Photometric Aspects of Visible Light and Colours

C H A P T E R

13 Photometric Aspects of Visible Light and Colours O U T L I N E 13.1 Visible Light and Colour Perception

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13.2 Trichromatic Theory and Metamers

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13.3 Munsell Colour System (HSV System)

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13.4 CIE Chromaticity Diagram

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13.5 The RGB Additive Light System 13.5.1 RGB Primaries and the Additive Light Mixing 13.5.2 RGB Complementary Colours 13.5.3 Three-Dimensional Representation of the RGB System

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13.6 The CMY Subtractive Colour System 13.6.1 CMY Primaries and the Subtractive Colour Mixing 13.6.2 CMY Complementary Colours 13.6.3 Three-Dimensional Representation of the CMY System

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13.8 The Colour of Objects, Polychromies, and Paintings

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13.9 Use of Complementary Colours in Visual Arts

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13.10 Optics of Halftone Imaging and the Neo-Impressionism

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13.11 How to Improve the Colour Rendering of Electric Lighting

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13.12 What Is the Colour of Solar Light?

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References

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13.1 VISIBLE LIGHT AND COLOUR PERCEPTION Photometry is a branch of science concerning light and its measurement, but in terms of brightness and colour perceived by the viewer (e.g. luminance ¼ lm sr1 m2). Photometry is focused to interpret the combined response of the eye and the brain when they receive a physical stimulation from impinging light. Even if light is an objective, physical entity constituted by photons, the perception of colours is a human sensation formed in the brain. The vision requires the presence of an observer. Photons constitute the physical stimulus that enters the eye and reaches light receptors in the retina; an impulse is transmitted through the optical nerve

Microclimate for Cultural Heritage https://doi.org/10.1016/B978-0-444-64106-9.00013-4

13.7 Transformation Between the RGB and CMY Colour Spaces

to the brain cortex and this signal is finally interpreted as a particular colour with a certain brightness. The transformation and interpretation of this signal from the eye receptors to the cortex is governed by physiological and psychological mechanisms that are essential to perception. The enjoyment of visual arts is based on three steps. The first is lighting: ideally pure white light, emitted from a convenient source. The second is the interaction between the light and the artwork, e.g. diffuse reflection from colour coating of paintings, or transmission though glassworks. Finally, the perception of the observer and the interpretation of the luminous stimulus. The last two steps of this complex chain are the aim of this chapter.

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© 2019 Elsevier B.V. All rights reserved.

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The eye is sensitive to photons having wavelength (λ) in the spectral band from violet (λ ¼ 380 nm) to red (λ ¼ 720 nm), and this part of the electromagnetic spectrum is called visible light. The retina contains two types of light receptors: rods and cones. Rods are responsive at low illumination, but remain dormant at high illumination. They are useful in the night vision, to distinguish shapes but in a contrast of black and grey tones. Cones are responsive at medium-to-high illumination and with their photoreceptor cells may distinguish wavelengths. Three types of photoreceptor cells exist: i.e. one preferring short wavelengths, picked at λ ¼ 420 nm on blue (B), which is the less sensitive one; one preferring middle wavelengths, picked at λ ¼ 530 nm on green (G); and one preferring long wavelengths, picked on red (R) (Bowmaker and Dartnall, 1980; Hunt, 2004; Goldstein, 2007). Their response may be represented in terms of real or normalized absorbance as in the CIE (2006) physiological model (Fig. 13.1). There is a considerable overlap among the three response curves. When a single wavelength enters the eye, it may activate two, or, more frequently, three photoreceptors, but to different degrees (Kuehni and Schwarz, 2008). This composite situation may cause some problems. The majority of people have almost the same colour perception; however, about 8% of males and 0.4% of females may have vision problems, e.g. because one type of cone receptor is missing, or has a shifted wavelength or bad channel wiring. The gender difference is explained because these colour deficiencies are linked to the X chromosome and males have only one of them, whereas females have two (Foley and Matlin, 2016). The colour depends on various factors that may condition the activity of photoreceptors and the final interpretation. It might seem obvious that different wavelengths of light will produce different sensations; however, what

FIG. 13.1 Spectral distribution of normalized human photoreceptor absorbances of red, green, and blue cone receptors and rods for different wavelengths of light. From Anatomy & Physiology, Connexions Web site: http://cnx.org/content/col11496/1.6/ Author: Open Stax College, CCA 3.0 Unported.

will happen with a mixture of photons at different wavelengths is not a foregone conclusion because the brain stimulus will change with the combination of wavelengths and their mixing ratio. Contrariwise to the case of acoustic waves, where two voices, or two musical instruments playing together preserve their identities and are perceived distinctly and independently, each one with its own original wavelength, two light beams with different wavelengths mixed together are perceived as a single colour, different from the two constituent ones. A beam is called monochromatic when composed of photons with the same wavelength, e.g. a laser beam, or lying in a narrow spectral band. This corresponds to a well-defined hue, e.g. red. A beam is called polychromatic when the photons have wavelengths distributed in a broad interval band, e.g. from yellow to red and, in this case, they will be perceived as orange colour. A beam is called achromatic when the photons have wavelengths homogeneously distributed over the whole spectrum, so that no particular chromatic sensation dominates, and the beam is perceived white or grey, depending on the luminous intensity. At high-to-normal intensity, mixing all colours gives white, e.g. the famous Newton’s colour wheel experiment. At low luminous intensities (i.e. below the threshold of cones but above the threshold of rods), white light, as well as any colour, is perceived in terms of grey; at very low (i.e. below the threshold of both cones and rods), as darkness. A light beam cannot be black; the black sensation is in the absence of (sufficient) light. Although light cannot be black, and any colour may appear black at very low light intensities, black pigments and black paints exist, and are perceived black because they absorb all the light impinging on them, i.e. they do not reflect any light. Humans and animals have a different colour perception because they haven’t the same number of receptors and type of photopigments. Although it is impossible to exactly know what is the perception of the various animals, some scientific experiments and the analysis of the visual pigments and eye receptors of animals have found a multifaceted situation ( Jacobs, 1993, 1996; Yokoyama and Radlwimmera, 1999; Fuchigami et al., 2001; Osorio and Vorobyev, 2008; Swanston and Wade, 2013; Land, 2014). For instance, bulls are colour blind. Most mammals, including dogs, have colour perception based on two receptor types (dichromatic colour vision) and their spectrum is limited to yellow, blue, and green. Human vision is based on three receptor types (Trichromatic colour vision). Monkeys and fish living in shallow water have a good colour vision with pigments tuned to various wavelengths, including some colours that we cannot perceive. Birds have four receptor types (Tetrachromatic colour vision). Some animals utilize other bands of the electromagnetic spectrum. Cats have a high concentration of rod receptors (useful in the nocturnal vision)

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13.2 TRICHROMATIC THEORY AND METAMERS

and a low concentration of cone receptors and they have difficulty in discriminating colours. Most snakes, including vipers, boas, and pythons, have thermal vision for heat sensors sensitive to infrared (IR) arranged around their slips that integrate their eye vision. Bees are sensitive to the ultraviolet (UV) spectrum.

13.2 TRICHROMATIC THEORY AND METAMERS The existence of three eye photoreceptors and the theory of colour vision based on them are due to Thomas Young and Hermann von Helmholtz, who developed the so-called Trichromatic theory, i.e. the theory of the three-component colours. It was derived from the discovery of the human perception of colours by Young (1802) and the colour-matching experiments by von Helmholtz (1852). As Maxwell (1872) said, the ground of this theory is ‘not in the nature of light, but in the constitution of man’. The theory is based on three primary colours, i.e. red (R), green (G), and blue (B), to which cones are sensitive and a psycho-physiological procedure to combine colours, called colour matching. This makes possible to express every colour in a simple mathematical form with the Trichromatic equation (Abney 1913; Goldstein 2007) as follows. Every visible colour CV is supposed to be defined in terms of the weighted sum of three colour matching functions (CMF), denoted by r, g, and b, that represent the intensities that R, G, and B should have to match the selected colour, i.e. CV ¼ rR + gG + bB

(13.1)

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In Young’s hypothesis, three CMF represent the spectral absorbances of the retina receptors multiplied by the spectral transmittances of the part of the eye crossed by the light beam before reaching the receptors and were experimentally determined with some observers ( Judd, 1979). The theory that every colour may be represented with the Trichromatic equation explains why two different stimuli may produce similar responses, i.e. different combinations of spectral bands in the eye may produce the same colour sensation in the brain cortex. The phenomenon of perceiving a certain colour from a combination of differently coloured spectral bands is called metamerism and the colours that match are called metamers (Fig. 13.2; Gunther, 2011). The brain averages the stimuli of various spectral bands and perceives a specific hue. If the bands are contiguous in the spectrum, they will be perceived as a central value of wavelength, e.g. a beam of photons in a wide spectral band from yellow to red is perceived orange (Fig. 13.2 top row). If the photons belong to distant spectral bands, a totally different colour may be perceived, even ‘new’ colours not included in the solar spectrum. For instance, a beam of photons with wavelength in the yellow band of the spectrum (i.e. λ ¼ 570 nm) is perceived yellow; however, the same perception is given receiving a mixture of photons in the green (λ ¼ 530 nm) and red (λ ¼ 650 nm) bands (Fig. 13.2 middle row). A mixture of red and blue (λ ¼ 460 nm) photons will give the perception of magenta (Fig. 13.2 bottom row), i.e. a nonspectral colour, not included in the rainbow. The Trichromatic theory gave an excellent impulse to neurosciences. It was useful to explain most visual perceptions, and has been used to develop the CIE FIG. 13.2 Examples of metamers. Upper row: the band from yellow to orange is perceived orange, i.e. an average in the middle of the band. Middle row: the presence of a green and a red band is perceived yellow, i.e. a third colour with different location in the spectrum. Lower row: the presence of both a blue and a red band is perceived magenta, i.e. a third colour, not included in the solar spectrum.

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chromaticity diagram (see later) and to develop coloured monitor technology. However, it is unable to explain all visual perceptions for some flaws in it. One of the major flaws is that there are some colours CV that cannot be matched by any combination of primaries. The rainbow colours, or those that are generated when a white light beam passes across a prism, do not constitute the totality of the colours. The so-called nonspectral colours may be obtained with mixtures of some particular colours. Metamers explain the nonspectral mixtures, e.g. brown ¼ red + green; tan ¼ red + green + white; magenta ¼ red + blue; pink ¼ red + blue + white.

13.3 MUNSELL COLOUR SYSTEM (HSV SYSTEM) The visual sensation of colours may be characterized by a few parameters and may be finally expressed as a series of numbers. Various systems have been devised, and the first Colour System that will be considered is by the painter and educator Munsell (1905). This system has been represented in a three-dimensional (3D) space in various ways, e.g. a sphere (Fig. 13.3A), or cone (Fig. 13.3B), or hexcone (Fig. 13.3C) (Wyszecki and Stiles, 1982; Urland, 1999; Green and MacDonald, 2002; Kuehni, 2002; Bathia, 2008; Kuehni and Schwarz, 2008). The early Munsell scheme was a sphere, printed in black and white with hues indicated in letters on the equatorial belt. In Fig. 13.3A, colours have been added to better explain the system. In the lower hemisphere, colours are mixed with black, with the proportion increasing with latitude, until the south pole that is completely black. The same for the upper hemisphere, but with white. The Munsell system is based on three parameters H, S, and V. By combining them, one obtains the HSV Colour

System, able to identify every colour. The three parameters are • Hue (H) (Fig. 13.4) is the visual sensation that attributes a specific colour to any lighted surface, as we perceive it. This sensation is irrespective of how the colour has been generated, i.e. either by a monochromatic or a polychromatic beam, or by metamers. The original Munsell scale was divided into five principal hues (i.e. red, yellow, green, blue, and purple) and five intermediate hues for a total of ten major hues. Hue is measured by the angle around the equator, or the circle topping the cone, or the regular hexagon, starting from red (i.e. red H ¼ 0) to yellow, green, blue, and purple, i.e. 0 < H  360. The hue scale is generally divided into 100 steps; an average person may distinguish about 1000 hues. • Saturation (S) (also called chroma, or purity) (Fig. 13.4) of a colour refers to its purity and vividness (i.e. a pure monochromatic beam), or how much it has been diluted by white or grey. A saturated colour is due to a narrow band of wavelengths; it is vivid, i.e. pure hue. An unsaturated colour is due to a broad band of wavelengths; it appears duller. Saturation is the normalized radial distance, horizontally measured from the vertical axis of the sphere, the cone or the hexcone. The saturation scale ranges from S ¼ 0 (neutral) and increases with the vividness up to S ¼ 8 to10 (depending on the pigment colour) and even S ¼16 for the strongest one. • Value (V) (also called brightness or luminosity or tone) (Fig. 13.4) refers to the luminous intensity of a colour, i.e. the visual sensation of brightness, according to which a surface appears to be lighter or darker. In the graphical representation, the value is the vertical level measured along the symmetry axis that represents the greyscale, i.e. 0  V  1, where black has V¼ 0 and white V ¼ 1. Grey lies in the central position, i.e. V ¼ 0.5.

FIG. 13.3 (A) Sphere representing the original Munsell Colour System (Munsell, 1905, but with colours added). (B) Cone representing the Colour System, including all colours and with the HSV parameters in evidence. The blue front piece has been removed to show the interior. (C) Scheme the HSV hexcone with the main colours at the vertexes. Hue (H) is the angle around the circle, or the hexagon, starting from red. Saturation (S) is the normalized radial distance from the axis. Value (V) is the vertical level along the axis, starting from the black vertex on the bottom. (A) Modified from Munsell (1905).

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13.4 CIE CHROMATICITY DIAGRAM

and B required to obtain a specified match of light by mixing R, G, and B in appropriate proportions. Because of the particular choice of the primaries, the variable Y is also related to luminous properties, i.e. reflectance, or transmittance, or luminance. Every colour is represented in terms of three stimuli but, once the colour has been mathematically defined, even an expert has difficulty to visualize the colour from the X, Y, Z input. To be friendly, the chromaticity diagram has been reported on two dimensions (2D), i.e. the plane where X + Y + Z ¼ 1. In this plane representation, the border of the visible cone is transformed in a horseshoe shape (Fig. 13.5A). In this horseshoe area, every colour is represented by two chromatic coordinates (x,y) (Fig. 13.5B) related to the stimuli X, Y, Z by the equations FIG. 13.4 The three parameters used by Munsell, i.e. the wheel of Hues: red (R), yellow (Y), green (G), blue (B), purple (P); the intermediate colours obtained mixing them, e.g. the rod of values from black (0) to white (10) and an example of saturation applied to red, but limited to five levels, from grey (R0) to pure red (R4).

A note about black, grey, and white. In this system, all hues lie along the circumference. Black, grey, and white are located in the centre, suggesting that they are not colours, but a different thing, i.e. the value, representative of luminous intensity, without hue sensation. Saturation gives the relative level of perceived hue. The Munsell Colour System has inspired standards, i.e. DIN 6164 (1980) and ASTM Standard D 1535 (1996).

13.4 CIE CHROMATICITY DIAGRAM The Commission Internationale de l’Eclairage (CIE, International Commission on Illumination) developed a physiological colourimetric system in terms of a standard numerical diagram, based on experimental results of tests made with real observers, performed by Wright (1929) and Guild (1931). This was the first mathematically defined colour space. It was presented in 1931 and was updated, especially in 1976 and later with minor adjustments to provide smoother colour changes or better specifications (CIE 1932, 1978, 2004, 2006). It is widely used and illustrated in several textbooks (Smith and Guild, 1931–32; Faulkner, 1972; Agoston 1979; Wyszecki and Stiles, 1982; Kuehni, 2002; Broadbent, 2004; Trezona, 2001; Ohta and Robertson, 2002; Schanda, 2007; Kuehni and Schwarz, 2008; Oleari, 2016; Best, 2017). The CIE diagram is an additive colour system that enables to specify every colour (more precisely, every coloured light) as points within a 3D colour space based on three parameters X, Y, Z, called tristimulus values. These values represent the stimuli that drive the perception of a standard observer. More precisely, X, Y, and Z indicate the respective amounts of the primaries R, G,

x ¼ X=ðX + Y + ZÞ y ¼ Y=ðX + Y + ZÞ

(13.2)

The most popular 1931 chromaticity diagram has the following properties. • The CIE chromaticity diagram has several analogies with the hue and saturation parameters of the Munsell HSV model. The value is kept constant, equal to 1. • Range. The range of both the x and y axes is from 0 to around 0.8. • Colour representation. Every colour is represented by a pair of coordinates (x,y) on the diagram. • Pure colours. Monochromatic colours, or pure hue, lie at the edge of the diagram. • Rainbow colours, from about λ ¼ 380 nm to λ ¼ 700 nm, lie at the curved edge of the horseshoe diagram. Related wavelength values are indicated on the edge side. • The lower part of the diagram, below the white spot, and from blue to red, includes nonspectral colours, generated as metamers, e.g. magenta, pink. This explains why no wavelength values are indicated on the bottom straight edge. • Every other colour, different from pure hue, is determined by a point located inside the diagram. It can be obtained as a mixture of pure hue and white (see additive colour mixing). • White point (WP). Inside the diagram, an achromatic spot is visible around WP (Fig. 13.5C). This particular point is generated when X ¼ Y ¼ Z; hence, the (x,y) coordinates of WP are (0.333, 0.333). • Saturation (S) is related to the position of the colour point inside the diagram and its distance from the white point (WP) and the edge. Saturation levels decrease internally. At the edge, S ¼ 1; at WP, S ¼ 0. Considering a straight line connecting a selected colour point (CP1) with WP, the saturation level is given by the ratio of the distance from the selected colour point to the white point (i.e. CP1  WP), divided by the

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FIG. 13.5 CIE chromaticity diagram. (A) A view of the XYZ stimulus space, the cone-shaped envelope of all colours (thin blue lines) with the vertex at the origin and connecting the edge of the chromaticity diagram on the x,y colour plane. (B) CIE 1931 chromaticity diagram in (x,y) coordinates. The blue numbers around the horseshoe edge represent the wavelength of the rainbow colours, i.e. 380 to 700 nm. The lower edge of the diagram has no wavelength indication because it is composed of nonspectral colours, e.g. magenta. Every colour is represented by pair of (x,y) coordinates. (C) How to measure the saturation level of a selected colour (CP1). WP, white point; E, intercept of the edge with the straight line through WP and CP1. The parentheses indicate the lengths of the segments that should be considered in the ratio that gives the saturation level of CP1. (D) How to apply the additive mixing and find the colour (MC) obtained by mixing together CP1 and CP2 in various proportions. The parenthesis indicates the interval where MC is expected to lie. (E) How to find the complementary colour (CC) of a selected colour (CP1). The parenthesis indicates the interval where CC is expected to lie. (F) CIE 1976 chromaticity diagram in (u0 ,v0 ) coordinates. (G) The gamut, i.e. the triangle defined by the vertexes representing the highest saturation level (R1, G1, B1) of the three primary colours (red, green, and blue, respectively) that a screen is able to reproduce.

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13.5 THE RGB ADDITIVE LIGHT SYSTEM

•

•

• •

distance from the white point to the edge (E) measured on the straight line passing across the selected colour point and the white point (i.e. WP  E). Briefly S ¼ (CP1  WP)/(WP  E) (Fig. 13.5C). Additive colour mixing. It is possible to predict the effect of additively combining various colours. Once two colour points have been selected on the diagram (e.g. CP1 and CP2), every colour (MC) that may be obtained lies internal to the straight line connecting the two selected colour points, with the ‘law of the lever’, i.e. the distance of MC from each mixed colour (CP1 and CP2) is inversely proportional to the mixed amounts of them. In the example (Fig. 13.5D) if CP1 and CP2 are mixed in equal amounts, the result is pale yellow; if CP1 dominates, MC moves to the green area. Complementary colours. By definition, complementary coloured lights mixed together produce achromatic (white) light. Therefore, any selected colour (CP1) and its complementary (CC) should lie on the opposite sides of the white point (WP), on the straight line that starts from CP1 and passes through WP, but on the opposite side (Fig. 13.5E). If CP1 is at the edge, CC too lies at the edge. If CP1 is internal to the diagram, CC too is internal, at the same saturation level of CP1. White is formally included as a colour. The system is based on coloured lights and white represents the part of luminance concerning brightness. Grey and black are missing. This is not surprising, because black is absence of light and grey is a too low luminous intensity, not sufficient to activate cones.

In the 1976 revision, the CIE diagram underwent a slightly different transformation to be used in textiles, paints, plastics, and photography. The revised diagram (Fig. 13.5F) is in u0 , v0 units that may be related to the X, Y, Z stimuli, or to the x, y variables, by the equations: u0 ¼ 4X=ðX + 15Y + 3ZÞ v0 ¼ 9Y=ðX + 15Y + 3ZÞ u0 ¼ 4x=ð2x + 12y + 3Þ v0 ¼ 9y=ð2x + 12y + 3Þ

(13.3)

The CIE system has been used to show the performances of technological devices, e.g. colour screens of television, personal computers, smartphones. It is obvious that these devices cannot reproduce every colour in the diagram, but they will be limited to a certain restricted area inside the diagram. The actual range of colours that may be reproduced by a technological device is called gamut.1 A gamut is an area, typically a triangle defined by the vertexes representing the highest saturation level of the three primary colours, i.e. red, green, and blue (see next section), which a device is able to reproduce (Fig. 13.5G). The colours visible in the screen fall inside the gamut

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area. The higher the reached saturation levels, the wider the gamut area, the better the quality of the screen.

13.5 THE RGB ADDITIVE LIGHT SYSTEM 13.5.1 RGB Primaries and the Additive Light Mixing The RGB system (Faulkner, 1972; Agoston 1979; Kuehni, 2002; Boughen 2003; Broadbent, 2004; Hunt, 2004; Kuehni and Schwarz, 2008; Best, 2017) applies when coloured light beams overlap each other (hence the name Additive System) and essentially simulate the action of the three cone receptors as explained with the Trichromatic theory. The light, either white or coloured, is thought to be composed of three fundamental colours, i.e. RGB, called primaries. Every colour is determined by the amount of each RGB primary that is mixed (i.e. the intensities of the primary light beams that are overlapped). The system may be either represented with coloured circles on a plane, or in a 3D space with a cube, as discussed later. The 2D representation is easier; the 3D is useful to calculate secondary and complementary colours and to be used in image processing. The RGB system may be related to the CIE system; it is possible to make a mathematical conversion from vectors in the XYZ space to RGB colours, with a matrix. It may be useful to specify that in the RGB system the term ‘mixing’ should not be considered as for paints, but it should be regarded as the simultaneous projection on a screen of some selected lights, in particular the primaries and any other generated colours. It may be applied to the light emitted by coloured lamps, or the light passing through coloured filters, e.g. coloured stained glass windows, or the light reflected by coloured surfaces. As an example, blue may be obtained in various ways: e.g. using a prism and selecting the blue spectral band; a blue lamp emits only wavelengths of blue; a blue filter transmits only blue light and absorbs other wavelengths; a blue surface reflects only blue light and absorbs other wavelengths; blue may be obtained mixing cyan and magenta, or subtracting red to magenta with a filter. The popular 2D representation of the RGB additive system is the image obtained projecting on a screen the light beams of a red, a green, and a blue lamp (Fig. 13.6A). In the area where two of these coloured light beams overlap on the screen, the spot assumes a different colour, explained in terms of metamer. The RGB colours are called additive primaries, because in appropriate mixtures they can match lights of any hue. By overlapping

gamut derives from the mediaeval Latin ‘gamma ut’ indicating the whole range of musical notes. In the mediaeval music representation (i.e. the Guidonian hand), a hexachord permits notes within different octaves. The lowest pitch was designated by the Greek letter gamma and was named gamma ut. This term designated the range of notes available, and later it was applied to indicate a complete set of anything.

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FIG. 13.6 Additive system, two-dimensional (2D), and three-dimensional (3D) representations. Primary colours: red (R), green (G), and blue (B); secondary colours derived from additive mixing: yellow (Y), magenta (M), and cyan (C); tertiary: white (W). (A) Popular 2D presentation with RGB circles; secondary colours where two circles overlap each other; white spot in the centre where all primaries overlap. (B) The same but aerial view expanded in 3D, with the luminous intensity (LI) of colours on the vertical axis, distributed over four levels. Primaries have LI ¼ 1/3; secondaries are due to the superposition of two primaries and LI ¼2/3; white is due to the superposition of three primaries and LI ¼3/3. Bottom: on the horizontal plane (2D), perspective view of the projection of the 3D diagram. (C) Examples of additive mixing. First three rows: detail of how the secondary colours are generated by addition from the primary ones; the same but with four metamer examples for white.

two primaries, one obtains yellow, cyan, and magenta called secondary colours. By overlapping the three primaries, the spot appears white. However, one should consider that, when two coloured light beams overlap on a screen, the luminous intensity (LI) of the common area is the sum of the two components, as shown in the 3D representation in Fig. 13.6B, where colour leaves lie at three LI levels. Primaries lie on the lowest LI level, i.e. LI¼ 1/3. Secondaries have twice the luminous intensity of their two generating primaries and lie at the intermediate LI level i.e. LI¼ 2/3. The sum of the three primaries produces white that has three times the luminous intensity of each of the generating primaries, i.e. LI ¼ 1. White is at the top LI level, and is popularly related to brightness. Some examples of metamer combinations to produce secondaries and white using primaries and/or secondaries are shown in Fig. 13.6C. A theoretical note concerns the interpretation of black, white, and grey in the RGB system, i.e. are they real colours? Black is not present in any part of the figure that shows the superposition of the three RGB primaries. In this system black is not a colour, but darkness, i.e. absence of light and has no place where stay in a system dealing with light combinations. As opposed, white is the incoming solar beam that is decomposed into red, green, and blue. In addition, it appears as a tertiary colour, given by the superposition of the three primaries. Consequently, white should be considered a real colour. Grey cannot be obtained as a superposition of the primaries, but is perceived when the light intensity is weak and the cones are no more able to distinguish colours; therefore, in this system, grey cannot be considered a real colour.

The property of additive colour mixing is used in television, computer, smartphone, and other monitors, or to correct the colour rendering of electric lighting (e.g. LED, fluorescent lamps) with the help of RGB phosphors.

13.5.2 RGB Complementary Colours Complementary colours play a fundamental role in this and other systems because, when they are combined together, they cancel each other out to produce an achromatic mixture that may be white, grey, or black. In the additive system, reference is made to white because white is the sum of all coloured lights. A given coloured light (C1) is said to be complement of another one (C2) when, mixed together, they give white (W). This statement is summarized with the formula C1 + C2 ¼ W

(13.4)

The definition is clear, but not easy to apply. If you try to find the complement of a given colour, e.g. C1, you need to start superposing one by one all the spectral bands to the selected light spot, until the overlap becomes uncoloured and reveals the complement C2. However, the same formula may be written in the form C1 ¼ W  C2; C2 ¼ W  C1

(13.5)

i.e. removing a selected colour from the spectrum of a white light beam, one obtains the complement of that colour. With the definition of complementary given in this form, matched pairs of complementary colours can be found with a simple experiment (Fig. 13.7). A beam of white light, e.g. a solar beam, passes through a prism.

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W¼R+G+B

(13.6)

and this equation is useful to derive the complement of each primary (Fig. 13.8A), i.e.:

FIG. 13.7 How to create complementary light colours. A white light beam passes through a prism (P) and is dispersed into coloured spectral bands. A lens (L) placed in the middle recombines the spectral components forming a bright spot on a white screen (S) located at the focal point distance. In this example, the yellow band is intercepted at B in front of the lens, originating a dark band, and the bright spot on the screen appears blue.

The outcoming beam is dispersed into spectral components, and all wavelengths are separated forming a continuous spectrum like a rainbow. According to Newton (1704), white light is divided into seven colours, i.e. red, orange, yellow, green, blue, indigo, and violet. Initially, he distinguished five colours but, more later, probably inspired by Pythagoras, Aristotle, Boethius and other philosophers, he supposed that the colours of the rainbow should have similarities to the notes of the musical scale and added orange and indigo to reach seven colours (Nassau, 1983; Kuehni, 2002; Kuehni and Schwarz, 2008; Taylor, 2017). This crude representation in distinct coloured bands is still very popular, and may be useful for a clearer explanation of the concept, without losing scientific rigour. With the help of a lens placed at a certain distance from the prism, it is possible to combine again the various spectral bands, and obtain a bright white spot on a screen located at the focal distance. If a strip is placed in front of the lens to absorb a selected spectral band, the spot on the screen will appear coloured, e.g. blue if yellow is absorbed. The experiment may be repeated with all the spectral bands to match every colour with its complementary one. A special note concerns the complement C2 of white light. From the complementary matched pairs formula, one obtains C2 ¼ W  W, i.e. the empty set, or zero light. Similarly, if in the experiment in Fig. 13.7 one intercepts all coloured spectral bands reaching the lens, the bright spot on the screen will disappear, and the screen will become fully black. Consequently, black (i.e. no light at all) is the complement of white light (i.e. all wavelengths), although it may appear a nonsense to discuss about ‘black light’ that does not exist. In this extreme example, the complement is just the opposite. The same result may be obtained considering that in the RGB system the white light is composed of three additive primaries, i.e.

• Complement of red ¼ cyan, i.e. R ¼ W  (G + B) and G +B¼C • Complement of green ¼ magenta, i.e. G ¼ W – (R + B) and R + B ¼ M • Complement of blue ¼ yellow, i.e. G ¼ W – (R + G) and R + G ¼ Y. This gives the fundamental result that the complement of a primary is the secondary derived from the additive mixing of the other two primaries, mixed in equal amounts, i.e. equal intensities. This becomes obvious considering that the sum of the three primaries gives white. In the previous diagram with the superposition of the RGB circles (Fig. 13.8A), the complements of R, G, and B are located on the opposite sides of the white curved triangle indicated W. It is possible to graphically apply this methodology to every colour. The wheel with the representation of the main colours and their complementary ones is represented in Fig. 13.8B. Each colour and its complement are located at opposite sides of the wheel; white in the centre represents their additive mixing. The theory of complementary colours may be used to improve the colour rendering of lamps. For example, a white LED lamp2 compared with the light of a solar beam has a deficiency in the red band and an excessive peak in the blue one (Fig. 13.9). The deficiency on the red band may be solved adding a red LED of convenient intensity. The blue peak may be damped applying the complementary yellow: either by selective absorption using a so-called yellow filter (the third row in the figure), as suggested by CEN-TS 16163 (2013), or adding a yellow LED of convenient intensity.

13.5.3 Three-Dimensional Representation of the RGB System The RGB system is simple and intuitive, but the foregoing qualitative concepts on a 2D plane are not sufficient when quantitative evaluations are needed, e.g. when some selected colour should be obtained by mixing primaries at various intensities, i.e. with different weights. Precise quantitative evaluations are only possible when these concepts are mathematically expressed. The calculation of complements or other colours obtained from various mixtures requires a mathematical system where every colour is numerically defined in a 3D space in orthonormal coordinates (Broadbent, 2004).

2

The figure refers to a White LED of the 2013 generation, the most popular LED in 2019, when this third edition has been updated and concluded. A new LED generation with better performances is getting commercialized.

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FIG. 13.8 (A) RGB primaries (first row) and their additive complementary colours (second row). The complementary colours are obtained as additive mixing of matched pairs of RGB primaries (third row). (B) The wheel of additive complementary colours. Every colour and its complement are located at opposite sides of the white centre. Colours: red (R), orange, yellow (Y), Chartreuse green, green (G), spring green, cyan (C), azure, blue (B), violet, magenta (M), and pink. Triangles connect primaries and secondaries, respectively.

FIG. 13.9 Comparison between the spectra of solar light (top row), of a white LED lamp and the absorption of a yellow filter (middle row). Bottom row: spectral density distribution of yellow filters used to reduce the intensity of the blue peak of white LED lamps. The first two are emission spectra; as opposed, the third is an absorption spectrum.

Every colour is described by a triple of numbers (x,y,z) and all colours are arranged to form a cube; each coordinate ranges from 0 to 1 (Fig. 13.10A and B). The eight vertices are composed of three primaries (i.e. red, green, and blue), three secondaries (i.e. magenta, cyan, and yellow), white (i.e. brightness), and black (i.e. darkness). Matched pairs of complementary colours are diagonally opposed in the cube, following a symmetry with respect to the grey point in the centre of the cube with coordinates (0.5, 0.5, 0.5) (Fig. 13.10C). White, black, and grey tones (i.e. the HSV value) are added to the colour system for practical reasons. They lie on the diagonal, where x ¼ y ¼ z. White and black occupy complementary positions. Reference colours and their coordinates are reported in Table 13.1. A number of interesting observations may be derived, i.e.: • Black is located at the origin of the orthogonal system; white is diametrically opposed to it.

• The three primaries constitute the saturated value of each x, y, z axis, i.e. at distance 1 from the origin. • Grey is located in the centre of the cube, at mid distance between white and black. • The complementary of each primary is obtained by exchanging 0 with 1 and, vice versa, 1 with 0. In general, the complementary of every colour is at the same distance from the central (grey) point, but in the opposite direction. • For the selected symmetry, the cube representation suggests that adding two complementary colours results in grey that is located in the middle of the straight line connecting them. White is located on a vertex and cannot be found in the middle between two points. This is a flaw that requires a wider definition of complementary colours: their mixture may produce white or grey, i.e. an achromatic colour, depending on the representation. • For their particular position on opposite vertexes, white brightness and black darkness should be considered to be complementary of each other.

13.6 THE CMY SUBTRACTIVE COLOUR SYSTEM 13.6.1 CMY Primaries and the Subtractive Colour Mixing In the previous sections, the perception of coloured light was considered, i.e. the interactions of photons with the eye and the optical nerve to produce colour sensations in the brain cortex. This section is devoted to analyze the interactions of photons with the matter, in particular how the incoming light will be transformed when it is reflected or passes through a material. The absorbed part is not seen, but may generate complementaries or metamers. It typically applies to the absorption of particular wavelengths when a light beam impinges on a paint, or when paints of different colour are mixed together, or when light passes through coloured filters (e.g. coloured glass). This is a key issue for artists to compose selected colours for their palette and paintings.

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13.6 THE CMY SUBTRACTIVE COLOUR SYSTEM

FIG. 13.10 Cube representing the RGB additive colour system in Cartesian coordinates. (A) Schematic axonometric view. The vertexes represent the three primary colours (i.e. red, green, and blue), the three secondary colours (i.e. magenta, cyan, and yellow), plus brightness (white) and darkness (black). Grey is in the centre of the cube. The origin (0,0,0) is black. The dotted line from black to white, i.e. the diagonal (0,0,0) to (1,1,1), represents the value. (B) A (rotated) view from the origin of the same cube, but filled of all colours. (C) Perspective view of the central symmetry with respect to the central point (CP), located in the centre of the cube, i.e. grey. Coloured double arrows join diagonally opposed matched pairs of complementary colours.

TABLE 13.1

Reference Colours of the RGB Additive System and Their Coordinates

RGB primary

Coordinates

Secondary—complementary

Coordinates

Value

Coordinates

Red

1, 0, 0

Cyan

0,1,1

Black

0, 0, 0

Green

0, 1, 0

Magenta

1,0,1

Grey

0.5, 0.5, 0.5

Blue

0, 0, 1

Yellow

1,1,0

White

1, 1, 1

When a white light beam impinges on a surface, the matter will selectively absorb all the photons characterized by a wavelength that may interact with this material. The outcoming beam will be deprived of the absorbed photons. For instance, blue is complementary of yellow. A blue pigment has this appearance because it absorbs light with wavelengths complementary to blue, i.e. yellow. A yellow pigment absorbs all wavelengths except yellow. If one mixes blue with yellow pigments, all wavelengths are absorbed and the result will be black or dark grey. This system considers that photons with certain selected wavelengths are removed and the light intensity is reduced for a subtractive mechanism, hence the name Subtractive System, typical of pigments and dyes (Faulkner, 1972; Agoston 1979; Bathia, 2008; Oleari, 2016; Best, 2017). One should consider that a pigment has a given coloured appearance because it acts as a filter, i.e. it absorbs all

wavelengths except the wavelength that is reflected. The colour perceived is the complement of the absorbed wavelengths or a metamer from reflected light. The CMY subtractive system is based on selective light absorption operated by dyes, pigments, or filters. In the example shown in Fig. 13.11, a white light beam crosses a series of three filters, i.e. cyan, magenta, and yellow, arranged in various orders, i.e. CMY, YCM, MYC. After the first subtraction, one primary component is absorbed, the beam and the luminous intensity is reduced to 2/3 of the incoming one; after the second, another primary is absorbed and the luminous intensity is 1/3 the original one; after the third the beam is almost extinguished, i.e. darkness or black, named key (K). If the primaries have high luminous intensities, or the filters are not strong enough, the darkness is not properly a real black, but a dark grey tone.

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FIG. 13.11 (A) Selective light absorption operated by coloured filters (C, M, Y squares). Each row has filters arranged in different order. Each filter removes a primary RGB component of the incoming light, changing colour and reducing by 1/3 the luminous intensity (LI) of the outcoming beam. Colour code B: blue; C: cyan; G: green; K: darkness; M: magenta; R: red; Y: yellow. Light beams are presented showing their RGB components and their metamer appearance, e.g. GB ¼C, RG¼Y, RB¼M. (B) Luminous intensity of coloured light beams in the subtractive system: white (W), primary (CMY), and secondary (RGB) colours and darkness (K). The W, C, M, and Y bars are associated with their components in the RGB additive system (on the left of each bar), and the additive composition is indicated on top. This explains the different luminous intensities of the various colours.

In the RGB additive system, the complement of a primary is the secondary derived from the additive mixing of the other two primaries, i.e. the complements of red, green, and blue are cyan, magenta, and yellow, respectively. On the other hand, in the CMY system cyan subtracts red; magenta subtracts green; and yellow subtracts blue. Mixing two pigments subtracts their opposites. A painter may obtain every colour of his palette mixing cyan, magenta, and yellow in various proportions. Hence the name CMY to this system. For both RGB and CMY systems, secondary colours are complementaries too; primaries in RGB are

secondaries in CMY and vice versa. The general features of the subtractive system are reported in Fig. 13.12. A note may be useful about black, white, and grey in the CMY system, as illustrated in Fig. 13.12. White is the input and cannot be found in the subtractive mixing diagram. It cannot be considered a colour obtainable from the three primaries of the CMY system. In colour printing, white is not necessary because it is obtained leaving the paper sheet unprinted. Pale hues are obtained printing spaced tiny dots. Similarly, painters on watercolour, gouache, and tempera may dilute their paint and take benefit of the natural hue of white paper sheet. As opposed, oil colours are opaque, and painters need to add the white colour as an additional primary in their palette to obtain white or pale hues. Grey is practically obtained mixing black (i.e. a colour) with white (not a colour), or mixing complementary colours. In the last option, however, it might be considered a colour, but hardly it will be pure grey. A black area emerges at the centre of the various intersections and, therefore, it should be considered a real colour characterized by no transparency and no reflectivity. It cannot stimulate cones; nevertheless, it generates a particular stimulus in the brain. It is not surprising to find black in the central area because it has been obtained subtracting the three primaries, i.e. all colours. In addition, this black area occupies the position that white had in the RGB system, and black is the complement of white. White is light composed of all wavelengths; as opposed, black is complete absence of light. In the real world, a painter, or a journal printer might obtain black by mixing cyan, magenta, and yellow. However, this would be very expensive and, in addition, the black obtained from colour mixing might differ from pure black, e.g. when the mixing is not made in precise proportions, or the three primaries are not adequately pure. Therefore, black is used as a fourth primary. This is deliberately applied in the CMYK system, typical of printers, where K (key) is for black or darkness.

13.6.2 CMY Complementary Colours Matched pairs of CMY complementary colours are experimentally found. Key differences from the RGB system are: (i) the CMY system is subtractive (RGB was additive); (ii) reference should be made to pigments that absorb light (RGB was based on adding light); (iii) the achromatic mixture is derived from absorption of light below the threshold of cones, which is perceived black or grey (in RGB was the highest excitation, i.e. white glare). CMY complementary colours are matched pairs of colours that, when combined, will absorb most of the impinging light and produce grey or black sensation.

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FIG. 13.12 Subtractive system, twodimensional (2D) and three-dimensional (3D) representations. Primary colours: cyan (C), magenta (M), and yellow (Y); secondary colours: red (R), green (G), and blue (B); tertiary: darkness (K). (A) The popular 2D presentation with CMY circles, the secondary colours where two circles overlap each other, and the black spot in the centre where all primaries overlap. (B) The same but aerial view exploded in 3D, with the luminous intensity (LI) of colours on the vertical axis, distributed over three levels. Primaries have LI ¼ 2/3; secondaries LI ¼1/3: darkness is due to the absorption of light and LI ¼0. Bottom: on the horizontal plane (2D), perspective view of the projection of the 3D diagram. (C) Examples of subtractive mixing. Detail of how the subtractive secondary colours RGB are generated from the primary ones; the same but with four metamer examples for black (K).

FIG. 13.13

(A) CMY primaries (first row); their subtractive complementary colours (second row); the complementary colours obtained as subtractive mixing of matched pairs of CMY primaries (third row). (B) The CMY wheel of subtractive complementary colours. Every colour and its subtractive complement are located at opposite sides of the black centre.

Examples are reported in Fig. 13.13. By the way, Fig. 13.13B is identical to Fig. 13.8B, except for the centre that is black or grey, i.e. the obvious result of (coloured) light subtraction.

13.6.3 Three-Dimensional Representation of the CMY System The cube representing the CMY system is shown in Fig. 13.14 and the coordinates of the main colours are reported in Table 13.2. The comments to the CMY cube and Table 13.2 are essentially similar to those for RGB cube and Table 13.1.

13.7 TRANSFORMATION BETWEEN THE RGB AND CMY COLOUR SPACES The transformation between the two-colour spaces, i.e. the RGB cube and the CMY cube, applies a central symmetry with respect to the point in the centre of the cube, i.e. grey. Every RGB colour point has a matching CMY point that is at the same distance from the central point, but in the opposite direction. This is not surprising, because either space uses as own primaries the complementary colours of the primaries of the other space. The comparison between the RGB and CMY systems shows that they are complement to each other. Every primary, or secondary, or complementary colour may pass from the RGB space to the CMY space using a vector

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FIG. 13.14 Axonometric view of the cube representing the CMY subtractive colour system in Cartesian coordinates. (A) Scheme of the cube and its vertexes; grey in the centre. The origin (0,0,0) is white. The dotted line from black to white represents the value. (B) A (rotated) view from the origin of the same cube, but filled of all colours.

TABLE 13.2

Reference Colours of the CMY Subtractive System and Their Coordinates

CMY primary

Coordinates

Secondary—complementary

Coordinates

Value

Coordinates

Cyan

1, 0, 0

Red

0,1,1

White

0, 0, 0

Magenta

0, 1, 0

Green

1,0,1

Grey

0.5, 0.5, 0.5

Yellow

0, 0, 1

Blue

1,1,0

Black

1, 1, 1

transformation that exchanges 0 with 1 and vice versa. The transformation formulae (Elias, 2014) are 2 3 2 3 2 3 2 3 2 3 2 3 1 C C 1 R R 4 G 5 ¼ 4 1 5  4 M 5 (13.7) 4 M 5 ¼ 4 1 5  4 G 5; Y 1 B B 1 Y The first formula is to pass from RGB to CMY space, and the second one from CMY to RGB. The unit column vector represents white in the RGB space, and black in the CMY space. In either transformation, a selected CMY or RGB vector is subtracted from the achromatic unit column vector to obtain the related vector representing the primary, or secondary, or complementary colour, or any other combination of them. Similar transformations can be made with the HSV or other spaces. The vector conversion from one colour space to another is theoretically correct. In the real world, however, these conversions may be unable to reproduce exact colours with technological devices, e.g. digital printers, for some flaws or unresolved issues.

13.8 THE COLOUR OF OBJECTS, POLYCHROMIES, AND PAINTINGS The combined use of the RGB and CMY systems gives the key to explain many important issues of visual arts, as shown in the following examples. To the viewer, a

coloured surface will have an appearance that is result of two mechanisms: in the air, the mechanism is the additive RGB lighting, or the RGB recombination of the outcoming photons, as discussed in the previous sections; in contact with the matter, the mechanism is the CMY subtractive interaction with the electrons. An example to elucidate this basic mechanism is reported in Fig. 13.15. For any surface, the reflection of light may be either specular (mirror-like) or diffuse (all directions), depending on the nature of the surface. Glass, polished metals, and gilded objects are examples of the former mode; rough surfaces, polychromies, and paintings of the latter. However, the diffusion mechanism is quite complex, especially in the case of polychromies and paintings because it occurs in the outermost part of the paint layer, or within the whole thickness of it. A very glossy paint or a glassy protective varnish may specularly reflect light and the viewer will have the perception of a bright spot. To be visible, a paint should selectively absorb certain wavelengths, and diffusely reflect others. However, the comprehension of this mechanism and the application of the above additive and subtractive systems require some preliminary explanations about paints and their constituents (Cennini, 1437; Vasari, 1568; Nassau, 1983; Freitag and Stoye, 1998; NIIR, 2006; G€ urses et al., 2016). Paint is a homogeneous mixture composed of pigments, dispersed in a transparent binder (e.g. gum Arabic

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13.8 THE COLOUR OF OBJECTS, POLYCHROMIES, AND PAINTINGS

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FIG. 13.16

Why a surface appears coloured. Some disks are represented, with a coloured reflecting (Refl) upper surface; the lower disc shows the complementary colour. Below, the coloured small circles show the absorbed (Abs) wavelengths. White light composed of RGB primary colours impinges on all discs, represented by RGB arrows. The reflected light and the colour perceived by the viewer are represented by outcoming arrows, as follows. (A) The disc absorbs blue and green (i.e. cyan) and reflects red. It appears red. (B) The disc absorbs blue and red (i.e. magenta) and reflects green. It appears green. (C) The disc absorbs green and red (i.e. yellow) and reflects blue. It appears blue. (D) The disc absorbs green and reflects blue and red. It appears magenta. (E) The disc absorbs blue and reflects green and red. It appears yellow. (F) The disc absorbs red and reflects blue and green. It appears cyan.

The white ground layer as a primer between the paint coat and the support. The paint coat is composed of pigments (blue particles) suspended in a transparent binder (yellow layer). Red arrows escaping from the paint coat represent the diffuse reflection emerging from the paint surface and perceived by the viewer. (A) The incident light is completely scattered (red arrows) within the paint coat, and is unable to reach the white ground, i.e. good hiding power. (B) The incident light crosses the paint coat, and is partially reflected by the white ground, i.e. poor hiding power. The ground enhances the effectiveness of pigments. In the absence of white ground, the support will absorb the incoming light and the dark background will become partly visible. (C) The incident light undergoes specular reflection on the surface of the paint coat, i.e. reflective paint, and is perceived as a disturbing glare. Note: casual choice of colours.

resin, linseed, or poppy oil), dissolved in a particular solvent (e.g. water, turpentine) that applied on the surface will form a solid thin layer for artistic, aesthetic, or conservation purposes. Binders are aimed to bind and protect pigments, fillers, and additives, and guarantee adhesion to the support medium. A surface may be coloured with dyes or pigments. Both of them may be derived from animals, vegetables, or finely ground minerals, or may be artificially generated. The main difference is that dyes are soluble in the substrate, while pigments are insoluble particles and are homogeneously dispersed within the paint. Dyes go into solution into the medium and will impart colour by selective absorption of light, depending on their chemical structure. Pigments need binders to remain bound to the surface and the colour they provide depends on the physical characteristics of the particles, either for selective absorption and/or scattering of light. Pigments are used for coloration, i.e. to confer a specific colour appearance, and for opacity, i.e. to absorb impinging light. The photons of the illuminating light penetrate into the paint layer, impinge on pigments, are scattered by the pigments and leave the paint layer as a diffuse reflection (Fig. 13.16A). Inside the paint layer, the pigments will selectively absorb photons and determine the colour as explained with the CMY model. The fraction of light that is diffused out of the paint will be perceived following the

RGB model and is responsible of the visual appearance that we get of it. When the paint coating is not sufficient to prevent light from reaching an opaque substrate, the colour loses brightness. In such a case, it is necessary to add a layer, named ground, which physically separates the paint from the support (Fig. 13.16B). The ground is a separation barrier between the paint and the support, and provides a chemically stable surface to take paint properly. Boards, canvas, or panels need to be adequately primed, i.e. prepared to hold the paint with the application of a white ground layer. The most popular ground follows the tradition by Theophilus Presbyter (XI Century)3 and Cennino Cennini (1437). The ground layer was composed of an inorganic filler (typically gypsum, or chalk) with animal glue (e.g. rabbit skin) as a binder; oil paints used linseed or another oil in place of the animal glue; gelatine, casein, or egg were mainly used for tempera. To enhance reflectivity, the ground may include a white pigment, especially when the paint has poor hiding, because the impinging light crosses the paint layer, reaches the white ground and is reflected back increasing colour brightness. A thin, transparent, varnish layer may be applied over the colour coating to protect it. It might alter the surface roughness and reflectivity (Fig. 13.16C). However, in the following examples, it will be neglected because its presence is not relevant to the discussion.

FIG. 13.15

3

Theophilus Presbyter, also known as monk Roger of Helmarshausen.

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The hiding power is the ability of a paint to cover a surface and mask it from view (Talbert, 2007) so that an underlying paint cannot be seen in visible light. It is also referred as opacity. Opacity is measured directly by the contrast ratio formula ( Judd, 1934) based on the Y variable of CIE, which is related to brightness, as follows. The value of the brightness Y is first measured for a given paint applied to a black background (black baking), i.e. Ybb; then the measurement is repeated for the same paint but applied to a white background (white baking), i.e. Ywb. The opacity is then expressed as the percent ratio OpacityðYÞ ¼

Ybb  100 ð%Þ Ywb

(13.8)

Opacity values range from a maximum of 100% for perfectly opaque coatings to nearly 0% for transparent ones. The paint layer is viewed opaque when the particles constituting the pigment do scatter and/or absorb light sufficiently to prevent it from reaching the substrate. Pigment particle size is relevant in determining light scattering efficiency. The finer the pigment size, the most efficient the scattering and the greater the hiding power. The average diameter of pigment particles generally lies from 0.015 to 5 μm. The colour strength is enhanced with the finest particles, and is substantially diminished for medium and coarse particles. The most effective scattering is reached when the wavelength of the impinging light is twice the particle size. Scattering may be either due to reflection at the pigment surface (opaque but reflective), or transmission through it (transparent but with high reflective index n >1.5; note that in transparent materials n generally lies from 1 and 2). Among the pigments with the highest n values, red lead (n ¼ 2.4), cadmium yellow (n ¼ 2.4), chrome green (n ¼ 2.6), and vermillion (n ¼ 3.0) should be mentioned. The higher the refractive index, the greater the hiding power.

13.9 USE OF COMPLEMENTARY COLOURS IN VISUAL ARTS Special effects may be obtained using complementary colours, and painters used and developed them since antiquity. In his treatise on painting, Cennino Cennini (1437) explained the technique of complementary colours used by Giotto4 to create a three-dimensional appearance and coloured shades (Fig. 13.17). The text is here reported: ‘When you have sketched out the form of the face, if the proportions or any other thing should displease you, with a large brush steeped in water rub over the intonaco (i.e. lime plaster), efface and repair what you have done. Then take a little verde terra (i.e. green earth), 4

FIG. 13.17 Use of green earth paint to create coloured shadows in the face. Giotto, fresco in Basilica Superiore, Assisi, Italy. Courtesy of Bruno Zanardi.

very liquid, in another vase, and with a pencil of hog’s bristles, without a point, squeezed with the fingers and thumb of the left hand, begin to shade under the chin, and all those parts which should be darkest, under the lips, the corners of the mouth, under the nose, and under the eyebrow, making the shade darker near the nose, a little on the edge of the eye towards the ear; and in the same manner shading with judgement the whole face and hands, which are hereafter to be coloured with the flesh-colour. Next take a pointed pencil of minever (i.e. a very small brush, composed of a thin bundle of hairs sprang from a goose-quill ferrule) and perfect all the outlines of the nose, eyes, lips, and ears, with the verdaccio (i.e. green earth). There are some masters who, when the face is advanced thus far, with a little bianco sangiovanni (i.e. white lime pigment) tempered with water put on the high lights in their proper places; then give the rose-colours (i.e. flesh pink) to the lips and cheeks; then wash over the whole with the flesh-colours very liquid with water, and this will complete the colouring of the head. It is a good plan to retouch afterwards the high lights with a little white. Some painters wash over the whole face with the flesh-colour first, on that they put

Giotto da Bondone, born c.1267, died 1319.

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13.9 USE OF COMPLEMENTARY COLOURS IN VISUAL ARTS

the verdaccio and carnations, and retouch the lights, and the work is finished.’5 Zanardi (1996) explained that Giotto and his co-workers had to paint a series of narrative panels representing scenes of the life of St Francis where the characters should keep exactly the same colour appearance in the face and the dressing, as they had moved from a panel to the next one. If colours were mixed in a palette, it would have been impossible to obtain this goal, e.g. changing flesh colour, or creating unbalances mixing too much white or black to simulate light or shadow. Giotto decided to normalize the procedure and prepared a series of pots of particular colours to be added in separate, independent layers on the top of each other, applied with a precise protocol. First the sage green used as background; then the basic flesh, then the darker and clearer tones. This operative protocol, operated under the strict supervision of Giotto, guaranteed the same results, independent of the individual co-worker. However, which pairs of colours should be considered complementary depends on aims, theoretical approach, and definition. In reality, Newton6 published the first scientific colour wheel (Newton, 1704), composed of seven colours obtained from the prism decomposition of sunlight: violet, indigo, blue, green, yellow, orange, and red (Fig. 13.18A). One century later, the poet, artist, and politician Goethe7 published a theory of colours (Goethe, 1810) in which he opposed the physical approach by Newton, the idea that colours are an inherent property of light. Goethe

289

proposed a human-based approach combining visual appearance with harmony, culture, sensations, and psychological impact. The Goethe wheel was entitled ‘allegorical, symbolic, mystic use of colour’, and was composed of six hues each associated with a specific sensation, i.e. red (the beautiful), orange (the noble), yellow (the good), green (the useful), blue (the common), and violet (the unnecessary) (Fig. 13.18B and C). The position on the wheel was harmonically relevant: the colours in opposite position generated a strong psychological contrast and were called ‘opposite colours’. Primary colours were yellow, blue, and red (YBR), and opposite were green, violet, and orange. The Goethe wheel is similar to the colour picker wheel of Microsoft Power Point © after some rotation and specular reflection (Fig. 13.18D). Goethe’s wheel and the particular matching of opposites became popular and was used by Monet,8 van Gogh,9 and many other artists to create an aesthetically pleasant appearance, but especially to create strong and guided sensations. In the Impressionism movement,10 the special impact given by the combination of opposite colours, how they were placed side by side, the choice of the extension of the covered areas were deliberately aimed to create special psychological effects and sensations. As an example, let us apply Goethe’s wheel and its allegorical meaning to ‘the Starry Night’ (painted 1889) by van Gogh (Fig. 13.19). The painting is characterized by a giant yellow-orange moon and a few stars, lying on a blue sky, over a blue landscape. Applying this

FIG. 13.18

Colour wheels. (A) Newton’s seven-colour wheel published in Opticks (1704). In the original, the pie was empty with indicated colour names, i.e. red, orange, yellow, green, blue, indigo, violet. Here the pie has been coloured. (B) Goethe’s six-colour wheel published in Z€ ur Farbenlehre (1810), i.e. red, orange, yellow, green, blue, and violet after the original book (1810). (C) The same but with reconstructed colours. (D) Comparison with the colour picker wheel of Microsoft Power Point © after rotation and specular reflection.

5

Cennini, Part 3, Chapter 67, English translation by M.P. Merrifield (1844).

6

Isaac Newton (1642–1727).

7

Johann Wolfgang von Goethe (1749–1832).

8

Claude Monet (1840–1926).

9

Vincent van Gogh (1853–90).

10

The term ‘Impressionism’ was derived from a painting by Monet, painted 1872, entitled ‘impressions, sunrise’.

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FIG. 13.19 ‘The Starry Night’ by Vincent van Gogh, oil on canvas (1889) (MoMA, Museum of Modern Art, New York City).

language, and translating colours into concepts, the yellow and orange, i.e. ‘the noble’ and ‘good’, of the moon and the stars (the artists?) emerge from, and contrast with the ‘common-ordinary’ that characterizes their ‘blue’ environment, i.e. the sky and the landscape (his contemporaries, either located in high or low places?). A dark cypress looks like a high black flame generated from the centre of the human settlement: the darkness of this flame seems to be his evaluation of what humans may produce: only obscure, burning things. If this interpretation is correct, in Goethe’s colour language, the conclusion is: artists are the only lights shining in an obscure, bad world. The beginning of the 20th century was characterized by the fundamental developments made by Munsell, CIE, etc. In the most recent decades, novel software and computer graphic systems have been developed, most of them based on these systems. For instance, the popular software Adobe Photoshop© for visual design utilizes four colour models: HSV, RGB, CIE, and CMYK. If one wants to adjust colour hue, saturation, and brightness, or convert colours of an image, various options are available, as well as a selective colour dialogue box (Fig. 13.20A) with nine source channels: red, yellow, green, cyan, blue, magenta, white, grey, and black, i.e. the RGB or CMY primary and secondary colours, plus the three achromatic colours. For each source channel, it is possible to act dragging a specific slider, i.e. cyan, magenta, yellow, and black. If one selects the white channel, i.e. the possibility of converting white colours, with the cyan slider one passes from white to cyan; with the magenta slider from white to magenta

etc. If one wants to convert from white to red, he should act with magenta and yellow; from white to blue, he should act with magenta and cyan; from white to green he should act with yellow and cyan as already discussed with the basic CMY system and the additional control of the greyscale, i.e. CMYK. In the same programme, the colour balance dialogue box is composed of three channels with adjustment sliders that move from neutral to cyan/red, or magenta/green or yellow/blue respectively, i.e. the RGB, CMY, and CIE complementary pairs. One may also find a dialogue box to adjust hue, saturation, and lightness, and so on. Similarly, the visual communication software Office Power Point© by Microsoft© has a colour picker wheel based on these systems, with opposed complementaries and white point in the centre (Fig. 13.20B). In addition, it has sliders with RGB, CMYK, HSV and greyscale options, in line with the previous sections. In general, individual software programmes may present some operative differences, but are all substantially based on the same ground. The theory may be useful for a better use of computer graphics.

13.10 OPTICS OF HALFTONE IMAGING AND THE NEO-IMPRESSIONISM Around the mid 19th century, the scientific developments and the theory of colours opened new horizons and inspired new applications. The basic idea was that the visual perception is formed in the mind; a painting constitutes the input, i.e. an intermediate step, of a perceptive

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13.10 OPTICS OF HALFTONE IMAGING AND THE NEO-IMPRESSIONISM

FIG. 13.20

(A) Dialogue boxes to select and balance colours in Adobe Photoshop ©. (B) The colour picker wheel in Microsoft Power Point ©.

process that will be concluded in the brain. This suggested an easy technological solution to print photographs or drawings, and a provocative visual art movement, called Neo-Impressionism, where paintings were not finished in the traditional way, but prepared to supply to the eye the necessary input to be perceived. The real artwork and its beauty are only virtual, and should be realized in the observer’s mind. The modern technology of digital camera, scanners, computer graphics, image reconstruction and transmission is based on the subdivision of the real image into small single-coloured rectangles, called pixels, their individual mathematical or transmission treatment, and the final recombination of the ordered array of all pixels, called bitmap. The method is called pixellation and is strictly linked to the modern technology; however, its roots are far away in time. The subtractive principle was applied to halftone printing, invented by Talbot in 1852 and soon applied to print photographs, magazines, and books. The halftone technique (Stulik and Kaplan, 2013; Oleari, 2016) breaks up an image into a series of black and white dots varying either in size or in spacing, so as to reproduce the full tone range of a photograph (Fig. 13.21A and B). At normal distance, the human eye perceives tiny halftone dots as smooth tones as an optical illusion. These images in black and white with illusion of grey tones were called duotone, or duplex, images. From the practical point of view, halftone was essentially an ON–OFF system based on only one ink type, i.e. black ink, the white being naturally provided by the paper sheet (white baking). 11

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Halftone colour printing (Fig. 13.21C) was later developed by repeating the halftone process extended to four coloured inks, i.e. cyan, magenta, yellow, and black ink, following the CMYK system. The image represented with tiny dots was transferred on halftone printing plates or cylinders. The final print was obtained printing four times selected highlights of the same image, but each time applying a differently coloured ink, i.e. cyan, magenta, yellow, and black ink, on adjusted printing plates. Laser, LED, or inkjet printers use the same principle, and are provided of four tone cartridges, i.e. cyan, magenta, yellow, and black. The most recent technology has transformed this methodology in digital form, controlled by a computer, and the CMYK system or other analogous systems are used for printing. In visual arts, the new scientific findings generated innovative ideas, especially in the Neo-Impressionism. This art movement first appeared as Pointillism and evolved in Divisionism and others aspects of the so-called Academic Art. Fathers of Pointillism were Seurat and Signac11 who developed the idea in 1886. Seurat was focused to combine psychological effects and emotions with the cutting-edge knowledge of colours in the 19th century, obtaining special effects with isolated colour strokes on the canvas to be recombined by the observer (Foa, 2015). The viewer looking at the picture from a distance merged in his brain the colours that resulted from the additive/subtractive mixing. In Pointillism, the image was composed of many distinct small dots or brush strokes of different colours

George Seurat (1859–91); Paul Signac (1863–1935).

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FIG. 13.21 Halftone printing. (A) Halftone pattern of black circles of different size on white backing to create grey tones, and (B) the smooth tone perceived as optical illusion. (C) Halftone pattern of circles creating a CMY spectrum of colour. (C) Image from cr103/stockarch.com licensed under a CCA 3.0 Unported License.

near each other, distributed in patterns to form an image. In Divisionism, the image was composed of individual patches of contrasting or complementing colours that interacted optically to create shadows and volumes. This basic concept of Pointillism may be clarified with an example. In the close-up view of the face (Fig. 13.22A), cyan, magenta, and orange dots are applied without mixing the colours (that would give blue in the subtractive CMY system), but are distributed side by side in order to obtain the additive RGB effect of flesh pink in the viewer’s brain. This effect can be recognized looking in the middle of the straight

line joining cyan and magenta or cyan and orange in the CIE diagram, which is strictly related to the RGB additive system. Briefly, it is fundamentally different when the incident white light is simultaneously reflected back by two different coloured strokes, acting in parallel, because the perception is additive, i.e. RGB system (Fig. 13.22B and C). As opposed, when light enters the colour coating and crosses a series of two or more colours, applied in overlapped layers, or mixed together, the perception is subtractive, i.e. CMY system (Fig. 13.22D).

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13.11 HOW TO IMPROVE THE COLOUR RENDERING OF ELECTRIC LIGHTING

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FIG. 13.22 (A) Close-up of the face of a lady in the Pointillist painting ‘A Sunday on La Grande Jatte’ (1884/6), oil on canvas by George Seurat (The Art Institute of Chicago). (B) Coloured strokes separated and placed side by side, as in the above face: light impacts either on one stroke or another, and the perception is additive. (C) CIE chromaticity diagram showing the effect of mixing cyan (C) and magenta (M) or cyan (C) and orange (M) strokes in the brain: two slightly different flesh pink colours (FP1 and FP2). (D) Coloured pigments applied in overlapped layers: light crosses both the magenta and cyan layers, and the perception is subtractive (i.e. blue).

13.11 HOW TO IMPROVE THE COLOUR RENDERING OF ELECTRIC LIGHTING Every lamp emits light with a typical spectrum. The halogen lamp is based on the blackbody emission from an incandescent tungsten filament; the spectrum is

continuous, and constitutes the best approximation of solar light. Fluorescent lamps provide an uneven spectral band, including gaps or particular brilliant bands, and have been improved with various strategies to obtain a continuous spectrum and better colour rendering. A popular strategy is based on phosphors, i.e. luminescent

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materials excited by electron beams, or ultraviolet (UV) and visible radiation, used as transducers for the conversion of electrical energy into visible light. Phosphors are generally composed of either oxides or oxyacid salts, coated inside the glass tube of the lamp and are excited when the internal gas is ionized and emits UV radiation. A number of differently coloured phosphors, generally the three RGB primaries (i.e. tri-band or tricolour lamp phosphors), or more colours, are used as colour converter to improve the spectral distribution, as close as possible to white light. The same technology

has been recently applied to LEDs, to obtain highbrightness LEDs (HBLED) and high-colour rendering index. Although the last LED generation (i.e. after 2017) is reaching excellent results, an example is made with a popular LED type produced in 2014, as a useful exercise to improve the colour rendering of lamps using the RGB additive and CMY subtractive systems. A Warm White LED (3100 K) and a halogen lamp (3500 K) as reference are considered (Fig. 13.23). The first step is to normalize the spectra and make a comparison of the two spectral

FIG. 13.23

How to improve the colour rendering of LED lamps, 2014 generation, making reference to a Halogen lamp. (A) Comparison between the normalized spectra of Halogen 3500 K and Warm White LED 3000 K (WWLED). Arrows pinpoint the main departures that need compensation, i.e. blue peak, cyan–green, and red deficit. (B) Difference between the normalized spectra of the above Halogen and WW LED. The yellow arrow shows the excess of blue peak in WWLED that may be dimmed with a complementary colour, i.e. yellow LED (Y LED) light; the cyan and red arrows show the deficiency of the corresponding bands that may be compensated using cyan–green LED and red LED lights (C–G LED, R LED). Ordinate in arbitrary unit (AU). (C) Normalized spectra of coloured LEDs, i.e. Y LED, C–G LED, and R LED that may be used to improve the colour rendering of WW LED.

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13.12 WHAT IS THE COLOUR OF SOLAR LIGHT?

distributions, highlighting the departures of the selected LED from the reference lamp, in terms of excess or deficit of certain spectral bands (Fig. 13.23A). The comparison shows that the main excess is a blue peak, while the main deficiencies are in the cyan–green and red bands (Fig. 13.23B). The blue peak may be compensated in two ways: with the subtractive principle, using a yellow filter that absorbs blue, as suggested in CEN-TS 16163 (2013); with the additive principle, dimming the blue peak with the complementary yellow light, and this may be adding a yellow LED of convenient intensity. The cyan–green and the red deficit may be compensated using the additive principle (Fig. 13.23C), i.e. adding cyan–green LEDs and red LEDs in convenient proportions, or tuning their intensities. The brightness of incandescent lamps (e.g. halogen lamps) is due to the filament temperature, which can be controlled tuning the feeding voltage. As opposed, LEDs are current-driven devices, i.e. diodes. Their brightness may be controlled with the intensity of the current flowing through them, or using pulse modulation (PWM), i.e. in repeating bursts. To exactly tune the individual light intensities of the LEDs that are necessary to compensate the Warm White LED is difficult and expensive. The easiest solution is to mix a number of Warm White LEDs with a selection of some other LEDs in convenient proportions to reach the desired colour rendering index, close to the reference halogen light. In 2014, this additive principle was used to obtain daylight illumination of the Sistine Chapel, Rome, by mixing an accurate selection of 7000 white and coloured LEDs (Bogani and Kroes, 2015).

13.12 WHAT IS THE COLOUR OF SOLAR LIGHT? Sunlight is optically white, being composed of a mixture of all wavelengths in the spectrum. However, when the solar radiation penetrates the atmosphere, nitrogen and oxygen molecules resonate with short wavelengths, i.e. UV, violet and blue, and disperse them following the Rayleigh formula of scattering (Fig. 13.24). Aerosols resonate with longer wavelengths and disperse them following the Mie formula of scattering (Fig. 13.25) (Minnaert, 1954; Nassau, 1983). The selective dispersion of wavelengths associated with distinct colours may cause spectacular effects, e.g. blue sky, red sunrise and sunset, rainbow. The scattering intensity (I) calculated with the Rayleigh formula (Fig. 13.24A and B) has a strong wavelength dependence, i.e. I ¼ I0

 8π 4 Nα2  1 + cos 2 θ 4 2 λ R

(13.9)

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FIG. 13.24

(A) Rayleigh scattering of sunlight from air molecules. R: distance from the scatter; θ: angle between the solar beam (yellow arrow) and the observer’s eye. (B) Normalized intensity of scattered light according to the Rayleigh formula. Violet and blue dispersion are largely dominant.

where N is the number of scatters, i.e. collisions between photons and air molecules, α is the polarizability, R the distance from the scatter, and θ the angle between the solar beam and the observer. All things being equal, the scattered light intensity is inversely proportional to λ4. Consequently, shorter wavelengths (e.g. UV, violet, and blue) are scattered much more than longer wavelengths (e.g. red and orange). This explains the colour of the solar disc at sunset: red and orange photons are less depleted, while all other wavelengths, and especially the shortest ones, are dispersed away at increasing proportions. Looking up at the sky on a clear day, it appears intense blue for the Rayleigh dispersion of short wavelengths, but violet passes unobserved because the human eye is more sensitive to blue than violet. During the day, the sun changes height over the horizon and the sky colour changes with the path that sunrays follow travelling across the atmosphere (Rayleigh scattering), and in proportion to the quantities of dust and minute water

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FIG. 13.25 Mie scattering of light from suspended particles (A) Light scattered from a fine particle (red dot) (Mie scattering). (B) As above, but for a larger particle.

droplets of various diameters suspended in air (Mie scattering). Under such condition, the dispersion of light is not selective but distributed over the whole spectrum and the sky assumes a lighter blue colour in the presence of fine particles (Fig. 13.25A) or a whitish colour with larger particles (Fig. 13.25B). When water droplets are organized in huge amounts to form clouds, their appearance is white in reflected light, but becomes grey or dark in transmitted light, i.e. for the light absorption.

Outside the Earth’s atmosphere, the solar radiation is white, but after it enters, it changes colour with the scattering of the short wavelengths (Fig. 13.26). When at midday the sun is high, the solar path is shorter and its rays (and the solar disc) are bright, white with a pale-yellow appearance. When the sun approaches the horizon (sunrise and sunset), rays are at a grazing angle and cross a very thick atmospheric layer, thus appearing yellow, orange, and red. This effect is more evident at sunset than at sunrise for the airborne particles produced during the day and the increased moisture content due to soil evaporation. Smoke from wildfire or volcanic aerosols may enhance this spectacular effect, and several artists have been inspired by the splendid colour and their paintings may provide proxy information on the aerosol optical depth after the major volcanic eruptions since AD 1500 (Zerefos et al., 2007, 2014). For instance, Turner12 documented a series of sunsets, including the scarlet sky for the Tambora Volcano eruption in 1815; Ascroft13 for the Krakatoa eruption in 1883. Krakatoa inspired Munch14 in his famous ‘The Scream’ (Fig. 13.27), painted ten years after the eruption. When the concentration of aerosol and pollutants with larger size is high, colour brightness and saturation may be penalized with a brown colour. A similar situation holds for the UV radiation that has shorter wavelength and higher dispersion. In the atmosphere, UV reaches remarkable intensities only in the middle of the day when the sun is high over the horizon. Even in unpolluted areas, UV in combination with

FIG. 13.26 Daytime light colours. (A) The atmospheric scattering (indicated with cyan arrows) disperses the short wavelengths in all directions. The effect increases with the atmospheric path travelled by the solar rays. The eye perception includes blue sky, pale yellow afternoon light, and red sunset colour (B) Colour temperature of daylight under different conditions. Moon light is also reported. (A) Modified from a picture taken by NASA.

12

Joseph Mallord William Turner (1775–1851).

13

William Ascroft (1832–1914).

14

Edward Munch (1863–1944).

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FIG. 13.27 ‘The Scream’ by Edward Munch, oil, tempera, pastel, and crayon on cardboard (1893). Nasjonalmuseet, Oslo. See Credits.

volatile organic compounds (VOC), especially terpenes, released by forests, may generate haze or natural smog. This is the typical atmosphere in the fascinating landscapes by Leonardo da Vinci.

Finally, a note about moon. Its light is the solar light reflected by the moon surface, but its intensity is about one million times fainter than sun. By night, when the moon is high over the horizon, it is perceived pale yellow like the sun near noon; when it is very low it tends to become orange colour, like the setting sun, but much less evident for the lower light intensity. During the day, the moon is perceived white because the blue scattered by the sky is added to the above yellowish moon light. Natural light is continually changeable, with regular cycles and spectacular appearances. Because of its variability, it cannot be assumed as a reference for art lighting or painting restoration purposes and halogen lamps are preferred for the unchangeable light colour. The situation at sunset is clearly illustrated in a satellite picture15 (Fig. 13.28). The Earth’s curvature is visible along the horizon line that extends across the image from centre left to lower right. Above the darkened surface of the Earth (on the bottom), a brilliant sequence of colours roughly denotes several layers of the atmosphere. Deep oranges and yellows appear in the troposphere, which extends from the Earth’s surface to 6–20 km high. This layer contains over 80% of the mass of the atmosphere and almost all of the water vapour, clouds, and precipitation. Dark cloud layers are visible within this layer. Changes in colour are due mainly to varying concentrations of either clouds or aerosols (airborne particles or droplets). The pink-towhite region above the clouds is the lower stratosphere; this atmospheric layer generally has few or no clouds, and it extends up to approximately 50 km above the Earth’s surface. Above the stratosphere, blue layers mark the transition between the middle and upper atmosphere as it gradually fades into the blackness of outer space.

FIG. 13.28

Sunset over the Indian Ocean 356 km spacecraft altitude, the 25th 05 2010. Legend: E, earth; T, troposphere; S, stratosphere; MA, middle atmosphere; UA, upper atmosphere; OS, outer space. Courtesy by NASA.

15

NASA astronauts aboard the International Space Station (ISS), Observations experiment and Image Science & Analysis Laboratory, Johnson Space Center. III. RADIATION, LIGHT AND COLOURS

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Zerefos, C.S., Gerogiannis, V.T., Balis, D., Zerefos, S.C., Kazantzidis, A., 2007. Atmospheric effects of volcanic eruptions as seen by famous artists and depicted in their paintings. Atmos. Chem. Phys. 7, 4027–4042. Zerefos, C.S., Tetsis, P., Kazantzidis, A., Amiridis, V., Zerefos, S.C., Luterbacher, J., Eleftheratos, K., Gerasopoulos, E., Kazadzis, S., Papayannis, A., 2014. Further evidence of important environmental information content in red-to-green ratios as depicted in paintings by great masters. Atmos. Chem. Phys. 14, 2987–3015.

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