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Basic concepts of colour measurement

Colours in our Daily Life

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People involved with colour and colour reproduction needed a unique and unambiguous specification of colour, leading to colours being expressed in numeric codes, which is explained in detail in this article like the perception of colours, the representation of colours, and other interesting semantics of it.

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 the 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  (bar stands for statistical average data of a number of colour normal observers) and subsequently transformed into more usable CIE standard observer functions,   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 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  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 a light source may vary, but that of the illuminant is constant or defined and hence, it is used for quantification of colour as mentioned above.

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

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 perceives 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 4 shows chromaticity dia­gram along with the location of different spectral colours (i.e. mono­chromatic lights of different wave­length­s). 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 a line indicating the locations of non-spectral purple colours.

Figure 4. CIE 1931 Chromaticity Diagram and Locations of Object Colours when Viewed under Daylight.

 

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 the 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.

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