Appearance of Materials, West Conshohocken, PA: American Society for Testing and Materials. CIE Publication 13.2:1988, Method of specifying and measuring colour rendering properties of light sources, 2nd Ed., revised. CIE 15.3:2004, Colorimetry, 3rd Ed., Vienna: Commission Internationale de l’Éclairage. ISO 7589:2002 Photography — Illuminants for sensitometry — Specifications for daylight, incandescent tungsten and printer, Geneva: International Organization for Standardization. ISO 9845‐1:1992 Solar energy — Reference solar spectral irradiance at the ground at different receiving conditions — Part 1: Direct normal and hemispherical solar irradiance for air mass 1,5, Geneva: International Organization for Standardization. ISO 11664‐1:2007, Colorimetry — Part 1: CIE standard colorimetric observers, Geneva: International Organization for Standardization.
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Engelhardt K and Seitz P (1993) Optimum color filters for CCD digital cameras, Applied Optics, 32(16), 3015‐3023. Fairman HS, Brill MH and Hemmendinger H (1997) How the CIE 1931 color‐matching functions were derived from Wright‐Guild data, Color Research & Application, 22(1), 11‐23. Gardner JL (2006) Uncertainties in surface colour measurements, Good Practice Guide No. 95, Teddington UK: National Physical Laboratory, London. http://publications.npl.co.uk/ Guild J (1931) The colorimetric properties of the spectrum, Philos. Trans. Roy. Soc., A 230, 149‐187. Hunter RS and Judd DB (1939) Development of a method of classifying paints according to gloss, ASTM Bulletin, March 11, 118. Johnston RM and Stanziola R (1969) Angular color measurement on automotive materials, Proc. Intl. Automation Engineering Congress, Pub. 690241, Warrendale, PA: Soc. Automotive Engineers. Judd DB, MacAdam DL and Wyszecki G (1964) Spectral distribution of typical daylight as a function of correlated color temperature, J. Opt. Soc. Am. 54(8), 1031–1040. Judd DB (1968) The 1964 CIE Supplementary Observer Applied to the Colorimetry of Rutile and Anatase Forms of Titanium Dioxide, J. Opt. Soc. Am. 58, 1638‐1648. McCamy CS, Marcus H and Davidson JG (1976) A Color‐Rendition Chart, J. Applied Photographic Engineering, 2(3) 95‐99. McCamy CS (1992) Correlated Color Temperature as an Explicit Function of Chromaticity Coordinates, Color Res. & Appl., 17(2) 142‐144. McCamy CS (1996) Observation and measurement of the appearance of metallic materials: I. Macro appearance, Color Res. & Appl., 21(4), 292‐304. Pascale D (2005) www.babelcolor.com/main_level/ColorChecker.htm Pointer MR (2006) Technical Report: A Framework for the Measurement of Visual Appearance, CIE Publication 175:2006, Vienna. Rich D (2002) Instruments and Methods for Colour Measurement, in Green PG and MacDonald LW (Eds) Colour Engineering: Achieving Device Independent Colour, Chichester: John Wiley, Ch 2, 19‐48. Robertson AR (1968) Computation of correlated color temperature and distribution temperature, J. Opt. Soc. Am. 58, 1528‐1535. Rössler G (1990) Multigeometry color measurement of effect surfaces, Die Farbe, 37, 111‐121. Sharpe LT, Stockman A, Jagla W and Jägle H (2005) A luminous efficiency function, V*(λ), for daylight adaptation, Journal of Vision, 5(11) 948‐968. http://journalofvision.org/5/11/3/article.aspx Trezza TA and Krochta JM, Specular reflection, gloss, roughness and surface heterogeneity of biopolymer coatings, J. Applied Polymer Science 79(12), 2221‐2229. Wright WD (1929) A re‐determination of the trichromatic coefficients of the spectral colours, Trans. Opt. Soc. 30, 141‐164. Wyble DR and Rich DC (2007) Evaluation of Methods for Verifying the Performance of Color‐ Measuring Instruments. Part I: Repeatability, Color Res. & Appl., 32(3), 166‐175. Yang H, Zhu S and Pan N (2009) On the Kubelka‐Munk Single‐Constant/Two‐Constant Theory, Textile Research Journal, 1‐8.
Lindsay MacDonald, London College of Communication
pre-congress seminar: INTRODUCTION TO COLOUR MEASUREMENT by Prof. Lindsay MacDonald
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