Light and Colour

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Light and Colour

Increasing emphasis is being placed on cosmetic dentistry, essentially the invisible repair of teeth. This ‘invisibility’ requires that the optical properties of colour, gloss and translucency of tooth substance be reproduced in the restorative material. The factors concerned in this, and the conditions under which it may be obtained, involve understanding the nature of colour. Colour itself is a product of the interpretation by our brain of physical stimuli. Discussion of the factors and conditions relevant to colour matching involves defining the terminology and the nature and dimensions of colour. The roles of the absorption of light by the object and the spectrum of the illumination are explained, as well as the interactions between them. Understanding of these basic principles is necessary to deal with the issues affecting colour matching in practice, as applied to the real problems of shade selection. Other physical attributes of materials also affect the optical appearance of materials. The most important of these is refractive index, and the effects operating at boundaries. This has implications for the design of materials, and the effects of faults and surface conditions, especially roughness. The chemical basis of colour is also outlined in terms of the absorption (and emission) of light. This bears on the means of colouring various types of material, and also their colour stability over time. Colour is another topic that is generally neglected but yet is an important issue, affecting as it does the conditions under which shade matching is undertaken. Comprehension of these issues is necessary to avoid the wastage of effort in high-value cosmetic dentistry.

Materials Science for Dentistry https://doi.org/10.1016/B978-0-08-101035-8.50024-9 Copyright © 2018 Elsevier Ltd. All rights reserved.

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Whilst a major role of dental treatment is to restore form and function to the dental apparatus, rehabilitation, the vanity of man is such that merely functional restoration is often insufficient and the appearance of the prosthesis, be it anywhere from fissure sealant to full denture, assumes great importance. ‘Aesthetic dentistry’ is a greatly overworked phrase, for it surely depends on the eye of the beholder and opinions differ: black denture teeth found favour in at least one country, gold work is often prominently displayed, and a diamond has been seen worn in at least one upper central incisor. As appearance (or, at least, intended appearance) is the wearer’s choice, the term ‘cosmetic dentistry’ is perhaps more honest. This includes ‘tooth whitening’ - noticing that natural teeth are not truly white - and which often represents an attempt to change appearance to match some perceived but unrealistic ideal. A quick glance at a dental shade guide will convince you of this. However, both terms are frequently interpreted as meaning only reproduction of the appearance of natural tissue so that the restoration is undetected by onlookers in day to day life. Clearly, if that is the case, neither term is being used properly. If, however, we accept that the matching of the colour and other optical attributes of a restoration to those of the replaced or surrounding tissue is a worthwhile goal, which seems not to be a difficult proposition, then the nature of colour, its generation, and the factors that influence its perception, should be understood. This is to enable the practitioner to achieve several goals. Firstly, the ‘taking of a shade’ is a critical process upon which patient acceptance depends. Secondly, limitations to the quality of the match that can be attained need to be understood to inform the selection of material. Thirdly, the patient needs to receive advice on what can be achieved and what is to be expected, especially when a material may show age-related changes in appearance. A related problem occurs in connection with tooth whitening when restorations of any type are present: it is extremely unlikely that there could be any change in the restorative material to match that in the teeth. This would leave the restorations rather obvious, presumably requiring replacement, which could be a very expensive proposition. Fourthly, appearance is affected by the surface condition (scratches) and internal structure of a material (e.g. porosity) and is therefore under at least some control in terms of finishing treatments and perhaps mixing.

§1. The Sensation of Colour ‘Light’ is generally understood to be electromagnetic radiation which may be detected by the receptors of the human eye, although no actual physical distinctions can be made to identify that particular portion of the continuous spectrum which ranges from extremely low frequency radio waves to gamma rays (Fig. 1.1). It is of course ‘visible’ only because of the simple chemical Fig. 1.1 Part of the electromagnetic spectrum. The visible region is fact of the energy of the radiation being able the central, shaded part. to reach those receptors and be absorbed at the sensitive organelle. Indeed, no distinct boundaries between portions of the visible spectrum (i.e. ‘colours’) can be drawn sharply anywhere. In fact, what wavelength range is visible varies widely between species. All of the many designations are essentially phenomenological; that is, the labels are applied according to the spread of wavelengths associated with particular kinds of physical effects. Visible light then is no more special in this regard than any other region. Our brain can utilize the information provided by the eyes to build up information about the disposition and nature of the immediate environment, coupled with other sensory input. As far as light is concerned, however, we may also distinguish a set of independent characteristics which are interpreted as the psychophysical sensation of colour. The term psychophysical means that colour is not, of course, a real physical attribute of radiation in the sense that frequency and wavelength are. Rather, it is an interpretative artefact of the brain, the psychological response to the physical stimulus. Thus, when we refer to the ‘colour’ of light, this interpretation will be taken as understood. The present discussion is restricted to vision dependent on the retinal cone cells, photopic vision, as the rods do not permit colour perception. Those cone cells comprise, in ‘normal’ colour vision, three distinct types, sensitive to different regions of the spectrum; the peak sensitivities lie respectively in the yellow, green and blue

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regions (Fig. 1.2). However, it must be appreciated that they are each sensitive to a range of wavelengths; for example, we see red because the ‘yellow’ peak cones1 have a response that extends to long wavelengths, and thus provide a visual signal in that region, while the other two have negligible response at those wavelengths. The brain2 interprets such a combination of signals in the three channels as ‘red’. Notice that it is the relative intensities of the responses (output signals) that provide the colour (i.e. wavelength) information for a single wavelength light. There are, therefore, only two degrees of freedom for assigning ‘colour’ since of the three comparisons, yellow vs. green, green vs. blue, and blue vs. yellow, only two need to be specified to determine the third, i.e. only two are independent (we are ignoring total intensity) (cf. the equivalent discussion of independent equations in 8§3.4). This is not the same, of course, as saying that only two signals are required by the brain, since there is a further dimension to consider, as we shall see below.

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Fig. 1.2 Relative absorption spectra for the three human eye cone photopigments (peak sensitivities adjusted to unity - “normalized”).

Colour gamut It is well known that a range of colours, the (visible) spectrum (the colours of the rainbow), may be obtained from white light by using a prism (Fig. 1.3) or a diffraction grating. However, this range is also very evidently only a very small part of the total colour gamut, the complete range of colours that can be created or perceived by humans. In fact, about 10,000,000 detectably different colours exist for anybody with ‘normal’ colour vision,3 and it is immediately obvious that most of these are not spectral, meaning that they do not correspond to the colour of any single wavelength. What is not so obvious is how these other colours arise, and it is now necessary to explore some aspects of colour science in order to understand the implications for dentistry. We shall do this by describing the results of some simple experiments. !1.1

We shall of necessity have to restrict the following discussion to normal human trichromatic vision, or trichromacy. There are, of course, various types of colour vision defect[1], and even rare instances of tetrachromacy (which also occurs in various other species). What follows can be extended easily in a natural way to cover such circumstances, as no principles are critically dependent on trichromacy as such, should the need arise. Even so, it would be wise to bear in mind the possibility of defective colour vision (‘colour blindness’) in the context of cosmetic dentistry and colour matching in general, for the patient certainly but especially for the dentist, given that (depending on region) as much as 10% of the population may be affected in some way (males : females ~ 20 : 1).

Fig. 1.3 White light may be dispersed by a prism or a diffraction grating to show the visible spectrum.

Visual matching Suppose that we illuminate a portion of a white4 screen by a lamp, which can be arbitrarily chosen but for example an ordinary tungsten filament bulb, such as can be done with a slide projector or theatrical spotlight. Three other such lamps are then set up to be able to illuminate (only) the adjacent portion of the same screen. These other three lamps have widely different colours (for example, but not necessarily, red, green and blue), the brightness of each of which is independently adjustable (as by an iris diaphragm - as will be explained below, changing the voltage on a filament lamp will change the colour). These lamps can have their colours determined !1.2

1 2 3 4

Commonly referred to as the “red” cones. This is a simplified story, and ignores the effective signal processing that occurs in the retina. This may be compared with the 16,777,215 (i.e. 224 - 1) colours supposedly obtainable with 24-bit computer colour systems. Which we define as reflecting diffusely all incident radiation – see §3.10.

Chapter 24 by selectively absorbent filters or any other appropriate means. The set-up is illustrated in Fig. 1.4. By trial and error it will be found that a perfect colour match can be produced, i.e. the light in the second portion of the screen will look as ‘white’ as that from the tungsten bulb; indeed it will be quite indistinguishable - by eye. Any small adjustment in the brightness of any of the three coloured lights will result in a distinct colour in the illuminated area. This experiment indicates that, as would be expected from the discussion above, ‘white’ is not really a property of the light as such but a particular response (on our part) to a particular set of stimuli. Furthermore, it does not matter how the lamp colours were established: the match can always be made perfect.

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Fig. 1.4 The experimental set-up for colour matching experiments. The lamps in the upper part of the apparatus are independently adjustable in brightness. For the simple colour-matching experiment, the external lamp is turned off so that the surround is effectively black.

If now one of the three coloured lights is turned off altogether (say the blue), adjustments of the other two will be found to produce only colours varying between green and red, with yellow as an intermediate colour. With the presently assumed lamps, or illuminants - to make it more general, under no conditions will white be produced, and certainly blue will not be approachable. Equivalent remarks may be made for the other two pairs possible. The sensation of colour is thus said to depend on three stimuli; the total illumination of the test screen is certainly three-dimensional. However, if we were very careful (and it is a difficult experiment to perform), two illuminants could be found which would allow white to be produced, that is, with an appropriate ratio of intensities. This requires, in addition, for an arbitrary first illuminant, a very precise selection of the colour of the second. This is equivalent to the situation described above: having found a perfect match using any three illuminants, only one is then allowed to vary in intensity, the other two establish in effect a single but mixedcolour illuminant. More than three coloured lights could be used to obtain a match, but in general no less than three will do. This outcome can be related directly to the fact that there are three separate wavelength-sensitive kinds of detector in the eye (Fig. 1.2). Three signals are generated, and information on the relative strengths of these three must be necessary to define a colour. Mixture diagram What we are really dealing with is a three-component mixture, and diagrams of the type shown in Fig. 8§1.6 can be used to plot the results of such mixtures.[2] These diagrams are generally called a colour-mixing triangle (Fig. 1.5). Notice that in such diagrams it is the proportions of the components which are relevant, not the total intensity. A wide range of colours is capable of being reproduced by such a system. Indeed, it is the method employed in colour television and computer screens to produce the image, as close inspection will show (it often comes as something of a surprise to see that the three coloured dots are red, blue and green – get up close with a magnifying glass; §3.11). Photographic colour film uses exactly the same principle, but with coloured dyes which act as filters. !1.3

This diagram also indicates some pairs of complementary colours, i.e. those which in appropriate intensity ratios will generate white. These are indicated by the ends (as well as intermediate points) of all lines which may be drawn through the white point. However, and significantly, there are always some colours which cannot be reproduced by any such system. This leads to

Fig. 1.5 The colour mixing triangle for showing the effect of mixing light as in Fig. 1.4. This is also called the ‘additive’ colour diagram.

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limitations on the image quality of both televisions and photographs, no matter what the advertising says about true-to-life colours. Rainbows in particular are always disappointing because they are spectral colours and cannot be reproduced. This failure needs explanation.

§2. The Chromaticity Diagram The tri-stimulus nature of the colour response has been stressed, so that the representation graphically of any particular combination of lights at specified intensities requires a three-dimensional plot. However, if we are concerned only with the proportions of each component, we can restrict our interest to the one plane where the sum of the photometric intensities R + G + B = 1, the so-called unit plane (Fig. 2.1). The ‘composition’ of the colour can be determined from the unit plane triangle in precisely the way that the composition of mixtures of three chemical components can be determined (8§1.2), relying on the idea of the perpendicular distances from the sides of the triangle representing proportions (Fig. 2.2). In other words, this is a colour mixing triangle for the chosen set of lights. Fig. 2.1 The unit plane is constructed such that in it the total photometric intensity is constant and has the value 1, in any convenient units. N represents the neutral colour vector (white).

Fig. 2.2 The relative proportions of each stimulus in the mixture are given by the relative heights of the plotted point above the corresponding zero-intensity base.

Fig. 2.3 Two separate colour mixing triangles in which corresponding matching colours have been identified.

Now, supposing we do exactly the same thing with a new set of different coloured lights (say, orange, cyan and violet) we would then have created a second colour mixing triangle. Then, using the set-up of Fig. 1.4, and replacing the lower lamp by the second set of coloured lights, we may be able to find a colour - for example, white – using the first set that we can match with the second set. The corresponding points can be plotted in the two diagrams. We go on to seek a second colour using the first set, say, Fig. 2.4 By rotation and scaling, the colours of the magenta, that we can match with the second set. We again right triangle of Fig. 2.3 (OCV), can be made to may plot the corresponding point in each diagram. This coincide exactly with the corresponding points in the situation is then similar to that shown in Fig. 2.3. However, RGB triangle. All overlapping points then match. we know that these colour points in the two diagrams are matched. By rotation and scaling the second diagram we can arrange for the two matched points to be superimposed. We would then find that all points common to the two triangles – that is, lying in the overlap area – correspond to colours that can be made by mixing either set of illuminants. Furthermore, all such points coincide in the new diagram (Fig. 2.4).

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Spectral locus If we were to continue creating and overlaying colour mixing triangles, using as wide a variety of illuminants as possible, we would gradually build up a map covering more and more of the colour gamut (Fig. 2.5). If we included in our list of tested illuminants the pure spectral colours, single wavelength lights (such as from a laser), after overlaying to match colours we would find that the spectral colours formed the outer boundary of the available colour gamut. This boundary is called the spectral locus, and the wavelengths of the spectral colours will be found to lie in order along it, although not on a uniform scale. Bear in mind that we are dealing with the psychophysical effects of light, and strict ‘calibration’ of our perceptions in wavelength – or frequency – could not be expected. No matter what illuminants we test, none will be found that will lie outside that boundary after the colour mixing triangle has been matched and overlain properly (Fig. 2.6).

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Fig. 2.5 Overlaying many colour mixing triangles includes more and more of the colour gamut.

Chromaticity coordinates Now, quite obviously, no single set of three illuminants can correspond to a colour mixing triangle that will give the entire colour gamut; no amount of scaling will change the shape of Fig. 2.6 to a triangle and maintain the proportionality requirements for plotting in that area. In other words, there are always colours that cannot be reproduced using any single set of three arbitrary ‘primaries’, even if these primaries are themselves pure spectral colours, i.e. single wavelength light which is by definition pure. !2.2

Obviously, if the spectral locus is to be plotted in a plane, there is a region outside it totally inaccessible through the mixing of any real illuminants. Subject to the condition of existence, therefore, colours may be identified in terms of rectangular coordinates. What this in effect means is that an arbitrary mixing triangle for three imaginary illuminants (which do not and cannot exist), can be drawn to enclose the spectral locus (and this is in fact done in some in some colour definition systems). Even so, it is far easier to specify any point within the colour gamut by rectangular coordinates, conveniently chosen. These are then called the chromaticity coordinates. (In fact, the diagram is scaled better to match human perceptions of the ‘distances’ between colours. The resulting, arbitrary coordinates are labelled v' and u'.) The line which closes the colour circuit, joining the red and blue ends of the spectral locus, is known as the purple line (Fig. 2.7). Colours along this section range from red through magenta to purple and violet, following the rules for a mixture line (8§1.1). However, these are not spectral colours, and can only be created as mixtures. Clearly, since the ends of the spectral locus are the limits of attainable spectral illuminants, the purple line is also an unpassable boundary: no colour exists outside it. This then completes the chromaticity diagram (Fig. 2.7).[3]

Fig. 2.6 The entire colour gamut can be built up from many overlapping tristimulus triangles, with the outer boundary defined by the spectral locus (the numbers on this are the corresponding spectral wavelengths in nm). W is the ‘white point’.

Fig. 2.7 The colour circuit.

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Note that although it is possible to specify coordinates that lie outside the colour circuit, they do not correspond to realizable colours. Even so, it is noteworthy that the range of wavelengths said to be visible is not clearly defined. Estimates of the long wavelength limit vary between about 680 ~ 740 nm, while the short wavelength limit is given variously between about 380 and 430 nm. This clearly depends on individual sensitivities, some may see further into the red or blue, or both, than others. Thus, the purple line may assume different positions for these people. Nevertheless, the remainder of the diagram and all the observed effects and phenomena will remain unaffected by this. Colour map The common named colours can now be mapped onto this diagram (Fig. 2.8), where conventional boundaries are identified by spectral wavelength. This can be seen to be insufficient for anything other than elementary work, and more detail can be added to take into account finer distinctions (Fig. 2.9). Even so, this is still not very precise, but it would rapidly become unwieldy if the process of subdivision were continued. It therefore becomes apparent that what is required is a formal means of specifying colour in a manner that is reasonably easy to interpret in terms of the psychophysical sensation, as opposed that is to the arbitrary scales of the CIE diagram. Some of the systems that have been developed are outlined in the next section. !2.3

No phosphor or dye can yield a pure spectral colour, so approach to the spectral locus is limited. However, the general convexity of the spectral locus ensures that no spectral colour can be created as a mixture of any other two, except perhaps in the red to yellow region. This means that, in general, a mixture line between two such pure colours cannot reproduce the appearance of intervening spectral colours, except where the locus is itself quite straight. These unavailable colours are said to be outside the gamut of the three particular stimuli chosen in the kind of experiment illustrated in Fig. 1.4. In the case of Fig. 1.5, for example, certain strong yellows, a range of greens, and violet to purple colours simply could not be produced. The situation of two illuminants being used to create white can now be mapped more precisely. For any arbitrary first light, there is only one line that passes through the white point; the second light must therefore lie on this line, but on the other side of the white point (Fig. 2.6). The special conditions attached to this possibility do not diminish the effect of the conclusion that colour as we sense it is best described as a tri-stimulus phenomenon.

Fig. 2.8 The regions of the chromaticity diagram labelled according to a simple list of perceived colours.

Fig. 2.9 The regions of the chromaticity diagram labelled according to a more detailed list of perceived colours.

Weighted mixtures In reaching the above conclusions we have only considered taking illuminants three at a time to create separate colour mixing triangles. What happens if we have four - or more - illuminants? Remember that if we take a pair of illuminants the result of mixing them is represented as a point on the mixture line joining their plotted positions. This is a weighted mean of the two illuminants, weighted by their intensity proportions. But this new point is itself equivalent to an illuminant, and we may repeat the process to calculate the corresponding mixture of this with the next illuminant. Ultimately, this process repeated will produce a weighted mean for any number of illuminants acting together, including the situation where all wavelengths are represented. We could, of course, have taken the illuminants in threes, using mixture triangles, to achieve exactly the same result. There are then many ways in which ‘white’ can be created, including the particular case of all wavelengths being !2.4

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represented uniformly. It also follows that any colour (except a spectral colour) can be made using a mixture line – that is, of just two illuminants, of any orientation or length (providing it lies within the colour circuit), that passes through that colour point. For example, white can be made by a suitable mixture of blue and yellow, or indeed of many other such pairs.

§3. Colour Specification Saturation The coordinate system of the chromaticity diagram is not very intuitive: the use of a coordinate pair does not lead to a good conception of the colour involved despite the technical advantages of a cartesian (rectangular) coordinate system map and, as we have seen, the use of word labels lacks precision. Several alternative approaches have been offered. They all take as the natural point of reference or origin the white point which represents, by definition, an absence of perceived colour. On the other hand, the strongest colours (what we may consider the most extreme illuminants physically possible) are those which lie on the colour circuit, the spectral colours themselves or the purple line mixtures. Thus, there is a gradation from white, through pastel shades, to what is termed a saturated colour. White is therefore the least saturated colour possible; indeed, its ‘saturation’ is defined as zero. The measure of saturation for a colour at a given point is therefore the relative distance along a line drawn from the white or neutral point to the colour circuit through that point of interest (Fig. 3.1). This is, in itself, a mixture line, where the two components are white and the saturated colour. !3.1

Fig. 3.1 A line of constant hue, drawn from the white or neutral point, W, to the spectral locus at C, where the colour is said to be fully saturated.

Hue To specify saturation is not enough. Since we are working in the plane, two values need to be specified, and in this case it is the direction to be taken in moving away from the neutral point. This corresponds to specifying wavelength (or frequency) on the spectral locus. We already have common names for the spectral colours: red - orange - yellow - green - cyan - blue - violet (cf. Fig. 2.8). Adding to this list, in order anticlockwise around the colour circuit, purple and magenta, we can specify the type of colour or hue in a natural manner that is easier perhaps to comprehend than wavelength. This kind of mapping is similar to a polar coordinate system: distance from centre and direction. Thus, in Fig. 3.1, W is the neutral point, C is a saturated colour (in this case, blue), while all points in between are whiter or paler or less saturated versions of the same hue. !3.2

Grey scale Notice that the photometric intensity of the illumination is not discussed (except to say that it is constant). This is because, except at extremely high levels when discomfort is involved and at low levels when scotopic vision starts to take over (i.e. the rods are doing the work), the psychophysical sensations of colour change very little, if at all. In addition, we have only discussed the appearance of the illumination of an assumed perfect diffusing surface, i.e. a ‘white’ screen. However, it is evident that ‘absence of colour’ has another dimension in that we are aware of shades of grey, ranging from a totally absorbent, non-reflective black to a totally diffusing pure white. Again, this is without reference to the actual amount, the photometric intensity of the light falling on the object. !3.3

Fig. 3.2 The grey scale.

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It is necessary then to introduce a further dimension to complete the statement of the colour of objects: the lightness or grey scale value (Fig. 3.2). (Plainly this cannot apply to the illuminants themselves – ‘grey’ light does not exist.) If we have plotted hue and saturation in a plane, the lightness dimension is normal to it (Fig. 3.3). This means that we are working in what is called a cylindrical coordinate system: direction and distance from the centre in a plane, and the height above or below the plane, and we now have a three-dimensional reference frame for colour specification. Since therefore the range of the neutral colour is from black to white, we may represent this in terms of the overall reflectance of the object, which value can then range from 0 to 100% of all that impinging on it. (This property, as a proportion, 0 ~ 1, is also sometimes called the albedo of a surface or body, especially in astronomy.) It is therefore an absolute, not subjective, measure. In this sense ‘grey’ is a physical property statement when applied to a body, implying less then perfect reflectance, but then not total absorption.

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Fig. 3.3 The lightness or grey scale axis is orthogonal to the chromaticity diagram.

Notice, however, that for us to judge that something is grey requires an object for comparison (as in detergent advertising). Imperfection in whiteness can only be detected by comparison with a whiter object. In low light conditions, for example, this page may appear ‘grey’. But what is the colour of a shadow on ‘white’ paper?5 The absence of returned light is an absolute: this is black.6[4] At the other end of the scale we have 100% reflectance as a definition of white; this is perfect behaviour,7[5] but clearly it is not dependent in any way on the photometric intensity of the illuminant – it still holds as a definition in complete darkness. We are dealing, then, with the interpretation of grey as being a relative measure of the returned light as a proportion of that incident on the body. It is automatically scaled in our perception according to the current lighting conditions, typically by (unconscious) reference to the lightest object in the field of view. Figure 3.2 is unaffected whether viewed under floodlights or a single, white, low-power LED lamp, or even starlight. Of course, shadows are not perfect black when there is any other source of illumination, whether diffuse or direct. Hence, in snow, a shadow from the sun may appear blue when there is a clear sky because of its blueness, while the snow itself is ‘white’ because it is illuminated by the sun. Such effects are often clear in stage lighting. White light remains white no matter its photometric intensity, while a ‘grey’ object, in the sense of its reflectivity being less than 100%, may appear white if it is the lightest object in view, and especially if more brightly lit than the surroundings. Confusion with photometric intensity is common: a ‘grey’ day is one that has low light (because of the density of the cloud cover) compared with a sunny day, although the light may be spectrally uniform. Differential absorption We have assumed, indeed required, for the experiments illustrated by Fig. 1.4 that there is no selective or differential absorption of the various wavelengths of the light impinging on the screen - that is why it is ‘white’. When we consider shades of grey the requirement is that all wavelengths are uniformly absorbed, which also means uniformly reflected. In this way the saturation remains zero and the colour neutral for white illumination, no matter what its spectral make-up. But, it is evident that many objects are coloured even though they are illuminated by white light. !3.4

Let us, for the moment, assume that the phrase “white light” means that all wavelengths are equally represented, i.e. uniform photometric intensity. The weighted mean of these in the chromaticity diagram therefore lies at the neutral point. But if the object illuminated absorbs any wavelengths preferentially, in general the weighted mean of the reflected light will no longer lie at the neutral point. This means that the saturation will have increased in the direction of some hue, and typically away from the hue of the light which has been absorbed. The colour of the object under white light illumination is therefore determined by the relative proportions of the different wavelengths which are reflected. Thus, the colour of objects in general arises from differential absorption. How this may work in practice can be seen in plots of reflectance vs. wavelength, such as might be obtained from a scanning spectrophotometer, so-called reflectance spectra (Fig. 3.4), where the 5 6 7

Assume white light, but it actually depends on the surroundings – see §4.12. Although this is impossible to achieve, a very close approach has now been made: Vantablack® – see the next reference. Again, impossible to attain, but a good approximation can be made: Spectralon® – see the next reference.

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reflectance indicates the proportion of incident light at each wavelength that is not absorbed. Thus, a ‘red’ object tends to absorb yellow to blue wavelengths, a ‘green’ object both blue and red wavelengths, and so on. In summary, the colour of an object – hue and saturation – depends on the weighted mean (§2.4) of the reflected light, as plotted in the chromaticity diagram, while the grey scale value or lightness depends on the overall reflectivity of the object, without regard to wavelength. The colour mixing triangle of Fig. 1.5 may be seen in effect to operate as an ‘additive’ colour diagram, the addition being of the lights impinging on the screen. In a complementary sense there are also ‘subtractive’ diagrams, which are used for paints, artists’ colours and pigments in general to indicate what might be expected when they are mixed (Fig. 3.5). These two diagrams differ, in part, in having respectively white and black at their centres as the neutral colour. However, although pigment formulation may require such concepts, and this could be relevant to the colouring of dental porcelain for example, as far as the eye is concerned it remains the total wavelength mixture that is received which is important, as is apparent from Fig. 3.4.

Fig. 3.4 Some examples of typical spectral reflectance curves for variously coloured objects.

Similar subtractive processes are operating in filters, where we would speak of transmission spectra, the essential similarity between filters and pigmented opaque objects (Fig. 3.6) being the spectral composition of the light received by the eye. In each case it is the intensity weighted mean of all the wavelengths present that determines what is perceived as the colour. There are several other ways of describing colour.[6] These have been developed for particular purposes but are necessarily still based on the ideas of illuminant mixing and so on described above. Since some of them at least may be encountered in dental contexts, they are described briefly.

Fig. 3.5 An example of a subtractive colour diagram. Such a diagram can only ever be approximate since it is based on the assumption that the spectral absorption curves for each pair of opposing colours are exactly complementary, leading to total absorption. Normally, the result of mixing like this with pigments is a muddy colour because each surface particle must scatter some light. Filters are a more effective demonstration.

Munsell system One of these colour specification schemes is the proprietary Munsell system, an elaboration of the scheme shown in Fig. 3.3. This takes into account the sensitivity of the perception of saturated colours at both high and low lightness. Clearly, any colour that is very light cannot simultaneously be very saturated, because this would require that the albedo is higher than the proportion of, say, red light in the white illuminant. Likewise, something that is very dark, not returning much light from the white Fig. 3.6 The effects of opaque objects (left) and filters (right) on the illuminant, cannot also appear to be saturated light seen are necessarily similar. – it simply is not seen. The Munsell colour space is therefore a kind of distorted double cone (bases together), the apices being white and black respectively. The direction relative to the black-white axis is still termed Hue (although, oddly, labelled in a clockwise direction), but saturation is now called Chroma, while lightness is termed Value (i.e. grey scale value) (Fig. 3.7). The notation is brief and easily !3.5

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understood. This therefore is still a kind of cylindrical coordinate system. The Munsell system is very useful for colour matching purposes as sets of colour ‘chips’ with specific hue, chroma and value have been prepared. These are used directly for colour determination by eye matching rather than by an instrument. For example, they are useful for hair, skin and mucosa. The latter would be relevant to the selection of an appropriately matching denture base acrylic (although it is noticeable that the range of colours offered commercially for such products is very small). A variant of this system is called the HSB model, that is Hue, Saturation, Brightness. Hue is described by the angle around the circle, 0E being red, proceeding through yellow at 60E. Saturation is dealt with as a percentage from 0 to 100, as is brightness. It can be seen that the colour maps of the Munsell and HSB systems do not overlay on each other exactly, even though conceptually similar.

Fig. 3.7 The Munsell colour diagram and labelling system. Hue is represented by an abbreviation (RP = red-purple, Y = yellow, ... etc.), grey scale value by the first digit (e.g. 7/), and saturation or chroma by the second number.

CIE L*a*b* system This is more likely to be encountered in connection with colour meters. The light returned from the test object on illumination with a white light (such as is obtained from a photographic flash) is analysed with a set of filters and then described by three numbers: L* is the lightness value, while a* and b* are the coordinates on red-green and blue-yellow axes respectively. This therefore is a three-dimensional rectangular coordinate system for the colour space, the origin of which lies at the neutral black point. There are a number of variants of this kind of scheme. !3.6

RGB system This is normally used for defining the colour to be displayed on television and computer monitors, and similar light-generating equipment. As mentioned above, a colour monitor has three light emitters, red, green and blue (corresponding to the RGB of the name). The intensities of these three primary colour components determine the overall colour, through a mixing triangle such as Fig. 1.5, as well as the overall intensity. However, because no triangle can cover the entire colour gamut, as explained above, there remain colours which cannot be specified in such a fashion – they are, anyway, incapable of being created by those emitters.

!3.7

CMYK system Colour printing, on the other hand, in its simplest form, employs dots of varying size of Cyan, Magenta and Yellow inks (see Fig. 1.5) (with blacK to adjust grey scale value, so-called four-colour printing), as can be easily seen with a hand lens. This, of course, is a subtractive system, but the same limitations on the gamut available apply. In addition, because it is subtractive, the seemingly odd selection of ‘primary’ colours is necessary to obtain an appropriate range: red plus green ink makes black, not yellow.

!3.8

There is a significance in both RGB and CMYK systems for dentistry. On the one hand, there could be errors in the colours that would be found if comparison were made of a real object with a colour monitor image, if it was desired to demonstrate colour matching with such equipment in the surgery. This would not be because the unsaturated colours appropriate for teeth and so on could not be made, but because it would demand accurate calibration of the screen (i.e. of the intensities of the output of the electron guns or LEDs, for which purpose special devices and software are available), and this would also depend on ageing effects in the light emitters and driving electronics (requiring regular checks). An indication of the problem can be gained from displays of televisions in shops: rarely do two have the same colour balance! A further problem is that with LED displays the perceived colour depends on viewing angle, sometimes quite markedly, and for only small angular changes.

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On the other hand, there are difficulties in making an accurate printed shade guide because of the high accuracy required for the amount of ink in each dot. High quality colour printing is expensive (and in fact may employ more than three colours to achieve good saturation and range of hues), but paper is a relatively fragile medium that does not lend itself to sterilization. In addition, printing ink dyes are fugitive, fading in time (§6.3). Each of these colour systems is, of course, dealing with the specification of colours from the same overall set. Conversion between them is therefore possible, using various formulae, but this has no immediate dental relevance. Ultimately, dentistry is mostly concerned with the problems of colour matching, as exemplified by the use of a ‘shade guide’, such as is used for restorative materials. Colour space Although there are three coordinates in, for example, the Munsell system, which may be specified independently, there are combinations which have no meaning. This excluded region has already been mentioned (§3.5), but it is worth emphasizing that this is a general condition, not relevant to only the one system. Just as there is an ‘inaccessible’ region outside the colour circuit (Fig. 2.7), so there are non-existent colour specifications outside the double-cone of the full realizable colour space (Fig. 3.8), the three-dimensional extension of the colour gamut (§1.1). It should be clear that a colour cannot simultaneously be fully-saturated and have either maximum or minimum lightness, indeed it follows that any deviation in the lightness direction for a fully-saturated colour is disallowed, remembering that Fig. 3.8 The nature of the limits of the available, lightness is not photometric but relative intensity. Notice realizable colour space. that since white is made up of all wavelengths, reducing the proportions of any wavelengths must simultaneously introduce a hue, increase the chroma, and reduce the grey-scale value. Reducing, then, the value for a single wavelength takes the colour towards black. But it is, of course, the same black regardless of the starting colour, and therefore this must be a single, unique point in the colour space, and the same as the lower end of the grey scale. !3.9

The effect can be envisaged by considering the double-cone of the colour space to be defined by the full series of mixture lines from the apices to the saturated circuit, for example white-purple, or black-yellow. Saturation therefore decreases as lightness increases. Similar mixture lines for unsaturated colours can also be considered, such as line a in Fig. 3.8. !3.10 Black, white and grey It is worth reviewing the meaning of ‘white’ at this juncture as it has three distinct senses in the development above, according to context: C White light – an illuminant with all wavelengths equally represented, i.e. a flat spectrum. C White object – diffusely and uniformly scattering all incident visible radiation, i.e. no absorption. C White perception – the end result of the eye receiving light whose weighted mean lies at the neutral point, i.e. which has zero saturation. These aspects are respectively a spectral description of an illuminant, a physical property of a material body, and the psychophysical outcome of seeing a particular spectral profile. Thus we may perceive as white a nonwhite object under a non-white illuminant when the weighted mean of the returned light is neutral. We may contrast these definitions with those for ‘black’: Black object – absorbing all incident visible radiation, i.e. no reflection or scattering. Black perception – the end result of the eye receiving no light. This may be for – a black object under any illuminant (albedo zero) – a coloured object absorbing all incident radiation, e.g. a ‘red’ object under blue light8 – the absence of any incident visible radiation Of course, ‘black’ light does not exist (despite the term being applied to that of ultraviolet lamps).

C C

8

That is, when there is no overlap whatsoever of the illuminant and reflection spectra.

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For completeness, we may add definitions for ‘grey’: Grey object – diffusely and uniformly scattering a fixed proportion less than 100%, but not zero, of all incident visible radiation, i.e. no differential absorption. C Grey perception – the end result of the eye receiving light whose weighted mean lies at the neutral point, i.e. which has zero saturation, but by reference either – to an object which is perceived to be of greater lightness, and which thereby becomes a standard for ‘white’, or – to the same object under more intense illumination, effectively putting the first area in shadow. Again, there is no such thing as ‘grey’ light, that attribute of dawn notwithstanding. C

Clearly, it is important to be sure when any such words are used (and indeed other colour terms), what exactly is meant: illuminant, material, or sensation. !3.11 LED colour Consideration of the way in which the LEDs of computer screens and the like work to generate colour is informative. We have three separately-controlled RGB emitters, which may be set at any value between 0 and 100% output (Fig. 3.9). Since at normal viewing distance the individual emitters are not resolvable by eye because of the visual acuity limitation (15§7.2), the emitted light is effectively mixed. This then gives a system as shown in Fig. 2.1 with the exception that there is now an upper bound to the intensity of each component, and of course we are not then limited to the unit plane. We therefore have the colour-mixing system shown in Fig. 3.10.9[7] At the coordinate position (0,0,0) lies black – all off, at (100,100,100)10 lies white – all on full. Yellow (100,100,0) is obtained with red and green full on, cyan (0,100,100) is green + blue, and magenta (100,0,100) is red + blue.

Fig. 3.9 Typical computer screen LEDs, as seen magnified when illuminated (use a hand-lens on any such screen).

If the view point is changed to look (almost) down the cube diagonal from (100,100,100) to (0,0,0), and removing a number of plotted combinations for clarity (Fig. 3.11), the grey scale is revealed as lying along that diagonal, while the triangle drawn between the pure colour (100%) corners can be seen to correspond to the unit plane, and is of course now at constant

Fig. 3.10 diagram.

Fig. 3.11 Cube-diagonal view to show the grey scale and unit plane. 9 10

Three-component colour space mixing

photometric intensity: the sum of the coordinates is 100 everywhere on it – this is the unit plane. Now, viewing just the visible (nearest) cube faces in Fig 3.11 gives Fig. 3.12. This is a kind of additive colour wheel, where the spokes correspond to mixture lines for the pure component at one end with the ‘100,100’ mixture at the other, or equally, mixture lines of the saturated colours at the periphery with white at the centre. Conversely, looking at the other three faces, from the opposite end of

Such a system was anticipated in the 13th century by Robert Grosseteste. In most computer programs, the RGB coordinates are specified on an 8-bit scale: 0 ~ 255, hence the figure in footnote 1: (28)3.

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the grey-scale diagonal (Fig. 3.13), we get a subtractive colour wheel similar to that shown in Fig. 3.5 Now we have mixture lines as diagonals showing in effect the behaviour of complementary colours again, whilst radiating from the centre are effectively mixture lines with black.

Fig. 3.12 The “additive” surfaces of the threecomponent colour space.

Fig. 3.13 The “subtractive” surfaces of the threecomponent colour space.

Rotating again, for a kind of ‘equatorial’ view, setting the grey-scale cube diagonal to be vertical (Fig. 3.14), we obtain the equivalent of Fig. 3.8, where primarily it can be seen why no colours can exist outside the double cone’s surface, as delimited by the mixture lines radiating from the white and black poles, and that this must be true no matter what (or how many) light sources are involved. Secondarily, we can see that the colour gamut accessible to a three-light source system such as this is necessarily limited, and will fail to reproduce a rainbow properly, for example, as indicated by each of the mixture triangles in Fig. 2.6.

Fig. 3.14 The nature of the limits of available colour space. The grey-scale axis is vertical.

It is also possible to appreciate the absence of absolute photometric intensity in these considerations since the scale represented by 100% is not defined. All values can be multiplied arbitrarily by the same factor without changing the diagram or its import. It should be noted, of course, that the portion of real colour space covered by such a diagram is necessarily dependent on the emission spectrum of each LED (again, as in Fig. 2.6). This accounts for the often startling variation in the displayed colours in the many screens showing the same image seen in shops.

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§4. Colour Matching in Practice The discussion so far has centred on the background of the identification and mapping of colour. It is now necessary to consider the practical implications and use of this in the process of colour matching, especially as it relates to the use of shade guides in the selection of a restorative material. Principles of colour matching The description above of the nature of the psychophysical sensation of colour can be summarized in three general principles. 1. Tri-stimulus: We are capable of distinguishing only three kinds of variation in, or attributes of, colour: hue, saturation and lightness. 2. Weighted mean: The perceived colour depends on the intensity weighted mean of the illuminants. Thus, if any one of the illuminants is steadily changed in intensity the colour perceived steadily changes, as the weighted mean varies. 3. Perceptive invariance: Separate stimuli of the same colour (i.e. the same hue, same saturation and the same lightness - a perfect match) produce exactly the same perception in all mixtures of the two, regardless of the spectral composition of the individual stimuli. This last principle is simultaneously the most important for colour matching, and the cause of all the problems encountered in this area. !4.1

The total colour gamut was shown earlier to be capable of physical expression only by overlaying a large number of three-component colour mixing triangles (Fig. 2.5). But, equally, there must be a large degree of overlap for many of these possibilities or else the idea of a colour match could not in general be realized. Thus, the matching colours may be made up from an endless series of combinations of pure spectral illuminants; that is the triangles may be drawn with their apices anywhere on the spectral locus so long as they enclosed the coordinates of interest. Any pair of these sets of three stimuli may be superimposed (that is, illuminate the same patch of white screen) without producing any difference in the perception of the colour. Similar remarks can be made for sets of stimuli which lie wholly or partly within the spectral locus. Now, given the idea of the weighted mean for more than three illuminants, as developed in §2.4, we may extend the above conclusion to say that the matching colours may be obtained by using any number of illuminants. In particular, those illuminants can be the spectral colours, and all of them at once, but with various intensities. Clearly, the same weighted mean can be attained in many ways, that is, there are many different spectra possible for the one colour. The spectra shown in Fig. 3.4 are very simple examples. Matching persistence There is a fourth principle which must be mentioned: that of the persistence of colour matches. First, suppose that using the set-up of Fig. 1.4 a match is obtained for the lamp using the three separate illuminants in a suitable combination. If the illumination of the surround to the viewing aperture (the ‘reduction screen’) is changed from dark to light, or to any colour whatsoever using the external lamp, the colours that were obtained on the internal screen will continue to match. !4.2

However, the perceived actual colour of the two will appear to change, often quite markedly, as the surround changes in colour. This means that our perception of a colour also depends on the environment. It illustrates how the viewing conditions, the brightness and colour of adjacent objects, may affect the psychophysical interpretation of the colour of an object of interest. Thus a shade guide sample must be held adjacent to the reference tooth, for example, if the surroundings are to have no effect on the selection. This emphasises the fact that our judgement of a colour can be faulty, depending on circumstances. Man does not have an absolute sense of colour, and attempting to create or choose a colour without a reference object is risky. Metamerism Now we are in a position to consider the combined effect of illuminant spectrum and object absorbance spectrum. Thus, if for a uniform perfect white screen, as in Fig. 1.4, using two sets of three coloured lights, we obtain an arbitrary colour on one side (i.e. using one set of lights), the Third Principle says that we can obtain a match on the other side, assuming only that the gamuts of the two three-stimulus groups overlap sufficiently. If now the colour of the screen itself is changed, that is, its saturation in respect of one hue is increased or decreased, in general there will no longer be a colour match for the two illuminants. By changing the colour of the screen we necessarily have differential absorption of the incident light. But that differential absorption means that there will be a greater or lesser effect on wavelengths represented more or less strongly in one illuminant !4.3

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but not the other. Thus, the colour changes of the two sides will be different. This is equivalent to saying that by adjusting the pigments in two coloured objects they can be made to match in colour under any arbitrary light source. However, they will not then, in general, match under any other source because light sources themselves differ very widely in their spectral makeup. This is the phenomenon of metamerism. There are in fact an essentially infinite number of spectral reflectance curves which will reproduce any given colour (hue, saturation, lightness) in an object under a given illumination. Thus, the objects corresponding to the spectral absorbance curves shown in Fig. 4.1 appear as the same neutral grey under white (spectrally uniform) illumination. There are many other Fig. 4.1 A set of metameric spectral reflectance curves. such curves. But if the spectrum of the illumination Under one white light they are all a perfectly matched were changed, however, then many of these metamers neutral grey. can be expected to show perceived colour changes. The implication of this is that if a colour match is obtained under one particular illumination there is no guarantee that the match will be maintained under a change of illumination. In fact it can be said more strongly than that: expect change. It also follows from the colour matching principles (§4.1) that there is no information to be obtained about either the reflectance curve or the illuminant from the perceived colour, which can be understood from the myriads of sets of illuminants that can produce the same weighted mean (§2.4). We can perhaps better appreciate this by considering the individual cone responses (Fig. 1.2). There are only three signal channels, and each represents the sum of the response of that type of cone over all wavelengths, suitably weighted by the sensitivity curve. Such an integrated signal value can be created in many, many ways – i.e. combinations of intensities over all possible wavelengths – the incident spectra. All of that extra information is now completely lost, it therefore cannot be transmitted to the brain, and thus spectral information cannot be perceived. This discussion, and especially from points made at §1.2 and §3.10, now leads immediately to the recognition of the existence of metamers in three distinct senses: C Metameric illuminants – having different spectral emittance curves that have the same weighted mean colour in the chromaticity diagram. (This is the basis of the illuminant colour matching of Fig. 1.4. using the white screen; §3.10.) Thus, any differentially-absorbing object would have a different perceived colour under each illuminant. C Metameric objects – having different diffuse spectral reflectance curves (or spectral transmission curves) for the one illuminant (i.e. of arbitrary spectrum) that have the same weighted mean colour in the chromaticity diagram (that is, as illustrated in Fig. 4.1). Thus, the match would be lost under a different illuminant. C Metameric perceptions – different spectra perceived by the one person as the same colour, due to (a) two illuminant + object combinations (neither of which components are metameric in themselves) yielding spectral reflectance (or transmission) curves that have the same weighted mean colour in the chromaticity diagram, or (b) limitations in the observer’s visual response itself, whether due to colour-blindness (a defect in the visual apparatus) or dark-adapted vision, when the cones are not (fully-)functional. In the last case, condition (a) is, of course, normal, and can be created in the apparatus of Fig. 1.4 by using different screens on the two sides, although it would be an unusual natural occurrence as it stands. However, it can now be seen that ‘white perception’ (§3.10) is in fact a metameric perception of this kind, using the concept or memory of lack of hue as an internal reference. Condition (b) is certainly a problem in low-light conditions, which is why lighting level is part of the specifications for workplaces where colour is important. Daylight Ordinarily, we take ‘daylight’ to be a nominal reference illumination. This is because of its naturalness: we suppose it to have a better quality in some sense. But if we were to take daylight to be a fixed illuminant we would be wrong: ‘daylight’ varies considerably (Fig. 4.2), as anyone who has been up at dawn or watched a spectacular sunset knows.[8] !4.4

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The light of day emanates ultimately from the sun, which is a Type G, main sequence star and therefore yellow-white, having a surface temperature of some 5800 K.[9] However, the sky itself is well-known to be blue, because blue light is scattered more than the red end of the spectrum by fine dust in the atmosphere, shifting the spectrum – and thus the colour of the light – more and more to the blue at greater angles of view from the sun direction. Clouds, however, with their large droplets of water or ice scatter all wavelengths more or less uniformly; hence they appear white. Early morning or late evening direct sunlight, however, tends to be very yellow or red as the blue light has been scattered away from the viewing direction. Daylight, therefore, is far from constant in colour, depending on time of day, direction viewed, cloud cover and other atmospheric conditions. Even so, diffuse daylight (i.e. not direct sun) of one kind or another represents a common type of illumination, even indoors. Artists are well aware of the effects of such changes in illumination: the “cold northern light” is much preferred (at least in the northern hemisphere!) as it avoids much of the interfering variation. Artificial lighting Artificial lighting, on the other hand, is much more variable. The spectrum of a tungsten filament incandescent lamp, for example, is very dependent on the voltage at which it is run (Fig. 4.3). The filament of such lamps is resistively heated by the current flowing through it, and that current therefore varies with the applied voltage. The temperature attained by that filament then depends on the balance of the energy supplied with that radiated and conducted away. When objects are heated they are well known first to glow dull red, then a brighter red, yellow-white, then blue-white. This is because the relative emittance of radiation towards the blue end of the spectrum increases steadily with increasing temperature, making the light ‘whiter’. The colours of stars show such a range for the same reason.

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Fig. 4.2 Daylight varies in its spectral intensity curve according to the part of the sky that is delivering the light. The blueness of the sky is due to differential scattering by dust in the atmosphere; it is wavelength and angle dependent. Clouds tend to reflect or diffuse light which is closer to the sun’s spectrum.

!4.5

Fig. 4.3 Some spectral emittance curves for a tungsten filament run at different voltages and therefore different temperatures. (Halogen lamps can be run at higher temperatures than ordinary gas-filled types.)

Black body emission This effect is explained ultimately by Planck’s radiation law. The emission power E, in W/m2, of a black body, at a given wavelength λ, is given by: !4.6

c1 5 E   c2 /T e 1

(4.1)

where T is the absolute temperature, and c1, c2 are constants. A black body11 is a theoretically-perfect, entirely passive emitter of radiation, emitting only by virtue of its temperature, without contributions from any other physical or chemical process or reaction. The nature of the emission curves is illustrated by Fig. 4.4, from which it can be seen that the peak emission moves steadily to shorter wavelengths, while the emitted power increases very rapidly, as the temperature rises.

11

Strictly, this is defined as a body that absorbs all incident radiation, without reflection or transmission, independent of direction and wavelength.

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The effect on the perceived colour of the emitted radiation can be seen by examining the region of the visible spectrum more closely (Fig. 4.5). Here, the emission curves have been normalized to the peak emission power (that is, scaled by dividing the values for a curve by the peak value for that curve) in order to avoid overall brightness affecting the picture. At 1000 K the emission is nearly all red, and this bias continues to 3000 K. After that there are substantial contributions from the blue end of the spectrum and the light becomes orange-red. By 5000 K, the power is fairly evenly spread with a peak around 550 nm, so that the colour is yellowish white. At 6500 K the peak is centred in the blue, corresponding to daylight’s bluish white, after which the light becomes increasingly blue. For comparison, electrical discharges such as in arc welding and lightning reach temperatures of at least 10 000 K, hence their very blue-white, even violet appearance.

613

Fig. 4.4 A set of black body spectral emission curves according to Planck’s radiation law. (Note the logarithmic scales.)

Colour temperature In fact, the wavelength, λp, of the peak emission of a black body is related to the absolute temperature, T, by the relationship:

!4.7

p  b / T

(4.2)

where the constant b = 2.898 × 106 nm.K. This is called Wien’s displacement law. Hence the spectrum, and thus the colour, of the emitted radiation is very sensitive to the voltage applied to the filament. Because quartz-halogen12 lamps (which are also tungsten filament lamps) can be run at a higher temperature, these produce simultaneously the brightest and whitest lights that can be obtained from this type of system. Illuminants such as photographic floodlights and flashguns, and indeed any lamp Fig. 4.5 The black body spectral emission curves for a range of temperatures (corresponding peaks indicated at the top). where the colour of the light is important, have Compare the 300 K curve with that for the 12 V Halogen lamp their output designated by their colour in Fig. 4.3. temperature. This is defined as the black body temperature that would give a colour of light identical to that obtained from the illuminant in question. In the case of a filament lamp it is closely related to the actual temperature of the filament (whose behaviour is quite close to that of a perfect black body). The colour of such a lamp may be plotted at a variety of temperatures directly on the chromaticity diagram (Fig. 4.6). The locus of that plot, the Planckian locus,[10] is a smooth curve which passes very close to the neutral point at about 5500 K. It can be seen that this corresponds to the ‘flattest’ curve over the visible range (Figs 4.4, 4.5) – nearest to the ideal ‘white’ illuminant. It is the strong predominance of red in the light from ordinary filament lamps that led to the use of ‘tungsten’ as opposed to ‘daylight’ colour photographic film when such illumination was unavoidable; the sensitivities of the dyes have been adjusted to give a better approximation to a ‘daylight’ appearance. Indeed, the same principle applies to the ‘white balance’ settings of a digital camera. Some idea of the range of colour temperatures that may be encountered can be obtained from Fig. 4.7. It is apparent that the variation in ‘daylight’ discussed above (§4.4) is indeed substantial, and that what we might 12

A quartz envelope to prevent it melting at the high running temperature, and a small amount of a halogen (often iodine) included in the envelope to reduce the net evaporation of the tungsten filament. Note: m.p. of tungsten is ~3387EC, b.p. ~5555EC.

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be used to as ordinary artificial lighting is far from natural. Special lamps are essential if daylight is to be simulated, but clearly one needs first to decide on a standard illuminant – which is why D65 is required for reference purposes. Colour temperature is also subjectively indicated by the common terms of ‘warm’ and ‘cold’ applied to lighting of yellowish to reddish or bluish effect respectively. Presumably, the associations are with the glow from open fires and the appearance of snow and ice under a blue sky, but these are psychological effects beyond the scope of this book. It is, however, worth noting that the association is inverted in that very hot bodies emit bluish light, while ‘red hot’ is, relatively speaking, rather cool. Fig. 4.6 The locus of the colour of the light from a tungsten filament at various temperatures (in kelvin) illustrating the idea of colour temperature. D65, ‘standard daylight’, is close to the black-body 6500 K point (>). Notice that the light becomes decidedly blue at very high temperatures, when the emission spectrum also includes significant amounts of ultraviolet (Fig. 4.4).

Ultraviolet emission Another consequence of Planck’s radiation law is that as the temperature of the emitter rises so the quantity of ultraviolet (UV) radiation produced also increases. UV is damaging to the eyes, one of the reasons why UV-initiated polymerization in resin restorative materials was abandoned (6§5.9). This means that lamps running at a high enough temperature, such as quartz-halogen types, emit sufficient UV to be of concern. This has been recognized to be a hazard in the context of domestic lamps of that kind (such as desk lamps) because of the long exposure times involved, and they are now frequently sold with a UV (blocking) filter. !4.8

Fig. 4.7 Approximate colour temperatures of some common natural and artificial illuminants.

Such filters should therefore be installed in dental operating lights, which can otherwise be expected to be a risk because they have to be operated at a high enough colour temperature to allow good matching of shades under daylight-like conditions. Indeed, dental lights, and other lamps for high-quality colour work, are sold with specific claims of daylight-like illumination. This is not altogether unreasonable but, as should be clear from Fig. 4.2, it should not be interpreted as being capable of being strictly true. Nevertheless, such illuminants are effectively standardized and therefore useful. Notice from Fig. 4.6 that ‘standard daylight’ corresponds to a colour temperature of about 6500 K. (Compare the sun’s surface temperature of ~5800 K.) Fig. 4.8 Relative sensitivity against wavelength of the light-adapted human eye (photopic vision)

It should also be borne in mind that the overall sensitivity of the eye varies according to wavelength (Fig. 4.8). As was pointed out in 6§5.12, the intensity in the

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blue region from curing lights will be far greater than appears to be the case. The effect will be increased if other wavelengths are filtered out. Add this to the relatively intense blue emission from quartz-halogen lamps (Fig. 4.3), and the risk of damage can be seen to be significant. The use of the viewing filter is very important. Fluorescent lamps The other commonly used source of artificial illumination is the so-called ‘fluorescent’ lamp or ‘tube’. These operate by the conversion of ultraviolet light, from a mercury vapour discharge set up within the tube, to visible light through the use of particular chemical compounds known as phosphors, some examples of which are given in Table 4.1. The mercury vapour discharge produces what is known as a line spectrum (Fig. 4.9), which arises from the ionization and re-reaction with electrons of mercury atoms in the electric discharge.[11] (These electrons are in outer shells, cf. Fig. 26§1.1.) It is called a line spectrum because the electronic transitions are associated with specific precise wavelengths, and these are therefore very strongly represented. !4.9

Fig. 4.9 The spectrum of a low-pressure mercury vapour discharge lamp, as used in fluorescent lamps. The bars indicate intense line emission.

Table 4.1 Some typical phosphors which emit after stimulation by ultra-violet light or electron bombardment. The light emitted is due to electron transitions to lower energy states after excitation. Phosphor Calcium tungstate Magnesium tungstate Zinc silicate Calcium halophosphate Calcium silicate Cadmium borate Calcium-strontium phosphate Magnesium arsenate

Wavelength/nm of max. emittance 440 480 540 590 610 615 640 660

Fig. 4.10 Two typical spectra for fluorescent lamps showing the dominance of the Hg lines, and the degrees of success obtained in ‘filling in’ the spectrum with phosphors; compared with curve of Fig. 4.9 (dotted).

Inevitably, these lines will figure prominently in the output of the fluorescent lamp because they are not absorbed completely, even though much broadening and ‘filling-in’ of the spectrum can be done by the phosphors (Fig. 4.10). Phosphors also operate by emitting light in the process of electronic transitions to lower energy states, but the spectrum is more complicated and ‘smeared out’ because in the solid state, and with multi-atom compounds, there are many more possibilities for intermediate states (cf. the vibrational decay in polymerization photosensitizers, Fig. 6§5.2). The dramatic difference between the spectrum of tungsten filament and these fluorescent lamps is obvious. By adjusting the mixtures of phosphors the spectral distributions of the light produced can be changed, but the strong lines are always present. It is therefore possible in principle to create the general perception of the colour of daylight (‘D65’, Fig. 4.11), even though the spectra are very

Fig. 4.11 The spectra of standard daylight (D65) and a typical fluorescent lamp show substantial differences.

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different in general shape: by adjusting the intensities the weighted mean can be made to correspond with the target colour. So-called “daylight” tubes are available which are claimed to be good matches, and for which a premium price may be payable. However, depending on the purposes of the user, the ‘cold’ (rather bluish) or ‘warm’ (somewhat pinkish) light products may be preferred. That there are in fact large differences between products is easily seen by inspecting from a distance the colour of the light in the windows of a block of flats in the evening - and each occupant is under the impression that the light is natural. However, because of metamerism, many objects, paint and so on may take on ‘peculiar’ colours under fluorescent lights. Fluorescent illumination is therefore not recommended for high quality colour work, such as for dental porcelain. Peculiar effects are also possible with colour television cameras and photographic film because of their characteristic sensitivities. !4.10 Ultraviolet emission (2) There is a further issue of relevance with fluorescent lamps: the absorption of the UV by the phosphors is not perfect. The intensity of the UV is not great enough to have caused any concern over potential eye damage, but there are two effects of interest. Many paper products and domestic detergents contain fluorescent compounds that convert UV into blue light, thereby tending to make the treated object appear whiter or brighter (hence the term ‘brightener’ for these compounds). In comparison, an untreated but truly neutral colour will appear relatively yellowish under the same illumination. This is a distortion of perception because colour is psychophysical, not absolute. Secondly, many microorganisms are sensitive to UV. It is therefore not a very good idea to use fluorescent lamps in microbiological laboratories, where the ability to culture organisms is critical to diagnosis and so on. This unintended emission was also a reason for UV-cured resin restorative materials setting prematurely (and quartz-halogen lamps also emit UV, §4.8), but the problem is, of course, far worse with blue light-sensitized materials, so that any exposure to room or natural light is undesirable. !4.11 Use of shade guides We may therefore be using several different kinds of illumination, with widely varying spectra. It is under these changes of illumination that metamerism is problematic. It is possible, indeed common, to observe colour matches under daylight which then show striking differences under artificial lighting, whether under ordinary tungsten filament lamps with their predominantly red emission, or fluorescent lamps with their very spiky spectra. This is a common problem with paint, clothing and cosmetics, particularly with the more saturated colours; hence the very sensible and practical utility of making comparisons outside the shop (in ‘daylight’ – which, of course, itself varies, §4.4), avoiding the distortions of artificial lighting. In dentistry, such effects can arise for all ‘tooth-like’ restorative materials – resin, GI, porcelain – with respect to adjacent tooth tissue, as well as between themselves, as in using a filled resin to repair a broken porcelain device. Thus, in dentistry, when identifying from a shade guide which shade of artificial tooth, restorative or other material to use, and appearance is important, it is good practice to check that the match is good at least under natural daylight, and preferably also under fluorescent tube illumination. This is to make sure that untoward effects do not occur. Checks with multiple illuminants are always necessary unless it is known with certainty that the shade guide material is identical in every respect to the actual material to be used, so that the absorbance spectrum is precisely the same. This is not likely to be the case with printed shade guides. (It also assumes that the manufacturer has already designed – and checked – the product to avoid problems from this source.) However, and worse, no dental material can possibly have precisely the same spectral absorbance spectrum as the tissue it is meant to be replacing. Metameric effects are therefore inevitable, given the sensitivity and discriminatory ability of our colour visual system. With care, these difficulties can be minimized. Again, it is a matter of compromise, to find the best match possible under a variety of lighting conditions. This is mostly the responsibility of the manufacturer, but the dentist still needs to recognize the nature of the problem if significant errors are to be avoided.[12] In passing, it should be noted that although the number-letter shade designations (‘A3’, and so on) used for restorative materials by many manufacturers are uniform in style, it should not be assumed that they are indistinguishable. In fact, there are appreciable differences between the colours they represent. Accordingly, a shade guide should only be used with the product for which it is intended. In this context it is worth noting the existence of a figure of merit for lamps called the Colour Rendering Index (CRI). This is a 0 ~ 100 scale that is supposed to indicate how accurately a light source will reproduce the colour of an object in comparison with a ‘natural’ illumination, such as a standardized ‘daylight’(e.g. D65) or a blackbody source. The calculation is complicated (and negative values are possible!), and not a little controversial.[13] In essence, it is derived from the arithmetic mean shift in measured chromaticity coordinates

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(Euclidean distance) between the two sources for a set of “representative” test colour swatches. Whilst high values may be reassuring, it is not sufficient to rely on the CRI for critical applications, and an actual visual check under daylight remains a sensible precaution. !4.12 Effect of surroundings A related but rarely recognized effect of the same kind can arise from the surroundings, not by influencing perception as such but by changing the effective illuminant. Thus, the light reflected from walls, ceilings and floors will have had its spectrum modified by the pigments in the paint and so on (Fig. 3.6). Red walls remove most of the blue from the light, leaving in effect a red illuminant to augment the direct illumination. The overall colour of the illumination thus moves towards the hue of the wall, and clearly will tend to give faulty shade matches (Fig. 4.12). Daylight reflected from hoardings outside the surgery window will also have a colour cast which depends on what is currently being advertised there, or affected by whether there are buildings, neon signs, street lighting, trees in leaf, or snow outside – which with a clear sky gives a very blue light, as mentioned earlier. Colour matching can thus be influenced by location, building orientation (via sun angle, §4.4), the weather, the seasons, and the time of day. In addition, the use of Fig. 4.12 Apparent colour is affected tinted windows changes the spectrum of the daylight entering. The by all aspects of the surroundings and wearing of brightly-coloured garments by the dentist will similarly illuminants. modify the light illuminating the patient, as will an aquarium lit with a strong UV component for visual effect, or a TV or computer screen (which tend to be bluedominant). Indeed, the patient’s clothes will also have an effect and, if of strong as opposed to neutral colours, these should be covered with a white or neutral (grey) drape. There is therefore considerable sense in the notion that dental surgeries should be decorated in pale colours, that tunics should be similarly neutral, and that attention be given to possible external interferences if serious colour matching is contemplated, quite apart from using a suitable standard illuminant. Given the increasing emphasis on ‘cosmetic dentistry’, this seems to acquire greater importance. Of course, in other kinds of practice, orthodontic or paediatric, for example, this might not matter. In summary, the illumination of the object of interest is the sum of all sources of light (Fig. 4.13), direct and scattered, and so the colour of that overall illuminant is dependent, in ordinary colour-mixing fashion, on their Fig. 4.13 The apparent colour of a tooth like-coloured colours. object is shifted by the addition to the intended white illuminant of some light reflected from coloured

These are dramatic effects. More subtle, so that it surroundings. is more important that it be recognized, is the effect of adjacent soft tissue. Quite clearly the colour of the mucosa will also create colour cast effects. Matching must therefore be done under the normal circumstances of the illumination of the anterior teeth being modified in that way, that is, including that reflected light. Green rubber dam will not help, and even the usual grey will screen the light scattered from oral tissues. Obviously, cosmetic lip colour should be avoided as well. (Incidentally, such colour can become infiltrated into tooth tissue through inadvertent – and frequent – contact, and this can result in odd staining, which of course affects shade matching.) In this discussion we are referring specifically to the effect of incident light. However, teeth are commonly sufficiently translucent that light transmitted through the tissue affects the perceived colouration, especially at incisal edges. While this is another reason for avoiding rubber dam (or other foreign materials) being present, it should also be recognized that if, say, a porcelain shade guide were not subject to the same retrograde illumination, and of appropriate thickness, it cannot result in a proper match.

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!4.13 Perception There is nevertheless a perception problem as well. We have learnt through long experience the colours of familiar objects: the blue of the sky, the colour of our own skin, the white of paper, and so on. Our brains have therefore adjusted the weight to be afforded each type of retinal cone’s signal for a reasonable colour balance in our view of the world. This is known as chromatic adaptation.[14] But if, for example, the amount of red light that is being received is greater than usual for any length of time, this is interpreted as a defect in processing and the gain, as it were, of the red channel is decreased in an attempt to restore ‘normality’ to the scene (this is also due in part to the relative bleaching of the retinal pigments on excessive exposure to more intense colour). After a while we become less aware of the red excess. But if now the illumination is returned to a more usual balance, everything appears distinctly greenish, because effectively the red gain is relatively too low. This effect fades in a few minutes. A similar and common example might be to use a microscope with a green filter in order to improve the contrast of certain images. Each time that one looks up after some extended use the surroundings are suffused with a rosy glow. The wearing of tinted sunglasses produces similar effects. Similarly, under water (scuba diving) where red light is filtered out, the strong blue effect becomes less noticeable with time – photographs taken without flash or filter indicate just how strong this bias is, sometimes surprisingly so. The point of this is that under a particular illumination, say tungsten filament light, which is rather deficient at the blue end of the spectrum and somewhat overstrong at the red end, the colour balance in our heads will have been adjusted appropriately for ‘normality’. Adding this effect to the system compounds the problem of metamerism by changing the way we process the tristimulus information being transmitted by the cones. It is no longer just a matter of the light which is reaching the objects being colour matched, but the general colour balance of the surroundings now has a bearing. This circumstance must be distinguished from that in Fig. 1.4 where illuminants are being compared, but it does account for the colour-shifts discussed under ‘Matching persistence’ (§4.2). Despite all of the above, it is important to recognize that there will be variation in shade selection due to observer preferences: nobody is really objective about their appearance. Our memory for colour is also extremely poor, and certainly not an absolute sense, so that attempting to select a well-matching colour without the reference is doomed. Furthermore, traditional and advertising emphases on the virtues of ‘white’ teeth (teeth are anything but white[15]) bias perceptions even more. The appropriate approach is to recognize the difficulties of the task and arrange the necessary circumstances for doing the best job possible. !4.14 Aesthetic dentistry The word ‘aesthetic’ appears very frequently in dentistry, even occurring in the titles of several journals. It is, however, essentially meaningless in many of these contexts, as it is never applied to the appreciation of beauty (a purely philosophical and personal matter), but rather nearly always to just the appearance of a restoration (and especially as the plural form: “aesthetics of ...”). However, an ‘aesthetic’ restoration, it would seem, is merely one which has achieved a high standard of similarity to the tooth tissue in or on which it sits. This confusion and abuse is unfortunate as it relates more to advertising than prowess, function, or material properties.[16] Appearance may be considered from two points of view. Mimicry of tooth tissue, essentially ‘invisible repair’, is the ordinary common – and quite reasonable – goal, as this seeks to match adjacent tooth tissue in shade, translucency, and so on, and often with heed given to the localized non-uniformities of natural teeth (as in high-quality porcelain work). The undetectability of the restoration is the measure of goodness: invisible dentistry the aim. On the other hand, cosmetic dentistry (an honest term in itself) is concerned with the reconstruction of the dentition is terms of arrangement (orthodontics), shape (extension for closure of diastemata, edge regularity), or blemish obliteration or whiteness (bleaching; 30§1.3), albeit far too often towards some imagined (and unnatural) paradigm of perfection. This may be confused with (the perhaps simultaneous) repair of congenital or developmental defects, or the repair of function otherwise impaired, or the reconstruction required following surgery or the rectification of pathological conditions, but the purposes are quite distinct: vanity-driven mutilation or exaggeration as opposed to re-establishment of anatomical and functional adequacy related to absence of undesirable side-effects or to quality of life. In contrast, there have been attempts to address appearance from the point of view of aesthetics (properly) in both classical[17] and pragmatic[18] terms. It should be borne in mind that standards of beauty are not universal, but culturally-determined. There remain societies in which, for example, anterior teeth are filed to sharp points or even removed (particularly in Africa), black teeth are thought to be desirable (in parts of Malaysia, the Philippines, and formerly Japan),

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societies in which demonstration of wealth is achieved through gold-capped or -inlaid anterior teeth (in China, even if the ‘gold’ is brass), inlaid diamonds are not unknown, and various other decorations are promoted. While people are usually vain (i.e. show appearance-consciousness), to a greater or lesser extent, and some account can legitimately be taken of this in prescribing a treatment, it remains inappropriate, misleading (and a source of bias) to describe any of this as “aesthetic” or involving “aesthetics”. The usages are meant to impress, but are essentially hollow and pretentious; their use unthinking and uncritical. Thus, wherever the words appear in dentistry, “aesthetics” can normally be replaced by words such as “appearance”, and “aesthetic” by “tooth (enamel)-like” or “cosmetic”, with no loss – in fact, with clearer meaning. Even so, it should still be recognized that the service performance of a material remains a major consideration of ethical dentistry. Thus, for posterior restorations, for example, strength and wear-resistance are extremely important, and may override the demand for tooth-like appearance altogether (silver amalgam, gold) or partially (machined ceramics). Thus, tolerance of non-tooth-like appearance, as for partial-denture clasps, is possible if not common. Cost is also pertinent.

§5. Physics of Light Colour as such is clearly the most important aspect of matching for a ‘tooth-like’ restorative material, artificial tooth or denture base acrylic, but there are other aspects of appearance which need to be noted for the full simulation of natural tissue. In other words, there are other optical properties which contribute to the appearance of objects. These factors include gloss, opacity and the natural fluorescence of tooth substance. The first two items are concerned with the physical effects of the medium on the light, apart from spectral effects. There will also be contributions from the surface texture (20§6) and what may be termed the granularity or scale of internal structure. These are outside the present scope but cannot, ultimately, be ignored. Refraction On meeting the boundary between two media of differing refractive index, a light ray is both refracted and reflected (Fig. 5.1) and the following familiar relationships apply: !5.1

(5.1) and, for the ray crossing the boundary, (5.2) where n1 and n2 are the refractive indices of the two media (Table 5.1) and the angles are measured from the perpendicular to that boundary, the ‘normal’. Thus a ray perpendicular to the surface is not deviated. The refractive index of a medium is in fact defined fundamentally by the following ratio: (5.3) In other words, any medium reduces the speed of light in it. Graphically, this can be expressed as a retardation of the wave front (Fig. 5.2). Refractive index varies with wavelength; an effect that is commonly seen to be operating in the dispersion of wavelengths by a glass prism to produce a spectrum (Fig. 1.3) or, of course, a rainbow by water droplets. The important point here is that at the boundary between two media (the interface) an incident

Fig. 5.1 Light is simultaneously reflected and refracted at a boundary between regions of differing refractive index. In this example n2 > n1.

Table 5.1 Some examples of refractive index (23 EC; λ = 589.3 nm - sodium yellow light). Diamond Zirconia Alumina Hydroxyapatite* Mylar (PET) Quartz* Feldspar Soda-lime glass PMMA Glycerol Water Ice (0 EC) Air (1 bar)

2.417 1.98 1.76 1.649, 1.643 1.641 1.544, 1.553 1.52 1.512 1.495 1.474 1.333 1.31 1.00029

* these materials show double refraction

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light ray is deviated from its original path, whether by reflection or by refraction, when the ray is not normal to that boundary. !5.2 Total internal reflection For a ray approaching a boundary from the medium with the higher refractive index, n2, we calculate the angle of the refracted ray by rearranging equation 5.2: (5.4) (i.e. swapping n1 and n2). From this it is obvious that if the right hand side has a value greater than 1, sin r is meaningless, i.e. the limiting case is (5.5)

Fig. 5.2 The velocity of light is reduced from its vacuum value in a denser medium according to the refractive index. It is said to be retarded.

so that r = 90E. This means that the emergent ray lies in the plane of the interface or, in other words, is tangent to it. So what happens if the right hand side of equation 5.4 is greater than 1? The ray is totally internally reflected (Fig. 5.3). When equation 5.5 is true the angle of incidence, i, is called the critical angle. Obviously, such an effect could be important in complicating the path taken by a ray of light through composite materials such as filled-resin restoratives, glass ionomer cement and dental porcelain. Reflectance However, as stated above, and except for the special case of total internal reflection, light approaching an interface is not simply either reflected or refracted: both usually occur, simultaneously. Part of the ray goes one way, part the other. This is the reason for reflections on water, the operation of ‘beam splitters’ as used in microscopes, the possibility of so-called ‘head up’ displays in cars and aircraft cockpits, and the annoying reflections on computer screens referred to as ‘glare’. !5.3

Fig. 5.3 Total internal reflection occurs when the angle of incidence from the medium with the higher refractive index exceeds the critical angle, e.g. at C.

The proportion, ρ, of light reflected at an interface as opposed to being transmitted, the reflectance, is also a function of refractive index and the angle of incidence. Thus, at 0E incidence (i.e. perpendicular rays) the proportion is given by: (5.6) For example, for an ordinary glass with a refractive index of 1.5, given that the refractive index of air at standard temperature and pressure is close enough to 1, ρ0 = 0.04. For other angles as i increases the proportion rises steadily to a value of 1, meaning complete reflection, at i = 90E, i.e. at grazing incidence (Fig. 5.4). There are a number of implications arising from this behaviour.[19]

Fig. 5.4 Variation in reflectance of a ray incident on the boundary from air into a another medium with variation in angle of incidence and the refractive index of the medium. n = 1.5 is near the value of that of ordinary soda glass, as used for windows and mirrors, amongst other things.

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It should be noticed that reflectance has nothing to do with the colour or transparency of the medium: this is purely a surface phenomenon (see ‘gloss’, §5.8, §5.9). Black glass is reflective. Multiple internal reflection The first effect is that of multiple internal reflection (Fig. 5.5). Here, the word ‘internal’ refers to the medium with the higher of the two refractive indices. A light ray reaching the surface of, say, a sheet of window glass is divided into two parts: the reflected ray with relative intensity ρ, and the refracted ray (1 ρ). This latter will pass through the sheet of glass and Fig. 5.5 Multiple internal reflections in a plain sheet of suffer some absorption (for no medium other than the glass for near normal incidence. The percentage of the vacuum is completely transparent, showing 100% original intensity in each ray is shown assuming T = 1 (no transmission), say by proportion T. Thus, what reaches absorption). the far interface is at T(1 - ρ) of the original intensity. At that same interface partial reflection again occurs, so that the intensity of that ‘internally’ reflected ray is T(1 - ρ)ρ of the original, while the emergent ray is T(1 - ρ)2. The intensity of the internally reflected ray reaching the first surface again is then T 2(1 - ρ)ρ. The process repeats itself indefinitely, although it is evident that the intensities rapidly diminish. Nevertheless, it is responsible for the slight degradation in the clarity of any image seen through a window, essentially because of the displacement of the second transmitted ray (no matter how high the quality of the glass) and for the slight dimming of the view. !5.4

Such reflections also reduce the amount of light in the primary image in telescopes and camera lenses and degrade that image by creating ‘stray’ light; the more interfaces (lens elements) the worse it gets (and the matte black inside of the containing tube or body still reflects some slight, especially at near grazing angles, Fig. 5.4). This effect can be seen when looking through a stack of 50 microscope slides. The other point to notice here is the pair of reflected rays of about 4% of the original intensity. These images are most apparent looking at a window from within a lighted room at night. Mirrors The same effect is, of course, operating in mirrors, where the highly reflective coating is applied to the second or rear surface (Fig. 5.6). This ‘silvering’ is indeed usually silver, and is therefore protected from sulphide tarnish on the critical surface by the glass (and by a special paint on the back). The same split of rays occurs at the ‘front’ surface as above, ρ reflected, (1 - ρ) refracted. As now the reflection, R, at the rear surface is very efficient (for convenience we shall assume 100%, but see Fig. 28§5.1), the ray re-emerging from the front surface has the relative intensity RT 2 (1 - ρ)2. After a further reflection from the rear surface, the next emergent ray has the intensity R2T4 ρ(1 - ρ)2. There are therefore two subsidiary reflection images, each of about 4% of the intensity of the main image. These lie either side of the main reflection, at least when the incident ray is not normal to the surface. Notice that the sequence and values of the intensities are the same as in the plain glass sheet (Fig. 5.5), but ‘folded’ so as to appear on the same side (ignoring the effects of less than perfect glass transmission T and mirror reflection R). !5.5

Fig. 5.6 Multiple internal reflections in a rear-silvered mirror for near normal incidence. Ray intensities as in Fig. 5.5; mirror reflectivity R = 1, transmission efficiency T = 1 (no absorption).

Dental mirrors This would not matter very much therefore in the case of a ‘looking glass’, when normally one can only view oneself from near normal incidence. However, in the case of dental mouth mirrors, where the object is to get a view of a region not directly visible and therefore larger angles of incidence are involved, the displacement effects are worse (Fig. 5.7). For detailed work, and when the contrasts in the objects may be small, the image degradation is an unacceptable interference. At small angles of incidence, the effect will appear to be a blurring of the main !5.6

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image, but at higher angles a clear separation will occur, and the first ‘ghost’ become very obvious (Fig. 5.8). A factor in this is the thickness of the glass, both by decreasing T and by increasing the spacing of successive images on increasing the thickness (Fig 5.8), for the necessary strength and rigidity. The successive image spacing d as seen in the viewing direction is given by:

d 

2 t tan[sin 1 (sin i / n)]

(5.7)

where t is the glass thickness. (Higher refractive index for the glass makes the separation less but the ghost image strengths greater.)

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Fig. 5.7 Double image in a back-silvered glass mouth mirror. Variation in the strength of the first ghost with angle is evident. (The third image, above the main one, is much weaker because of the viewing angle – see Fig. 5.8.)

In a looking glass the question of the weight of the mirror and its strength determines that the thickness must be relatively large (cheap, large, thin mirrors can distort noticeably), although in a dental mirror of a diameter of about 20 mm this might not be so significant; clearly there is a practical limit. Even so, rear surface mirrors are not good enough here because the glass cannot be made thin enough without making them too fragile or at risk of distortion. The solution is to use front surface mirrors, eliminating both absorption dimming and secondary images. Because the metal surface is now exposed, silver cannot be used and rhodium is the coating of choice Fig. 5.8 The relative strengths of the ghost images depend on the (although it is less reflective than silver, Fig. viewing angle, with the first ghost being similar to the main image at 28§5.1), a moderately hard (Hv ~ 120), ~80E incidence. The apparent separation is proportional to the glass thickness. (Calculated for n = 1.5.) oxidation-resistant metal. This is also the approach taken for astronomical telescope mirrors where dimming and multiple images are quite unacceptable (28§5). For disposable mirrors a simpler solution exists: a coating of aluminium on Mylar film (27§4) as a rear surface mirror is effective because the polymer film can be very thin while protecting the aluminium from oxidation, and it can also be stretched taught over a frame to create a flat enough surface, if the frame is rigid enough. Surface effects The reflection occurring in Fig. 5.1 is envisaged as being from a plane surface. Naturally, such reflection is a ‘local’ phenomenon, and on a rough surface each locality will present a different angle to the rays of an incoming beam. The reflected rays may therefore be at any angle with respect to the mean surface (cf. 20§6). Similarly, the refracted rays may be at a wide range of angles. On the one hand we have specular (‘mirror-like’) reflection and transmission through a transparent medium, in which there is no scrambling or confusion of a beam and images are coherent: the obvious example of transparency is plain !5.7

Fig. 5.9 On reaching a boundary, light may be transmitted (left) or reflected (right), either in a specular (top) or a diffuse (bottom) manner, or a wide range of intermediate conditions.

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window glass. On the other hand we have diffuse reflection from a matte surface and transmission through a translucent material, in which much scattering of the light occurs (Fig. 5.9) and no image information is preserved, such as with etched or grit-blasted glass. This scattering may be from macroscopic detail, such as an irregular surface (Fig. 5.10), but it is also affected by small particles of other phases which bend the light one way or another (Fig. 5.11), as well as bubbles of gas or liquid within the body. Size limit For scattering to occur requires that the object has a size greater than -½ the wavelength of the light, otherwise it simply is not ‘seen’. This does not prevent absorption by dye molecules, for example, which clearly are much smaller than that criterion. One of the implications of this limit is that while a rough surface will scatter light, if the scratches are made smaller than -½ wavelength the surface will appear polished and show specular reflection or transmission. Since blue light has a wavelength of about 400 nm, or 0.4 μm, a surface with scratches of less than about 0.2 μm will appear perfectly polished, even under a microscope, if it uses light for imaging. !5.8

Fig. 5.10 Scattering may be due to an irregular surface ...

The same applies to ‘micro-filled’ resins (6§3.2), Fig. 5.11 ... or due to small particles. Compare the where the average particle size of the fumed silica filler effect of dust in the air (Fig. 4.2). used ranges from about 7 to 50 nm, so that there is no scattering of visible light. Thus, unless other particulate phases are included on a large enough scale, or agglomerations are present (Fig. 4§7.11), such materials would be transparent. The effect is also seen with bubbles in porcelain (25§4.3). The reflectivity of smooth surfaces is known as gloss. It is an important property of paints and other decorative finishes, but it is also an important subjective means of assessing the quality of polishing, as in the finishing of dental restorations and prostheses. Gloss can be seen to be a mixed rather than fundamental property in that it combines the effects of lack of scattering due to roughness and refractive index, but it is also dependent on the angle of view (Fig. 5.4). If a ‘glossmeter’ is used for such assessments the angle of illumination and view must be specified. Chromaticity shift For an apparently opaque object to return light to the eye, and for the effects of differential absorption to be seen, i.e. for it to have colour and not a metallic appearance, the light must in the first instance have penetrated the surface, and then be scattered back out. However, as described above, there is always some superficial simple reflection. The importance of this is that the light received by the eye from any given non-metallic surface is always a mixture of the internally scattered and the superficially reflected. The superficially reflected light has not undergone any spectral modification by absorption within the medium; it is spectrally identical to the incident light. This then is light added to or mixed with the ‘coloured’ light, representing the result of differential absorption, emerging from within the object. This mixture necessarily gives a less-saturated colour to the object !5.9

Fig. 5.12 The chromaticity shift that may be observed with daylight on a reflective red object.

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than it would have in the absence of a surface gloss. In terms of the chromaticity diagram this effect is expressed by the chromaticity shift, the change in the coordinates towards those of the illuminant (Fig. 5.12), whatever it is. Again, this shows that the surroundings may influence the perceived colour of an object if it is glossy, but by yet a further mechanism. A similar effect is seen with stress-whitening (5§5.4, 7§2.4) in what are otherwise relatively translucent materials. As incident light is increasingly scattered from within by the structural changes occurring on deformation, so there is a chromaticity shift towards the illuminant, which is of course usually “white”. !5.10 Wet roughness Only a very small proportion of a rough surface will lie parallel to the nominal or mean surface. Thus, no matter what angle of incidence the illuminating rays may have to that mean surface, locally many will effectively have high angles of incidence. Therefore, no matter what the angle of view of such a surface, and no matter what the angle and direction of illumination, some superficial reflection in the view direction will occur. Under ordinary illumination conditions rough surfaces therefore tend to appear whitish, and not to show the real colour of the underlying bulk material. Hence the “frosty” appearance of etched enamel. However, if a film of liquid which wets the solid is spread on it, the rough surface is now against a medium of much higher refractive index. For example, applying equation 5.6 to water on PMMA (see Table 5.1), ρ0 = ~0.003 (compared with 0.04 before) so very little reflective scattering now occurs at that interface. On the other hand, for the air-water interface, which is necessarily smooth because of the surface tension effect (10§1), ρ0 = ~0.02 and glossy reflection will dominate. However, and most importantly, it becomes easy to find a viewing angle that avoids glossy highlights obscuring the underlying material, and its colour becomes obvious. In addition, if the PMMA is transparent, not containing any scattering or absorbing particles, an image viewed through the rough but wet surface will be clear, while the dry surface will scatter so much as to destroy the image. The same applies to water on ground glass, and even oil on paper, which becomes much more translucent by reducing the scattering at each fibre. This was the basis of the old ‘grease-spot’ photometer of school physics classes. In passing, it is just this air-polymer interface reflection that causes crazes in PMMA to be visible (§5.9, 5§5.4), even if they are very narrow. Similarly, the presence of bubbles in denture base resin through faulty mixing or processing causes less translucency, an opaque and milky appearance. Likewise, the elimination of the porosity of porcelain on sintering (25§4.1) converts the mass from an opaque to a translucent body. Note that even black glossy materials show roughened or scratched areas as grey or whitish because of such scattering of ambient light. The same kind of effect is operating when wax ‘polish’ is applied to a surface, or a varnish is used: the roughness is filled in by a high refractive index medium that is then given – or generates – a smooth surface. It is also effective in the context of a glaze on dental porcelain, even though the primary purpose is strengthening (25§5.1). The converse effect must also be borne in mind. If the roughness of a surface is to be assessed by eye, as during an (abrasive) polishing procedure, it is essential that this be done on the dry surface, irrespective of the need for coolant or lubricant during that process (20§2.6, 20§7). The same applies when examining an etched tooth surface, for example; it needs to be dried to determine whether the extent and depth of etching are in fact as intended. A similar effect is seen when teeth are dried. Tooth enamel is naturally slightly rough (through wear) as well as very slightly porous. The superficial film of saliva or water dominates the glossy appearance, and thus the associated chromaticity shift of highlights (§5.9). Thus, when this film is removed, although the gloss effect is lost, scattering at the roughness means that the chromaticity shift is more generalized, that is, the tooth appears both whiter and lighter. Further drying means that liquid in the porosity is lost, and progressively deeper. The extra scattering from the numerous air-enamel interfaces amplifies the whitening and lightening as the amount of differential absorption is reduced and the colour of the scattered light more nearly approaches that of the illuminant – assumed to be white. Obviously, the effect is similar to that of etching, mentioned above, but not as marked. This change in appearance clearly affects shade-matching (§4.11), and must be taken into account by allowing rehydration. Full recovery of ‘natural’ colour may take 20 ~ 30 minutes.

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!5.11 Composite materials The various phases present in translucent composite materials almost inevitably will have differing refractive indices. Indeed part of the design of restorative materials such as filled resins and porcelain takes this into account specifically to achieve the desired effects. This means that at every interface encountered there will be reflection and refraction. Since those deviated rays will themselves be subject to further deviation at successive interfaces, the net effect is for light to be scattered diffusely (Fig. 5.13). The path taken by any ray will therefore be complicated. In addition, there will be differential absorption if any phase is ‘coloured’. The optical appearance of the object therefore depends on the refractive indices and absorption characteristics of each phase present.

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Fig. 5.13 Many light paths are possible in a translucent composite medium through reflection and refraction when the refractive indices are different.

This effect is also seen in single-component polymers that are not completely amorphous (3§4.1). Here the refractive index varies from place to place as the crystallinity of the polymer varies, and thus the density. This variation in density is gradual rather than abrupt, resulting in the light path bending rather than being kinked, but the overall effect is the same. Polyethylene in very thin films is evidently quite transparent (“cling” film), but as the thickness increases so first a slight image distortion may be detectable (“polythene” bags), then increasing cloudiness (bottles), finally becoming quite opaque in thick sections (chopping boards). Where clarity is important, a polymer that might otherwise tend to crystallize (say, on cooling slowly after melt processing) may be modified as a copolymer simply to increase the irregularity of the chain and better preserve the amorphous structure. However, the refractive index of the matrix of filled resins depends on the polymerization shrinkage via degree of conversion. That is, it changes continuously during the curing process. Since it is the difference in refractive indices that affects the deviation and scattering, depending on how the filler is chosen, and the chemistry of the resin, the effect may increase or decrease the translucency. This then affects how underlying material affects the apparent shade (§5.12). This is in addition to the shade shift that occurs as the diketone is consumed (6§5.16). Hence, it is important to rely on the manufacturer’ shade guide (§4.11) and ignore the initial appearance of the unirradiated material. However, there is one context where this is not so reliable. If a light-cured resin is intended for luting a thin porcelain shell crown or veneer, using transillumination to effect the cure, shade selection is much harder as the combined effect of the three materials – tooth, lute and ceramic – is difficult to judge. Even so, trying the restoration in place with the proposed luting material cannot give the desired effect because its translucency and colour will change when cured. In any case, the sensitivity to ambient light is such that it would have partially set by the time removal was attempted (and making that removal very difficult). It has been suggested that a special try-in filled resin be used, one that cannot set on ambient irradiation (no diketone, or no amine) but which has the actual optical properties of the corresponding shade of set material (by adjusting the refractive index of the matrix). Thus, if a different shade needs to be checked it can be done readily because the try-in material is easily removed. Even so, if any slight remnants of this remain they will be bonded to the lute because the same polymerizable monomers are present. Thus, an elaborate clean-up is avoided (no solvents for set material), minimizing the risk of damage to the ceramic device. The alternative approach of the so-called try-in “gel” (see box in 7§8; §5.14), based for example on glycerine and fumed silica, cannot replicate the full optical characteristics of a filled resin and may present problems in clean-up and drying. The silanation of the porcelain may be affected, requiring it to be redone. !5.12 Chameleon effect In this sense of translucent scattering, dental restorative materials are designed to mimic tooth tissue, whether enamel (whose hydroxyapatite crystals are embedded in a protein matrix, no matter how little – the interfaces still exist) or dentine, where the tubules normally contain a more watery medium or cell substance as well as having a mineral-protein composite part. Thus, teeth are not glass-like and transparent. On the other hand, the translucency does mean that light may reach deeper sites after passing through tooth or restoration and then be returned by scattering to emerge at the surface again. If those deeper sites are discoloured or stained then the effect will be seen as a general shift in the colour of the tooth or restoration. To some extent this chromaticity shift (§5.9) is thought to be beneficial in that a restoration “tends to take on” the colour of the adjacent tooth (and vice versa), perhaps compensating for a not quite exact shade match in the first place. (Needless to say, this

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should not be relied upon to excuse less care and attention.) It is sometimes referred to as the “chameleon effect” (notwithstanding the fact that chameleons operate in a quite different way! It should not be thought that this is other than a purely passive, entirely physical effect). However, it may also be detrimental if is the intention that a stain is to be masked. Thus, an opaque liner for a resin or glass ionomer restoration may be necessary, or an opaque layer in a porcelain restoration used to advantage. For porcelain on metal devices, this is essential. If it were desirable to ‘switch-off’ the effect, so as to remove the influence of adjacent temporary, metallic or discoloured restorations, a mirror strip would need to be inserted so that all reflected light was the same as that emerging. This might be done with a ‘space blanket’ material, aluminium-coated Mylar film, for example. !5.13 Glass ionomer ageing A related effect is seen in glass ionomer cements. These, being composite, consist of a glass core and reaction product matrix, and clearly these will have different refractive indices (Fig. 9§7.6). Initially, when freshly set, these materials tend to be rather less translucent than they will eventually become when reactions are more complete. This extra scattering, and therefore relative opacity, is due in part to the magnitude of the difference. But, as the reaction proceeds, and more glass has been dissolved, the boundaries between the unaffected glass, its hydrated silica coat, and the matrix proper become blurred. There is then more a gradient of refractive index than a sharp interface. Reflection scattering therefore becomes less. It is thus necessary to ignore the fact that initially the match does not appear particularly good, and indeed to place one’s confidence in the shade guide to indicate the final appearance correctly. The same problem existed with silicate cements (9§7). !5.14 “Gel” toothpaste Some toothpastes are described as “gels”, apparently on the grounds that they are transparent. Such materials may well be plastic (4§7) in that they have a yield point, but there is no evidence that they are gels (7§8, 7§9) in the sense of having a network structure. This is a common use of the term gel, i.e. for viscous, possibly plastic, and transparent materials and it also turns up in cosmetic contexts. It is therefore an unhelpful usage. Nevertheless, the transparency of the toothpaste in the context of what must still by definition be an abrasive material requires consideration. It should now be obvious that all that is required is that the abrasive material itself is transparent and is suspended in a medium whose refractive index has been matched to that of the dispersed abrasive – which is therefore invisible as it does not scatter light by refraction. Similar effects are found for dentine ‘cleared’ by soaking in methyl salicylate (cf. Fig. 9§10.1) when refractive-index matching makes demineralized tooth roots more or less transparent (Fig. 5.14).[20] Likewise, ‘white spot lesions’ of enamel can be masked by infiltrating with a polymerizable resin precursor,[21] reducing the scattering of ambient light by reducing the refractive index mismatch from that of hydroxyapatite against saliva. The spot is ‘white’ because of the chromaticity shift to be expected (§5.9). Of course, if the match were perfect the spot would become translucent, i.e. ‘cleared’, the ideal condition that of matching the refractive index of enamel matrix, not that of its mineral component. !5.15 Curing lights The reflectance effects described in §5.3 have a bearing on the efficacy of curing light irradiation for filled resins. Primarily, it is the loss at the upper surface of a Mylar or similar matrix strip that will be apparent, but if there is an air-bubble underneath, that interface will also contribute, along with the top surface of the resin itself. If, as is now common, a polyethylene sheath is used for infection

Fig. 5.14 ‘Cleared’ demineralized tooth roots – refractive index-matched with methyl salicylate. Photograph courtesy of S. Rosler.

Fig. 5.15 Resin curing light reflection losses associated with the use of matrix strips and other accessory materials.

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control, both of those surfaces must also be counted. Indeed, if a protective cap is used to protect the glass-fibre exit window of the curing light, this too will contribute. (Bear in mind that the final figures are the products of the transmissions, they are not additive except as effective optical densities; cf. 26§5.7.) The figures given in Fig. 5.15 are for normal incidence, but as it is likely that a greater angle will be involved in many cases, the losses may increase substantially (Fig. 5.4). If, however, an oxygen barrier material is used (6§6), that is, instead of the matrix strip, and care is taken to fill the space between the sheath and the resin without bubbles, at least two surfaces can effectively be eliminated because of the better refractive index matching (Table 5.1). In principle, using such a high-refractive index fluid under the cap (if any), and between the cap and the sheath, will all but eliminate those losses.

§6. Chemistry of Colour As has been discussed above, colour commonly arises from differential absorption, assuming that we are given white (i.e. spectrally uniform) illumination. It is the range of mechanisms of that absorption that we now address. There are also light emission processes that sometimes also have to be taken into account. In summary there are the following classes of system: C dyes C pigments C spectral effects – diffraction, interference (which, however, have little relevance to dentistry) C emission – fluorescence. Colour arises from a number of fundamentally different types of process at the atomic or molecular level, resulting in the selective absorption or emission of light at particular wavelengths. Electromagnetic radiation in general interacts with matter through a variety of mechanisms (Fig. 6.1).[22] These interactions are due to changes in nuclear and electronic spin, molecular rotation and distortion (bond angles and lengths, but in the sense of the amplitudes of vibration), or electron redistribution. Which of these may occur depends on the energy of the radiation concerned, because each change is associated with a particular scale of energies. In addition, radiation is quantized, and close matching of the incoming radiation to the energy of the transition concerned is necessary. In particular, the absorbed quantum must have no less than the necessary energy. But, as can be seen from Fig. 6.1, only transitions in outer shell electrons are associated with energies equivalent to visible and ultraviolet light. These affected electrons are the valence electrons, or electrons in molecular orbitals. It should be noted that all of these processes are independent, meaning that in a mixture of several dyes or pigments, or both, each makes its own separate contribution to the perceived colour (unless, of course, there is a chemical interaction).

Fig. 6.1 The various possible atomic and molecular energy absorption processes for electromagnetic radiation. Only outer shell and molecular orbital electronic transitions are associated with colour. NB: the boundaries are not sharp and exact, as shown; there is considerable overlap at each, because while the processes are distinct their energies may have considerable range, depending on the chemistry.

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Electronic transitions In absorbing a quantum of radiation, an electron is promoted to a higher energy level. In atomic or molecular terms, this means promotion to a higher energy orbital.[23] In organic materials, such as the dyes used in colouring polymers and fabrics, only certain kinds of transition are allowed (Fig. 6.2): σ-bonding electrons may be promoted to σ*-antibonding orbitals (Fig. 6.3, left), π-bonding electrons may be promoted to π*-antibonding orbitals (Fig. 6.3, right), and electrons in non-bonding orbitals, n, may be promoted either to σ* or π* (Fig. 6.2). Notice that the transition σ 6 σ* is represented here as the highest energy type of transition. Were this to happen it would in fact mean the rupture of a molecule (if that were the only bond), the σ-bond being the primary bonding between two atoms. On the other hand, n 6 π* transitions are typically of the lowest energy and such transitions may easily cause absorption in the visible range, causing ‘colour’, whereas σ 6 σ* typically requires the energies associated with ultraviolet light. !6.1

Chapter 24 The energy E (J/mol) of e.m.r. quanta can be calculated from: E = NA.h.c /λ where NA is the Avogadro constant, h is Planck's constant, c the speed of light and λ is the wavelength. (See also 26§2.1)

Organic systems Fig. 6.2 The types of electronic transition The energy of π 6 π* transitions depends, amongst other available in an organic molecule. [24] things, on the extent of delocalization of the electrons. Thus, in a series of fused rings (Fig. 6.4), where the number of energy levels available increases and their spacing decreases, transitions from π-bonding (lower half) to π*-antibonding (upper half) orbitals become both more likely and of successively lower energy (ΔE). The absorptions due to these transitions therefore move steadily into the visible range with increasing numbers of rings. Another example is the conjugated ‘ene’ system Ph-(CH2=CH2)n-Ph (Ph = phenyl): as n increases from 1 to 7 the absorption band moves steadily from the ultraviolet range into the visible (Fig. 6.5). Any side groups which can act as part of resonant conjugated systems, such as -NO2, >C=O, >C=S, -NH2, -C/N, as well as many others, may act to Fig. 6.3 Approximate shapes of bonding and antibonding lower energy levels still further and so increase molecular orbitals for σ (left) and π (right) bonds. absorption. Such groups are known as chromophores. !6.2

Fig. 6.4 Energy levels of the π and π* orbitals of a series of fused ring compounds. All π-bonding orbitals are filled in these compounds.

Fig. 6.5 Absorption spectra for the series of compounds with conjugated double bonds Ph-(CH2=CH2)n-Ph, with n = 1 to 7.

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These extensive conjugated systems are the basis, for example, of the many pH indicators as well as virtually the whole of the dye-stuffs industry. In particular, they are the colorants used in dental polymers such as for denture bases and restorations. We may note here that such absorptions first occur at the blue end of the spectrum so that the colour of the substance tends to be yellowish. It is this effect that causes the yellowing discolouration of resin restorations, for example, when continued (but undesirable) reactions create more strongly absorbing molecules, such as with aromatic amines and eugenol (6§1.1, 9§2.3). Colour stability An unfortunate effect of the absorption mechanism is that the excited, higher energy state so created is reactive. Although the extra energy may decay away thermally (cf. photosensitizers, 6§5.2) through collisions, there is always the possibility of reaction with another molecule. This may create the coloured substances referred to just now, but equally, if the absorbing molecule is large and complicated (as dyes tend to be in order to achieve their strong visible light absorptions) the special structure may be spoilt, bleaching it. This is especially so in the presence of oxygen (which is difficult to avoid in the dental context), so that colours may fade with time. The oxidation that occurs is usually of the unsaturated, and therefore reactive, chromophores. This is very obvious on advertising posters exposed to sunlight (with its ultraviolet component). Dyes which are prone to this kind of effect are called fugitive. Taken together, the colour stability of resin restorative materials is a considerable challenge. !6.3

In some polymer systems the problem of UV bleaching has been addressed by the incorporation of (colourless) efficient UV absorbing compounds. These dissipate the energy of the radiation without involving the breakdown or activation of the dye molecules. These compounds are known as UV stabilizers. Metal ion complexes The generation of colour in metal oxides and similar systems again depends on changes in electron energy, but of a different type. The non-transitional elements, groups IA, IIA, and IIIB to VIIB, have electron configurations which may be written as: [(core), nsy, npz], where n is the first quantum number. The total number of valence shell electrons is y + z and has the range 1 - 8. In transition elements the electron configuration is: [(core), (n-1)dx, nsy], y = 1 or 2, x = 1 - 10. When the d shell is incomplete there is a very much larger number of electrons available for bonding than in the non-transition elements, and many more orbitals are possible, with smaller energy differences between them. This increased scope of bonding capacity is expressed in the chemistry of these metals by the ready formation of complexes, compounds in which the metal ion is bound tightly to a group of ligands, often in an octahedral arrangement (cf. Ca++ in its chelates, Fig. 9§8.2), i.e. with a coordination number of 6. The ligands themselves may be either negatively charged ions or species such as H2O and NH3 which can donate electrons to the bonding. (The lone pairs of these molecules are the source and are highly polarizable, Fig. 6.6 Ligand field splitting of the 10§3.3.) As these ligands provide or modify an electrostatic field energies of the d-orbitals in an octahedral around the metal ion, so the energies of the d-orbitals themselves, field (6 coordinating ligands). originally all equal (i.e. degenerate), are changed. !6.4

As an example: energy calculations based on the symmetry of octahedral complexes lead to the division of the five d-orbitals into two distinct groups (Fig. 6.6). The separation in energy between them, Δ0, depends on the electrostatic field strength of the ligands (cf. equation 9§8.1), but typically it is rather small.[25] Ligands may be arranged in a spectrochemical series, indicating their relative strength in this regard: (6.1) This so-called ligand field splitting of the d-orbital energies results in absorptions in the visible and ultraviolet, as when these orbitals are incompletely filled an electron may be promoted to a higher level (Fig. 6.7). Thus, in a complex such as the hydrated ion [Ti(H2O)6]3+

Fig. 6.7 For a d4 transition metal ion the ground state (lowest energy) is as on the left. The promotion of an electron to a higher energy by the absorption of radiation leads to the configuration on the right.

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in which there is only one d-electron, the absorption spectrum shows a band corresponding to the promotion energy from the lower to the higher level (Fig. 6.8), the peak absorption lying at about 500 nm (bluish-green). This complex is therefore in fact purple (red and blue wavelengths predominating). The same principles apply in the solid state, and no less in glasses, irrespective of the lack of crystallinity. The environment of the dissolved metal ions (as in the porcelains) will tend to be similar to that in solutions and crystals, forming coordination compounds, and so similar absorptions may occur generating colour. The oxygen ions surrounding the metal ion in oxides and silicate glasses will have similar ligand field strengths to the OH! and H2O ligands in the spectrochemical series, but the colours will vary according to the metal and its oxidation state (i.e. the number of d-electrons). Small changes will be observed due to other factors such as the glassy nature of the matrix, the temperature, and whether other anions are present, such as F-, which may arise from fluxes and which may lead to various mixtures of ligands around the metal ions. The same remarks apply to the colour of the corrosion products of dental and other alloys. With but few exceptions the components of these alloys are transition metals. Strong absorptions are therefore expected, given the presence of strong ligand fields due to sulphide (S=), oxide (O=) and hydroxide (OH–), modified by the presence of other ions found in saliva, such as chloride, sulphate, phosphate and so on. The colours of ferric oxide (Fe2O3), silver and mercuric sulphides (AgS, HgS) in particular, are well known and very strong. Fluorescence As was discussed under photosensitizers (6§5.2), absorbed light may not be degraded entirely to thermal energy but may be re-emitted as visible light, although always at longer wavelengths (i.e. lower energy).[26] Anthracene (Fig. 6.4) is an example of a compound which fluoresces under some conditions. Colourless by absorption (Fig. 6.9), if the energy is not rapidly dissipated by collisions some energy may be emitted in the visible region, so long as the illumination has some ultraviolet or far blue light in it. This is the basis of the dyes, histological “stains”, used for fluorescence microscopy. Similarly, some transition metal complexes may show fluorescence. The corresponding spectra for a solution of a deep red [Ru2+] complex are shown in Fig. 6.10. Notice that both the absorption and the emission occurs in the visible region, and so in this and similar cases the colour perceived will be modified by what we may call the self-luminance. !6.5

Fig. 6.8 The absorption spectrum for the aqueous ion [Ti(H2O)6]3+.

Fig. 6.9 The absorption and fluorescence emission spectra for anthracene. Note that the absorption is at wavelengths shorter than the visible range.

Fig. 6.10 Absorption and fluorescence emission spectra for an aqueous solution of a ruthenium complex.

Hydroxyapatite is the basis of some commercial phosphors (see Table 4.1: Ca-phosphate and Ca-Sr-phosphate) which are characterized by the use of small amounts of transition and other metal ions substituted for Ca++, as well as various anions substituted for OH–. These together give a variety of environments in which electronic transitions may be made and so a variety of absorptions, but notably there will also be fluorescent emission spectra.

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Hydroxyapatite, as the basis of tooth substance, is not a pure substance. It will contain various contaminating ions (fluoride included) and is the natural counterpart of the synthetic phosphors. Its fluorescence therefore under normal lighting conditions, in particular in sunlight with its significant ultraviolet component, is important in modifying its appearance. As a result of this type of behaviour it is plain that, in any attempt at a close simulation of tooth material, its own natural fluorescence ought be taken into account. At one time uranium salts were used to lend fluorescence to dental porcelains. Not unnaturally, this practice came in for some criticism because of the associated radioactivity, and their use was dropped (25§7). Dental dyes and pigments The distinction between a dye and a pigment is that the former is a coloured molecular structure, where in solution or bound, while a pigment is a dispersed particulate material which is essentially opaque. While there are many dyes used to colour, for example, dental waxes, their particular chemistry is of little importance except to note that they must all be ‘oil soluble’ or hydrophobic, firstly so that they can dissolve in such substances, but also so that they do not leach into the surroundings. !6.6

This requirement not to leach is also a concern when highly-polar or hydrophilic systems are involved. For example, dental plaster, stone and die-stones are frequently coloured so that they may be easily distinguished from each other in models, while impression plaster is commonly pink. This is done with a dye that reacts to become an insoluble substance known as a lake, by chelating with a polyvalent cation. Alizarin (Fig. 6.11) is the archetypal member of a very large family of such dyes, and widely used in dentistry, in which the key structural aspect is the adjacency of the hydroxyl and carbonyl groups. The calcium ions of gypsum products are functional in this respect (Fig. 6.12; cf. Fig. 9§8.1), the chelate being sufficiently strong that the colour does not bleed or run into adjacent material when the model is cast on the impression. Indeed, this class of dye is very commonly used as an histological calcification stain, where presumably the binding is to the surface of the calcification in much the same way as polycarboxylic acids (9§6, 9§8.7). The multiple hydroxyl and carbonyl groups means also that such dyes bind strongly to polar materials such as the proteins and polysaccharides of dental plaque and so are the common basis of disclosing agents. However, there is some risk of such materials dissolving in the resin of restorative materials leading to a chromaticity shift that would spoil any colour match. One would also expect chelation binding reactions to occur on the surface of glass ionomer cement, where calcium and aluminium ions, in particular, are present, if the stereochemistry of the relevant groups was favourable. [27]

Fig. 6.11 Alizarin.

Fig. 6.12 Alizarin complex with calcium – the insoluble lake. Water molecules may also be coordinated to make such complexes octahedral.

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___________________ References [1]

http://en.wikipedia.org/wiki/Color_blindness

[2]

Maxwell JC. On the theory of compound colours, and the relations of the colours of the spectrum. Phil Trans 150: 57 - 84, 1860

[3]

Clulow FW. Colour: Its Principles and their Application. Fountain, London, 1972.

[4]

https://www.surreynanosystems.com/vantablack

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https://www.labsphere.com/labsphere-products-solutions/materials-coatings-2/targets-standards/diffuse-reflectance-standards /diffuse-reflectance-standards/ https://www.labsphere.com/site/assets/files/2553/a-guide-to-reflectance-materials-and-coatings.pdf

[6]

see, for example, http://www.colorsystem.com

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Smithson HE et al. A three-dimensional color space from the 13th century. J Opt Soc Amer A 29(2): A346-A352, 2102 http://www.grosseteste.com/cgi-bin/textdisplay.cgi?text=de-colore.xml

[8]

Henderson ST. Daylight and its Spectrum. 2nd ed. Hilger, Bristol, 1977.

[9]

Ridpath I & Tirion W. Collins Guide to the Stars and Planets. Collins, London, 1984.

[10]

https://en.wikipedia.org/wiki/Planckian_locus

[11]

Wyszecki G & Stiles WS. Colour Science: Concepts and Methods, Quantitative Data and Formulas. Wiley, New York, 1967.

[12]

Lee YK & Powers JM. Metameric effect between resin composite and dentin. Dent Mater 21: 971 - 976, 2005.

[13]

https://en.wikipedia.org/wiki/Color_rendering_index

[14]

https://en.wikipedia.org/wiki/Chromatic_adaptation

[15]

Joiner A. Tooth colour: a review of the literature. J Dent 32: 3 - 12, 2004.

[16]

Darvell BW. Esthetic Dentistry. Amer J Esthet Dent 3 (3): 167 - 168, 2013.

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Levin EI. Dental esthetics and the golden proportion. J Prosthet Dent 1978;40:244–52, 1978.

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Burke FJT, Kelleher MGD, Wilson N & Bishop K Introducing the concept of pragmatic esthetics, with special reference to the treatment of tooth wear. J Esthetic Rest Dent 23 (5): 277-293, 2011.

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Judd DB & Wyszecki G. Colour in Business, Science and Industry. 3rd ed. Wiley, New York, 1975.

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Rosler S. Transparent teeth: A powerful educational tool. Roots 4: 30 - 31, 2010. http://www.oemus.com/archiv/pub/sim/ro/2010/ro0410/ro0410_30_31_rosler.pdf

[21]

S. Parisa, F. Schwendicke, J. Keltscha, C. Dörfera, H. Meyer-Lueckel. Masking of white spot lesions by resin infiltration in vitro J Dent 41, Suppl 5, e28–e34, 2013.

[22]

Banwell CN. Fundamentals of Molecular Spectroscopy. McGraw-Hill, New York, 1966.

[23]

Dyer JR. Applications of Absorption Spectroscopy of Organic Compounds. Prentice-Hall, New Jersey, 1965.

[24]

Smith LO & Cristol SJ. Organic Chemistry. Reinhold, New York, 1966.

[25]

Heslop RB & Jones K. Inorganic Chemistry. A Guide to Advanced Study. Elsevier, Amsterdam, 1976.

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Barrow GM. Physical Chemistry, 4th ed. McGraw-Hill, New York, 1979.

[27]

Hino DM, Mendes FM, De Figueiredo JLG, Gomide KLMN & Imparato JCP. Effects of plaque disclosing agents on esthetic restorative materials used in pediatric dentistry. J Clin Pediat Dent 29 (2): 143 - 146, 2005.