Whiteness is, in some respects, a difficult concept to explain easily. In a physical sense a white surface is a perfect diffuse reflector. No such surface exists in reality although some substances such as snow can come close. Whiteness is something quite different: a surface has a high whiteness if it is perceived as being very white.
Whiteness is therefore a property defined by the human perception of white; this differs from an actual physical white. In the paperboard industry a high whiteness is preferable to a truly white, or near white surface.
Interaction between materials and light
Visible light is part of the electromagnetic spectrum. The spectrum includes radio waves and X-rays, as well as ultraviolet and infrared light. Light can be described by its wavelength, for which the nanometre (nm) is a convenient unit of length. One nanometre is 1/1,000,000 mm. Light with a wavelength between 400 and 700 nm is visible to the human eye.
Reflectance of light. Click to enlarge images.
Light from the local light source, for example a tungsten bulb, impacts upon the object. The light is absorbed, reflected, transmitted or scattered according to the nature of the object. Colour perception is strongly linked to the absorption of certain wavelengths of light. A perfectly white object will reflect all the light at all the wavelengths; a sample with high whiteness will reflect most of the light; a red object will absorb most of the light and reflect only the light in the red portion of the incident light; a blue object will also absorb most of the light but it will reflect the blue light in the incident illumination. A black object will absorb most of the incident light.
The colour of the object can be considered in terms of its spectral reflectance curve. This is an indication of how much light of a specific wavelength will be reflected.
The images below illustrate the difference in spectral response between an OBA-containing paperboard and an OBA-free board under different illumination. Under normal daylight (left) the incident light contains a fair amount of low wavelength radiation activating the OBA thus making the two samples reflect different amounts of light in the blue spectrum. If the light is more like a tungsten light (right) the lack of low wavelength radiation make the samples look more alike due to the fact that the reflective powers at higher wavelengths are similar.
Click to enlarge images.
Transmission of light through a
Transmission is when light can pass through a material essentially unchanged. The light is said to be transmitted through the object and the material is described as transparent. If some of the light is absorbed then the object remains transparent but it will be coloured. For example, if the blue light is absorbed then the transmitted light is yellow, if red light is absorbed then the transmitted light is green and vice versa in both cases. If all the light is absorbed then no light is transmitted and the object is black and opaque.
Scattering is caused when light interacts with small particles in a material with a different refractive index to that of the surrounding material, which is usually air. Examples of light scattering
Absorption of light by a transparent coloured
the blue colour of the sky
and the white appearance of clouds and
snow are all due to scattering.
If the scattering is sufficiently intense that very little or no light passes straight through the object then the object will be opaque: it will have a high opacity. If the same amount of scattering occurs at every wavelength and there is no absorption then the object appears white.
Some light is transmitted and some is
diffusely reflected by scattering.
Opacity (ISO 2471)
The opacity of a sample is its lack of transparency.
A sample with an opacity of 100 % does not allow
any light to be transmitted through it and therefore
fully obscures anything lying under it.
A sample with an opacity near to zero is almost completely transparent and hides nothing. This standard still specifies the C illuminant rather than D65.
Assessment of CIE-Whiteness
The term, “white”, should not be applied to paperboard as white refers to the perfect diffuse reflector. Instead, it is meaningful to discuss paperboard in terms of whiteness. Because no paperboards are white, no paperboard should be described as being whiter than another but a paperboard can have a higher whiteness level than a competing product. (In reality very few people are this careful of their language when discussing paperboard.)
Many studies have been carried out and many formulae proposed to describe whiteness. The CIE whiteness and tint measurements are currently favoured (ISO 11475).
CIE Whiteness (ISO 11475)
The CIE whiteness and tint equations can be stated
W = 2.41L* – 4.45b*(1–0.009(L*–96))–141.4
T = –1.58a*–0.38b*
– 3 < T< 3
40 < W < 10.6L*– 852
This is not the normal way to define CIE whiteness but it is mathematically valid and serves to illustrate that a CIE whiteness value does not specify a point in L*,a*, b* space but instead specifies a plane. If both CIE whiteness and tint are specified then the result denotes a line in L*, a*, b* space. These are important considerations as it must be understood that samples with the same whiteness values need not have similar colour properties.
Although an increase in CIE whiteness usually corresponds to an increase in perceived whiteness, the whiteness scale is rather arbitrary. CIE lab coordinates can be very helpful in determining if a change in CIE whiteness values corresponds to a significant change in perceived whiteness.
Looking at the above equations is also helpful for understanding why FWAs and dyes are added to the paperboard. The dyes and FWAs both impart a blue colour to the paperboard. Blue is associated with negative values for b* and, as the above equation indicates, the greater the negative b* value the higher the perceived whiteness.
A CIE whiteness value should always be accompanied by a tint value (T), though this is often omitted.
A positive tint value corresponds to a green tint: a negative tint value corresponds to a red tint.
For a meaningful understanding of the CIE whiteness equations we must first understand the three-dimensional colour measurement system used to describe colour at the time when these equations were constructed.
The human eyeball contains two types of light sensor: rods and cones. The rods are sensitive to black and white; the cones are concerned with colour perception. There are three types of cone, each absorbent at long, medium or short wavelengths. (They used to be described as red, green and blue but this description is now out of favour.)
CIE 1934 xyz colour space chromaticity diagram. Click to enlarge.
A series of experiments was performed, in which a pure light, that is, light of a defined narrow band of wavelengths, was shown to a series of participants. The participants had then to match the colour that they were shown by filtering the output of three lamps, each of which lamp stimulated only one type of cone. The output from these experiments was a way of describing how light of a specific wavelength stimulates these three receptors.
These colour matching functions can be used in conjunction with a reflectance spectrum to calculate the tri-stimulus values X, Y and Z, which relate to the response of the long, medium and short wavelength cones respectively.
The X, Y and Z values were used to form a three-dimensional representation of colour.
The third axis is simply the Y axis: this is normally depicted as the vertical axis.
In further perceptual experiments it was shown that the perceived whiteness increased along a line between the x and y coordinates of the illuminant, denoted xn and yn, and the edge of the colour shape at a wavelength of 425 nm.
W = Y + 800 (xn – x) + 1700 (yn – y)
This equation simply indicates that if the sample moves along the line described then the perceived whiteness increases. As this line describes the addition of a violet colour to a neutral sample the addition of violet dyes can increase the perceived whiteness. This equation has a number of boundary conditions and should always be accompanied by a tint value.
The scaling for CIE whiteness is quite arbitrary. A unit change in whiteness is not associated with any particular perceived change. It must be remembered that a whole range of samples with quite different appearances can have the same CIE whiteness value and even matching CIE whiteness and tint values.
A perfectly white sample has a whiteness of 100. Samples with CIE whiteness levels above 100 therefore give a greater impression of whiteness than a truly white sample.
Whiteness is strongly influenced by the raw materials used. When paperboard is made from fibres with a low whiteness level these are often covered with layers of white chemical fibres, white pigmented coatings, or a combination of the two.
L*, a*, b* colour space. Click to enlarge.
Colour and shade
When measuring colour properties it is necessary to specify the illuminant used. At the time of writing it is normal to use the D65 illuminant when measuring the optical properties of paperboard. D65 indicates diffuse, that is, non-coherent, light with a colour temperature of 6500 Kelvin. Many graphic arts standards specify D50, which is diffuse illumination with a colour temperature of 5000 Kelvin. These two illuminants are broadly similar but D65 is significantly richer in ultraviolet light than D50.
L*, a*, b* Coordinates (ISO 5631-2)
The L*, a*, b* system is a three-dimensional system for describing colour. This system is very useful for considering differences between samples. The coordinate system was designed with the intention that a unit difference in the coordinates space should correspond to a perceptible change in colour. With measurements from two samples under the same illumination conditions, the coordinates give a clear indication of the differences in colour between the two samples. By measuring the same sample under a number of different illumination conditions, the variation in appearance of the sample accompanying changes in illumination can be considered in terms of figures relating to the human perception of colour.