Basic Concepts of Colour Measurement

Basic Concepts of Colour Measurement
Dr. Asim Kumar Roy Choudhury
Ex-Professor and HOD (Textile),
Govt. College of Engg. & Textile Technology, Serampore - 712201, Hooghly (W.B.), India
E-mail: akrc2008@yahoo.in




Colour in our Daily Life
From time immemorial, man must have watched inquisitive­ly the wonder-work of sunlight in creating blue colour of zenith sky, glowing scarlet of rising and setting sky and various hues of rainbow. Colour is also an integral part of our daily life, be it textiles, paints, plastics or printing. We can’t even imagine a colourless world around us. All our daily necessities are packed in attractive colourful packaging that tempts us to buy even if we do not need it. We can’t even imagine our television without colour. We choose our garments primarily by colour, which projects our personality. We select paints and furniture for our house by colour, which gives us pleasing atmosphere. The colour depicts the nature and inner personality of the car owner. Colour of a gem or precious stone also guides a person to overcome obstacles in his life. Colour has become a focal point of what we do every day.

Despite being so important and so close to everyone’s day-to-day life, it is not possible to express colour in unique or in specific language. We remember colour till we look at it. The moment we take away our sight from it, it gets erased from our memory. The colour scientists attempted to specify colour in explicit universal language so that it could be understood by everyone involved with colour and colour reproduction. This led to express colour numerically which is unique and unambiguous specification of colour.

Visual Perception of Colour

Colour may be viewed in two modes (Figure 1) namely:
  1. Illuminant mode- when the light stimulus comes directly from a source of light, say, an incandescent lamp or a candle.
  2. Object mode- when stimulus comes from an object either from its surface (surface mode) or through the object (volume mode). In this mode, the perception of an object is mostly in reference to the surrounding objects. Three ingredients are required to visualise the colour of an object, namely a light source, object itself and the human observer.
Fig-1: Two modes of viewing colours
A light source illuminates the object and is characterised by the energy at differ­ent wavelengths, which is denoted by the term spectral power distribution (SP­D). When a light beam falls on an object, it is modified by absorption, scatter­ing and other physical process­es depending on the physical and chem­ical construction of the object. The light (colour stimulus) that reaches the eye of the observer in the form of reflected light interacts with the photosensitive pigments present in the eye. This gives rise to nerve impulses which are transmitted to brain. The human eye-brain mechanism makes rapid and continuous evaluation of object appear­ance and colour. The light, which enters our eyes, contains the characteristic imprints of the light source and the object. Light can also fall directly (without interaction with object) on our eyes creating nerve impulses.

Colour Perception
The Committee on Colorimetry of the Optical Society of America in 1922 defined colour as the general name for all sensations arising from the activity of the retina of the eye and its attached nervous mechanisms, this activity being, in nearly every case in the normal individual, a specific response to radiant energy of certain wavelength and intensity (OSA, 1953).

Colour is sometimes used as a name for materials such as dyes and pigments, but the name Colorant will be more appropriate in these cases. The spectral composition of radiant energy and the spectral transmittance or reflectance of substances is also called colour, but it is again an inappropriate name for these purely physical concepts. Psychophysical concept of colour as character­istics of light dependant on human vision is most appropriate.

Perception of colour which is solely a prerogative of human beings is purely individualistic and hence subjective. As a result, objective communication of a particular colour becomes difficult. For expressing colour objectively one must measure and quantify it. The colour can be objectively expressed either by creating calibrated coloured physical samples or by an instrumental colour measuring devise and expressing it by numbers.

Colour Mixing
According to one reliable estimate, we can distinguish among ten million different colours (Judd and Wyszecki, 1975). Kuehni further estimated that the humans with normal colour vision can distinguish among some two million colours when viewed against a mid-grey background and perhaps double when the background is widely varied (Kuehni, 2005).

Newton explicitly stated that colour is a perceptual property, not a physical attribute, which meant that the light mixtures occurred in the eye, not in the light. Newton recognised three aspects of colour perception: brightness, hue and intensity. Painters and dyers already from before Newton’s time believed in three fundamental chromatic colours that they sometimes equated with pigments or dyes: yellow, red and blue, from which all other hues can be created. With long experience with paints and dyes they also affirmed that material colour mixtures and light mixtures behaved very differently.

Colour perception for humans is three-dimensional, a fact almost certainly stems from the existence in the retina of three different classes of light-receptive cells. LeBlon (1756) was first to make clear distinction between mixing pigment colours and mixing colours of light. He stated that all visible objects can be represented by three colours, yellow, red and blue and mixture of these three colours makes black or all other colours. He named those as material colours or those used by painters. He further added that for a mixture of spectral colours those proposed by Sir Isaac Newton cannot produce black, but the very contrary, white.

Primary colours are sets of colours that can be combined to make a useful range of colours. For human applications, three primary colours are usually used, since human colour vision is trichromatic.

Primary colours are not a fundamental property of light but are often related to the physiological response of the eye to light. Fundamentally, light is a continuous spectrum of the wavelengths that can be detected by the human eye in an infinite-dimensional stimulus space. However, the human eye normally contains only three types of colour receptors, called cone cells. Each colour receptor responds to different ranges of the colour spectrum. Humans and other species with three such types of colour receptors are known as trichromats. These species respond to the light stimulus via a three-dimensional sensation, which generally can be modelled as a mixture of three primary colours (Sobel, 1989).

Many birds and marsupials are tetrachromats (Backhaus and Werner, 1998), and it has been suggested that some human females are tetrachromats as well (Mollon and Jordan, 1993), having an extra variant version of the long-wave (L) cone type.

Most mammals other than primates have only two types of colour receptors and are, therefore, dichromats; to them, there are only two primary colours.

Any choice of primary colours is essentially arbitrary; for example, an early colour photographic process, autochrome, typically used orange, green, and violet primaries. However, unless negative amounts of a colour are allowed the gamut of colour generated will be restricted by the choice of primaries (http://en.wikipedia.org/wiki/Primary_color, accessed on 16.7.15).

Fundamental laws of colour mixing can, therefore, be classified into two types namely
  1. Additive colour mixing (Figure 2 a) occurs when two or more lights mix together.
  2. Subtractive colour mixing (Figure 2 b) occurs when colorants are mixed together.
Virtually all our visible colours can be produced by utilizing some combination of the three primary colours, either by additive or subtractive processes.
Fig-2: Additive and subtractive color mixing
For additive combination of colours, as in overlapping projected lights or in CRT displays, the primary colours normally used are red (R), green (G), and blue (B). The result of ad­ditive mixing of the primaries are listed below,

R + G = Y (Yellow),
G + B = C (Cyan or blue-green)
B + R = M (Magenta)
R + G + B = W (white)

For subtractive combination of colours, as in mixing of pigments or dyes, such as in dyeing or printing, the primaries normally used are cyan (C), magenta (M), and yellow (Y), though the set of red, yellow, blue is popular among artists.

The subtractive primaries can be obtained by removing red, green and blue from white light using respective coloured filters namely

W - R = C (- R)
W - G = M (- G),
W – B = Y (- B),

The mixing of subtractive primaries yellow, magenta and cyan can be predicted mathematically as fol­lows:

Y + M = (W - B) + (W - G) = W - B - G = R,
Y + C = (W - B) + (W - R) = W - B – R = G
M+ C = (W - G) + (W - R) = W - G - R = B,
Y + M + C = W - R - G - B = K (Black)

When the three subtrac­tive prima­ries are mixed in proper propor­tions as in case of mix­ing colorants, the mix­ture is unable to re­flect light anymore and ap­pear black (K) in colour. Similarly when white light is passed through filters of three subtractive colours, the whole of white light will be removed. Mixture of two primaries is called secondary. The most commonly used additive colour primaries are the secondary colours of the most commonly used subtractive colour primaries, and vice versa.

The age-old belief that three primary colours are required to make white was also proved false (Helmholtz, 1852). The idea of compli­mentary spectral colours came into existence and was subsequently defined by Grassman (1853) as follows:

To every colour belongs another homogeneous colour, which when mixed with it, gives colourless light.

Subsequently Helmholtz confirmed that every spectral colour does not have a spectral complement as proposed by Grassman. A range of green colours ranging from about 484 nm to about 570 nm, has complimentary colours in the non-spectral purple range.

Colour Communication
In colorant production and application industries, colours are to be communicated, compared, recorded and formulated on regular basis. This necessitates systematic classification of colours. The objects can be classified in various ways in terms of colour. The classification may be based on visually or instrumentally-assessed colour parameters (Roy Choudhury, 2000) .

While communicating or talking about colour, a language which is understandable by both the parties must be followed. A logical scheme for ordering and specifying colours on the basis of some clearly defined attributes is known as colour notation system. The attributes are generally three in number as our vision is trichromatic and they constitute the coordinates of the resultant ‘colour space’. Colour notation systems also encompass ‘colour order systems’ which are typically comprised of material standards in the form of colour atlas. Due to constraints of colorant gamut, the atlases may depict only a physically realisable subset of a colour order system.

Colour notations can be classified into three categories (Rhodes, 2002):
  1. Device dependant systems – the most common imaging devices used for reproducing colour are the computer controlled CRT displays and the colour printers. The associated colour order system and colour spaces are hardware-oriented and they lack perceptually based attributes.
  2. Mathematical systems – uniform colour spaces based on mathematical transformation of CIE tristimulus values such as CIELUV and CIELAB belong to this category.
  3. Systems based on database of aim points – colour order systems existing principally in physical form, the colour samples of which can be measured to establish a database of aim points. Using interpolation techniques among limited available samples, many more colours can be defined.
The monitors and printers follow device-dependant specification systems. In cathode ray tube (CRT) displays, colour television, and most computer video displays, colour stimuli are generated with three different types of phosphors after activated by electron beams. The three additive primary colours generated by such activation are orange-red, leaf green, and violet. A large number of colours can be created by their mixture.

Two most common additive systems used in connection with computer display are RGB (based on mixing of three additive primary colour red, green and blue produced by the phosphors of the display unit in cubic space) and HSB (hue, saturation and brightness in cylindrical form).

For instrumental colour measurement of an object, additive primaries are used to predict the quantity of subtractive colours required to reproduce that colour. This entails the use of standard source of light, viewing geometry and a standard observer. The expression of colour as numerals has been standardized by Commission Internationale de l’Eclairage (CIE) set up in 1931 for standardisation of measurement of colour. Thus the instrumental measurement of colour is helpful in, communication of colour across the entire supply chain as well as comparing samples and setting pass-fail criterion for sourcing and supply of products. In this form it is a useful tool for quality control.

It is very convenient, easily understandable and memorable when the colours are called by names similar to common objects orange, ultramarine, olive, malachite green, bottle-green, peanut-green, sea-green etc. But such colour names are very approximate, unreliable and temporary. Their meaning also changes with observer, time, place, style, technology, language, culture etc.

When we deal with a reasonable number of specimen, say a few thousands, to cover the whole range of possible colours (1millions or more), the specimen must be selected according to a system or plan. It is well known that the colours are three-dimen­sional. However, the dimensions of colour are expressed in various ways in different fields. For systematic arrangements, the dimensions should be independent of each other.

Visual Description of Colour
Wright (1984) identified two sets of visual attributes namely:
  • Group A attributes are lightness, hue and chroma
  • Group B attributes are whiteness, blackness and chromaticness.
According to him, group B attributes are more useful because it is most easily understood and is more fundamental for observers to represent colour appearance. However they are less studied in psychometric (equal perception) terms.

A colour order system is a systematic and rational method of arranging all possible colours or subsets by means of material samples. Once the colours are arranged systematically they are named in some descriptive terms and/or are numbered (Graham, 1985).

The colour order systems are of three types (Wyszecki, 1986):
  1. Colorant-mixture system based on subtractive mixture of colorants e.g. Pantone
  2. Colour-mixture system based on additive mixture of colour stimuli e.g. Ostwald system.
  3. Colour appearance system based on the principles of colour perception or colour appearance e.g. Munsell.
Examples of colorant-mixture systems are the colour atlases developed by different dye manufacturers. ICI colour atlas (1969) was a collection of 1379 original colours and 27,580 variations printed on papers.

Pantone Colour System (Figure 3) is basically a colourant mixture system. The Pantone system (www.pantone.co.uk) began life in 1963 in the USA, for defining colours for printers, but expanded into other fields later, e.g. textiles in 1984, plastics in 1993, and architecture and interiors (1925 colours) in 2002, each of which has a 6-digit numerical notation (e.g. # 19-1764) and an inspirational colour name. This is widely used in graphic art and also in textile industry mainly because of its low cost, though the colours are not equally spaced. The shades are prepared on paper using printing inks. It is not a colour order system since it does not include a continuous scale. It is more appropriately considered a colour naming system.
Pantone color guide
Fig-3: Pantone color guide
Colour appearance systems are based on the perception of colours by an observer with normal colour vision. The scales of these systems are chosen to represent attributes of perceived colours. However, attributes represented in various systems are different.

The main emphasis of appearance-based systems is the uniform visual spacing. The systems thus allow easy interpolation between the samples represented and extrapola­tion of colours not illustrated in a given collection. The collections of samples are generally represented in pages of constant hue.

Six popular colour order systems, country of origin and their respective colour attributes are as follows (Roy Choudhury, 2010) :
  1. Munsell (USA) – Hue, Value and Chroma
  2. Natural Colour System (Sweden) – Hue, Blackness and Chromaticness
  3. Ostwald system (Germany) – Hue, Lightness and Saturation
  4. DIN system (Germany) – Hue, Saturation degree and Darkness degree
  5. OSA-UCS (USA) - no separate scaling of three attributes
  6. Coloroid System (Hungary) – Hue, Saturation and Lightness.
Most popular appearance-based colour order system is Munsell system. The system (Figure 4, https://en.wikipedia.org/wiki/Albert_Henry_Munsell) consists of the following three independent dimensions which can be represented cylindrically in three dimensions as an irregular colour solid.
  1. Hue (H), measured along circumference of the horizontal circles
  2. Chroma (C) or purity of colour, measured radially outward from the neutral (grey) vertical axis
  3. Value (V), measured vertically from 0 (black) to 10 (white).
The complete Munsell specification of a sample is expressed as H V/C (e.g. 5R 4/8).
Munsell color system
Fig-4: Munsell color system
Munsell system divides each horizontal hue circle into five unique or principal hues: Red (5R), Yellow (5Y), Green (5G), Blue (5B), and Purple (5P), along with 5 intermediate hues (5YR, 5GY, 5BG, 5PB, 5RP) halfway between adjacent principal hues.

The Munsell atlas is usually available on painted paper in glossy (1488 chips) and matt forms (1277 chips). A method for specifying opaque object colours such as textiles, painted panel etc. by Munsell colour system has been described by ASTM (1980).

SCOTDIC, a textile version of Munsell created by fusion of two quite different systems - Standard Colour of Textile (Japan) and Dictionn­aire Internationale de la Couleur (France), is adopted by over 8,000 companies worldwide. Textile standard colours of the SCOTDIC colour system are widely used as colour tools by fashion colour professionals. The system has three versions - glossy (2468 colours on polyester crepe fabric), matt (2038 colours on cotton poplin fabric) and yarn (1100 colours on wool yarns). It has incorpo­rated many bright colours and the number of constant hue chart has been increased to 54 (20 for Wool). SCOTDIC system uses a six digit code for each standard colour – the first two digits for hue, the second two digits for value and the third two digits for chroma. The prefix corresponds to the material of textile bases – P for Polyester, C for Cotton, W for Wool. Therefore, the notation C-155010 means cotton Standard sample having hue = 15, value = 50 and chroma = 10 (Roy Choudhury, 2008).

Most of the material based atlases are now available in digitised form e.g. NCS Digital Atlas (www.ncscolour.com), Digital Colour Atlas 3.0 (www. dtpstudio.de) etc.

Figure 5 shows two pages from the Munsell Book of Colours. Figure 5 (a) shows hue circle having samples of 100 hues in two depths (moderate and dark shades) (samples of some hues are missing). Figure 5 (b) shows constant hue page of hue = 05. In these pages, rows represent constant values samples, while columns represent constant chroma samples.
Fig-5: SCOTDIC book of color (a) Hue circle (b) Constant Hue page (Hue = 05)
Instrumental Measurement of Colour
Newton said that (light) rays are not coloured, but merely has the power to simulate certain sensations in the mind of the observer. Human eye is a highly versatile detector of light and colour. An observer can perceive chromatic attributes and various geometric factors (direction, texture, shape and many others) simultaneously. An instrument till date is far behind in versatility. It can measure only one attribute at time. In other words, we need several instruments to measure various aspect of visual perception.

Basically there are three types of colorimetric instruments in use - colorimeter, spectrophotometer and spectroradiometer. They are available in the market with varying degrees of sophistication and specialisation. While the spectroradiometer measures in illuminant-mode, the other two generally measure in object mode. The recent trend on instrumental process control has resulted in use of on-line instruments. However majority of the colorimetric instruments till date are off-line and mostly used in laboratories. Laboratory instruments should be highly accurate and standardised, while on-line instruments should be rugged under various environments and should have good precision and firmness.

The colorimeters measure colour in terms of the quantities of the three primaries required to match the colour. On the other hand, spectrophotometer measures percent reflectance or transmittance of the object plotted against wavelength at regular intervals of 1 nm, 5 nm, 10 nm, 20 nm throughout the visible range of light i.e. 380-750 nm or for practical purposes 400-700 nm.

Colour by Numbers!
The colour of an object depends on the relative quantity of the light reflected at different wavelengths within the visible range (400-700 nm), but our colour sensation is not analytical in nature. We cannot judge the existence of lights of different wavelengths individually. We get the sensation from cumulative effect. As this cumulative quantity can be matched by mixing three primary lights it is proved that our eyes have three types of colour-detecting cones, the stimuli generated by them are mixed before reaching to brain. Various other phenomena of colour have also lead to the conclusion that our eyes have three types of cones only. Each object colour is sensed by each type of cone separately and each type sends a stimulus to the brain.

So, for each object colour, the brain receives three separate stimuli. Keeping similarity with colour mixing experiment, we can consider the three types of cones as red-sensitive r, green-sensitive g and blue-sensitive b equivalent to the three additive primaries. The spectral sensitivity of the three colour-detecting cones has been measured and named as colour matching data r(λ), g(λ), b(λ) (bar stands for statistical average data of a number of colour normal observers) and subsequently transformed into more usable CIE standard observer functions, x(λ), y(λ), z(λ). The area under the functions signifies the amounts of three stimuli to be transmitted to the brain for the incidence of light having one unit of energy at each of visible wavelength. These three stimuli are represented by three numbers called CIE tristimulus values (X, Y, Z) which may be calculated as follows:

Where E(λ) is the relative spectral energy distribution of the illumin­ant, R(λ) is the spectral reflectance factor of the object and x(λ), y(λ), z(λ) are the colour matching functions of the CIE standard observer. K is a normalising constant.

A light source is an essential component of visualisation and measurement of colour. Various light sources, such as daylight (D65), tungsten lamp (A), fluorescent lamp (F1 to F12), departmental lamp (TL84) etc., emit different amounts of energy in the visible region of the spectrum that can be expressed in the form of its relative spectral power distribution (SPD) curve. An illuminant is an ideal form of a light source with defined SPD. The SPD of light source may vary, but that of illuminant is constant or defined and hence, it is used for quantification of colour as mentioned above.

In the visual observing situation, the observer is the human eye that receives the light reflected from or transmitted through an object and the brain which perceives the vision. Since different human perceive colour in different ways, subjectively, attempts have been made to standardise the human observer as a numerical representation of what the average person sees. This standard observer could then be used in lieu of a human observer when assessments are made instrumentally. In 1931 CIE published the 2° CIE Standard Observer function based on colour matching by viewing through a hole of 2° field of view. Later it came to know that cones present in a larger area of the eye. Hence, in 1964, the 10° Standard Observer function was developed which is now universally used.

When two objects have equal tristimulus values under a particular illuminant, they will look alike in colour under the said illuminant. If their reflectance curves are same they will look alike in colour under any illuminant (universal match). Otherwise they may or may not differ in colour when the illuminant is changed. On the other hand, two alike colours with different lightness may have different tristimulus values. To express colours in two-dimensional space independent of lightness, chromaticity coordinates may be calculated as follows:
As x + y + z = 1, only two chromaticity coordinates x and y have been recommended by CIE to specify chromaticity. Instead of tristimulus values (X, Y, Z), colours can also be specified by a luminance parameter Y and two colour coordinates x and y (Yxy colour space).

However, none of the chromaticity coordinates is correlated with any meaningful visual attribute of colour.

When the chromaticity coordinates of spectral colours are plotted in such diagram, a horse-shoe shaped curve called chromaticity diagram is obtained. Chromaticity diagram is of great help in finding colours generated by additive colour mixing. If two lights are represented by two points on the chromaticity diagram, any additive mixture of the two will correspond to a point on the straight line joining the two points. Since the locus of spectral colours is concave, all real colours must fall within the area bounded by the spectrum locus and joining the ends.

Figure 6 shows CIE 1976 chromaticity dia­gram along with location of different spectral colours (i.e. mono­chromatic lights of different wave­length­s in nm). The figure also shows the regions of loca­tions of differ­ent surface colours viewed under day­lig­ht. Approximately in the centre of the curve is the neutral point, which represents the chromaticities of white, grey or blacks. The illum­inant C having chro­matici­ty co-ordinates x = 0.310 and y = 0.317 also lies at the centre of the curve (point C). The locations of other illuminants depend on their colour tempera­tures. The chromaticity diagram is closed by line indicating the locations of non-spectral purple colours.
Fig-6: Location of Spectral Colors in 1976 CIE Chromaticity Diagram
CIE system is very successful for colour specification and is universally used for colour measurement. The system is unchanged since 1931 except some minor change in 1964. CIE tristimulus values are related only to the colour. It ignores all other aspects like surface texture, gloss etc. which influence colour appearance significantly. It does not take into account geometrical arrangements for illumination and viewing and the instrumental measures will match visual assessments only if the above geometries are similar.

The main limitation of CIE system is its visual non-uniformity. Equal changes in Yxy colour space do not correspond to equal colour perception. In other words, the distribution of colours in CIE colour space is non-uniform with regard to visual perception.  
 
Uniform Colour Scales
CIE tri­stimulus values or chro­maticity coordinates are not very convenient for identifying colour of the objects, because these were designed for colour stimuli of different modes. None of the values are directly correlated with any visual attributes of colo­ur. Only Y value has high correlation with luminance and object lightness. The spacing of colours in chromaticity diagram is not visible uniform. A number of uniform colour scales are, therefore, developed which can represent colours with equal visual spacing and are directly related to meaningful attributes of colour appearance.

In 1976 CIE recommended CIELUV and CIELAB uniform colour spaces. Colorant industries were in favour of a formula similar to Adam-Nickerson (AN40) formula, popular at that time. The CIELAB formula was acceptable as colour-difference values were about 1.1 times those produced by AN40 formula. On the other hand, television industries preferred a colour space (CIELUV) associated with a chromaticity diagram because of its simple way of presentation of additive mixture which also occur in televi­sion and other display devices. No simple relation exists between the two colour scales.

Both CIELUV and CIELAB formulae are plotted on rectangular coordi­nat­es. Lightness L* function is same for both colour spaces and is represented by the formula,

L* = 116(Y/Yn)1/3 - 16    if Y/Yn  = 0.008856  
For CIELAB Colour Space,   Red-green attribute,      a* = 500[f(X/Xn) - f(Y/Yn)]      
Yellow-blue attribute,     b* = 200[f(Y/Yn) - f(Z/Zn)]     

Subscript n represent nominally white object colour stimulus given by a perfect reflecting diffuser as reference surface illuminated by standard illuminant. For standard daylight illuminant D65, the values are: Xn = 95.047, Yn = 100.000, Zn =108.883. White object has been taken into account because we perceive colours in relation to surrounding colours.

In recent years efforts have been made to define CIE correlates for perceptual attributes like lightness, chroma and hue. Hence, two new attributes corresponding to visual attributes have been derived from a* and b* values namely:

Metric chroma, C*ab = [(a*)2 + (b*)2] 1/2
                Hue angle, h = tan -1 (b*/a*).

CIELAB colour space is shown in the Figure 7. Lightness L* is represented in vertical axis with white (L* = 100) at the top and black (L* = 0) at the bottom. Chromatic colours are represented by two opponent a* and b* axes. Red and green are represented by a* axis – the positive values are for red and negative for green. Similarly positive b* values are for yellow and negative b* values are blue.
Fig-7: CIELAB color space
Colour Difference
Measurement of difference in colour between two objects is one of the most complicated aspects of colour vision. The colour discrimination may be general/overall or of specific psychophysical attribute like hue, chroma or lightness. For colorant users like textile, leather, paper or paint industries, the difference in colour of two specimens namely a standard and a sample or of different portions of a coloured specimen may be more important than the measurement of absolute colour (Luo, 1986). The prime difficulty is that the perception of colour-difference by an individual is not a precise phenomenon and may vary on successive assessment (Zeller and Hemmendinger, 1978). Colour-difference perception and evaluation may also vary widely among individuals.

The colour-difference evaluation is necessary for day to day colour control and for colour matching in colouration industries like textile, paint etc. Colour-difference formulae have accelerated the instrumental pass-fail device a success.

The colour differences are calculated by subtracting values of the standard from the respective values of the sample. The total colour-difference (ΔE) is intended to be single number metric for pass/fail decisions and in the CIELAB system ΔE is given by the following equation:

ΔE = [ (ΔL*)² + (Δa*)² + (Δb*)² ]1/2

In addition to the overall colour difference (ΔE), the difference in individual parameters of the standard and a sample are also estimated e.g. ΔL = L (sample) - L (standard).

These may indicate some specific visual difference such as

if ΔL < 0 or > 0, the sample is darker or lighter respectively,
if Δa* < 0 or > 0, the sample is greener or redder respectively,
if Δb* < 0 or > 0, the sample is bluer or yellower respectively.

ΔE (CIELAB) values are not always reliable in predicting perceptible differences between object colours, especially when the variations are in different visual attributes. This is due to the fact that the visual spacing along L, a* and b* axes are unequal.

The formulae based on surface-mode colour discrimination data mainly aimed at single number shade-passing. Much of the available visual data related to physical samples are supplied by the textile and dye industries, where prime criteria is that whether the colours will be acceptable against the respective standards.

Main reason for poor correlation with visual data of the earlier formulae was equal weighting of the colour parameters. The weighted values of lightness, chroma and hue showed significant improvement in performance of colour-difference equations. The weights can be determined by empirical fitting to experimental data-sets. These formulae are optimized by visual acceptability/ perceptibility scaling. They represent most closely the average visual results of judgments of colour difference of textile and other physical samples under normal evaluation conditions (Kuehni, 1984)

A few colour-difference formulae based on surface-mode colour discrimination data are:
  1. JPC79 colour-difference Formula
  2. CMC (l:c) colour-difference Formula
  3. BFD (l:c) colour-difference Formula
  4. CIE 94 colour-difference Formula
  5. CIE 2000 colour-difference Formula
However, none of the above formulae is completely satisfactory and acceptability of a particular formula is decided mutually by producers and users/salers.

Colorimetry is the science of quantitative measurement of colour. Even though study on colour science started as far back as the Newtonian age, research continues even today. Colour Science is a vast field. Hunt (1977) identified three phases of development of colorimetry - colour matching, colour difference evaluation and lastly, prediction of colour appearance. It is now possible to predict colour appearance of an object under a test illuminant from the colour appearance data under a reference illuminant with the help of complex mathematical transformations.

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