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Chapter 2 Light Sources, Types of Colorants, Observer In this chapter, the fundamental conditions for color production are discussed. In simplified terms, the visual color impression of non-self-luminous colors is ultimately due to three independent components: the light source, the colorants of the color pattern, and the observer. The color perception depends, therefore, on the specific properties of these factors. Factors of particular importance are as follows: – the spectral power distribution emitted of the light sources used; – the light interactions with the colorants of the color sample, especially the resultant absorption, scattering, reflection, transmission, as well as interference or diffraction; – the color perception capability of the observer. We will go into these three factors in more detail in the following sections. To begin with, we deal with the most important light sources used for color assessment and the most simple light interactions of colorants. The composition and the typical spectral properties of industrially applied colorant sorts are described in detail. The explanation of color sensation of the observer seems initially to be out of scope; however, this theme is necessary to consider for at least two reasons: first, some phenomena of the human color sense really stand out. These have to be taken into account during color assessment. Second, color perception is affected by the law of additive color mixing, upon which the entire colorimetry and the corresponding applications of industrial color physics are founded. 2.1 Optical Radiation Sources and Interactions of Light Without light there exists no color. The concept of color is bound to visible wavelengths. Therefore, we turn at first toward the typical properties of natural G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-1197-1_2, 11 12 2 Light Sources, Types of Colorants, Observer and man-made light sources because the spectral power distribution of an illuminant affects the color impression. Due to ever-present changes in natural daylight, such a source is unsuited for producing a consistent color sensation with an unchanging non-self-luminous color. On account of this uncertainty, we are forced to rely on man-made sources of constant and reproducible light emission – normally in the visible range. For a reliable assessment of colors in industry, the spectral power distributions of two commonly used man-made light sources have been standardized. The actual physical processes producing color appearances can be described by elements of simple geometrical optics as well as some effects of wave and quantum optics. In this section, these interactions are described in so far as they are significant for better understanding of the color physical properties of modern industrial colorants. 2.1.1 Visible Spectrum and Colors The electromagnetic spectrum covers an enormous range of wavelengths λ from, for example, values such as λ ≈ 1 fm (1 fm corresponds to 10–15 m) for cosmic radiation to λ ≈ 10 km for radio waves, therefore a range of around 19 orders of magnitude; see Fig. 2.1. On the other hand, the visible range of humans is only a small part of the spectrum of electromagnetic waves. Merely wavelengths in the very small interval from 380 to 780 nm are normally perceived by humans as visible light. Wavelengths at the left end of the range between 10–15 10–12 10–9 10–6 10–3 1 λ m 103 1 2 3 4 5 6 7 8 9 10 Violet Green Orange Blue Yellow Red 380 nm f Hz 1021 1018 780 nm 1015 1012 109 106 Fig. 2.1 Spectrum of electromagnetic waves: 1 cosmic radiation, 2 gamma radiation, 3 Xray radiation, 4 ultraviolet radiation, 5 near-ultraviolet radiation; 6 infrared radiation, 7 radar waves, 8 VHF waves, 9 television waves, 10 radio waves 2.1 Optical Radiation Sources and Interactions of Light 13 380 and 440 nm are perceived as violet. With increasing wavelength, the color impression changes to blue, green, yellow, orange, and finally red. Red is perceived at wavelengths above 600 nm. The associated wavelengths are subject to individual variations in color perception. The so-called spectral colors are the purest producible colors. They are characterized by a wavelength width of less than 1 nm (i.e., with a laser). On the other hand, if the radiation contains nearly all wavelengths of the visible spectrum and of equal intensity, the resulting color impression is white light (e.g., white clouds). For the entire range of visible light between about 380 and 780 nm to be perceived, there must be sufficiently high intensity. Under normal illumination conditions, the wavelength interval that can be seen by humans is restricted to between about 400 and 700 nm. Many modern color measuring instruments work in this limited range [1]. Apart from its wave character, light also exhibits simultaneously particlelike properties. To this day, perhaps, this dualism is not understood in terms of everyday human experience. The corresponding particles of electromagnetic radiation, and therefore of visible light, are the so-called photons. Photons in the visible range carry a sufficient amount of energy for selective stimulation of the photosensitive pigments in the retina of the eye to initiate color impression. The eyes should, however, be protected from dangerous ultraviolet (UV) or infrared (IR) radiation. However, radiation of wavelengths near the visible range which cannot be directly perceived by humans can, in conjunction with suitable colorants, cause different physical effects. Luminescence colorants, for example, absorb energy at UV wavelengths and then emit most of this energy at longer wavelengths – usually within the visible or IR range. The needed transitions from energetic steady states occur either spontaneously by fluorescence or delayed by phosphorescence. The energy surplus is converted into molecular vibration energy and leads macroscopically to a temperature increase. The energy absorption of normal absorption colorants in the visible or IR range is also transformed into molecular vibration energy. If this energy conversion is accompanied by a color change, such kinds of colorants are denoted as thermochromic. Moreover, colorants are termed as phototropic, if the color change is only caused by energy absorption at visible wavelengths. On the other hand, excessively high UV or IR radiation energy is sometimes able to initiate irreversible molecular changes, which result in bleaching or total loss of color. In contrast to the above-mentioned colorants, overall the greatest percentage of industrially used colorants contain absorption and effect colorants. In absorption colorants, the incident energy is sufficiently high to initiate partial absorption or scattering. Physically, light absorption in colorant molecules occurs only for certain transitions between quantum energy levels – therefore, in special wavelength regions of visible light. The corresponding processes are called selective absorption or scattering. On the other hand, scattering of light depends on the electrical charge distribution and the geometry of the colorant 14 2 Light Sources, Types of Colorants, Observer particles. In contrast to absorption pigments, dyes do not normally show any scattering because the size of the isolated molecules in solution is too small for such an interaction. The light reflected in the direction of the eye initiates in the retina signals which are perceived usually as non-self-luminous colors. The color separation of pearlescent, interference, and diffraction pigments is a consequence of the wave nature of light. In order to produce a suited interference effect, the pigment particles are built up of layers with different refractive indices of which the light waves interfere constructively or destructively depending on optical path length. The layer thicknesses are smaller than the interfering wavelengths. In contrast, the particles of diffraction pigments show an embossed regular grating structure at which suited wavelengths are diffracted. The distance between two light-transferring slits is about 1 μm. 2.1.2 Types of Light Sources The perception and assessment of non-self-luminous colors requires illumination with a suitable light source. Depending on the mechanism of light generation, optical radiation sources have different spectral power distributions. On the basis of the emitted spectrum, illuminants can be divided into two categories: temperature and luminescence radiators. The most important luminous sources of both classes are given in Table 2.1. In the following, we discuss details of both categories because the illumination of color samples is our primary context. In the near future, semiconductor diodes and lasers are expected to replace, in part, the light sources used to date. Therefore, we also discuss on these sources even though they are, thus far, rarely applied in color industry despite a multitude of advantages. Table 2.1 Kinds of optical light sources Temperature radiator Luminescence radiator Natural Artificial Artificial Sunlight, Scattered light of the Earth atmosphere, stars, galaxies Blackbody radiator, incandescent lamp, arc lamp Gas discharge tube, fluorescent lamp, light emitting diode (LED), source of coherent light (laser) For a common characterization, optical radiation source output distributions are often compared with the spectral energy distribution or temperature of a so-called blackbody radiator – also denoted as blackbody or cavity radiator. At lower temperatures, metals emit heat energy in form of IR radiation; gradually, with increasing temperature, dark-red glow emanates. With a further increase 2.1 Optical Radiation Sources and Interactions of Light 15 of temperature, the color changes to orange and yellow, finally to bluish white. During this process, both the radiation energy and the brightness of the emitted light increase. The wavelength with the most energy shifts to smaller wavelengths, i.e., a blue shift. For an ideal blackbody, this radiation is generated inside the cavity of a blackbody radiator and the outside of the cavity walls absorb all external electromagnetic waves. The ideal situation, therefore, is the emission of only the cavity radiation according to its temperature. The radiation power S(λ,T)dλ of a blackbody radiator at wavelength interval dλ is given by the Planck law of radiation [2]: S(λ,T)dλ = λ5 c1 dλ. · {exp [c2 (λT)] − 1} (2.1.1) The radiation constants c1 and c2 have values of c1 = 2πhc2 = 3.74185 × m2 and c2 = hc/k = 1.43884 × 10−2 m K. In Equation (2.1.1), the wavelength λ should be in units of meters and the temperature T in units of Kelvin. The radiation constants contain the velocity of light in vacuum c and the Boltzmann constant k. For derivation of Equation (2.1.1), Planck introduced h – now called the Planck constant. Figure 2.2 shows the spectral power distribution in wavelength given by Planck’s law. As can be seen, at a temperature of 500 K, the peak of spectral power is in the IR range. For an increase to much higher temperatures, i.e., to greater than 104 K, this peak shifts over the visible range into the UV range. For temperatures of about 7,600 and 3,700 K, the peak of the spectrum lies at the respective edges of the visible range. The Planckian formula (2.1.1) contains 10−16 W 109 Energy density / W.m–2.nm–1 Visual range g a: 500 K b: 1,000 K c: 2,000 K d: 4,000 K e: 6,000 K f: 10,000 K g: 20,000 K 106 f e d 103 c b 100 a 10–3 101 102 103 104 Fig. 2.2 Spectral power distribution of blackbody radiator of different temperatures λ nm 16 2 Light Sources, Types of Colorants, Observer two limiting cases: for short wavelengths Wien’s law of radiation and for long wavelengths Rayleigh–Jeans radiation formula. Before the quantum hypothesis was established, both laws lead to inconsistent infinite energies in the UV range (“UV catastrophe”). The primary assumption made by Planck is that a radiating system exchanges energy with the surrounding radiation field only with an integer multiple of the quantum energy E= hc = hf . λ (2.1.2) In this formula, f is the frequency of the corresponding wavelength. Both the continuous spectra of temperature radiators and the discontinuous line spectra of luminescence radiators are based on the emission of light quanta that are identical with the already mentioned photons. Because the color of the spectrum emitted by a blackbody radiator changes with temperature, it is useful to introduce the term color temperature. With this quantity, the emitted light of a source is compared with that of a blackbody radiator and thus characterized. The color temperature of an illuminant corresponds to the temperature of the blackbody radiator which emits the maximum of light at the same color as the actual illuminant. Strictly speaking, only a temperature radiator can be assigned a color temperature. Other optical radiators, such as luminescence radiators, are characterized by a so-called similar or correlated color temperature. The most well-known temperature radiator is the Sun. Inside the Sun, at temperatures higher than 107 K, deuterium is converted to helium by nuclear fusion (Bethe–Weizsäcker cycle) [3]. For generation of 1 mol helium, the gigantic energy of 1.55 × 102 GJ is released. The total solar fusion energy results in a Sun surface with a mean temperature of about 5,800 K and an exceptionally high radiation power of about 63.3 MW/m2 . Merely a small fraction of this power, namely the so-called solar constant with value 1.37 kW/m2 , reaches the Earth’s atmosphere. This value reduces to about 1.12 kW/m2 if the Sun is at its zenith and the atmosphere is free of clouds. Already these considerations indicate the necessity of carrying out outdoor exposure tests of industrial colors (Section 3.4.5). Along the way to the Earth’s surface, the light interacts with particles of the atmosphere; its intensity is reduced by absorption and scattering. The light scattering is caused by the molecules in the air and this is responsible, for example, for the blue sky. According to the Rayleigh law J= V π 2 (n − 1) 2 · · E · cos2 ϑ, N r 2 λ4 (2.1.3) short wavelength blue light is scattered more strongly than the long wavelength red light because λ is contained in the denominator of this expression. The 2.1 Optical Radiation Sources and Interactions of Light 17 further quantities in Equation (2.1.3) are defined as follows: J the intensity of the scattered light, N the number of scattering particles per unit volume V, n the refractive index of the scattering medium, r the particle radius, E the amount of the electric field strength, and cos2 ϑ the phase function (see Section 5.1.5); ϑ denotes the scattering angle with regard to the incident intensity. The Rayleigh law is only valid for wavelengths λ which are longer than the particle radius r. In contrast to the blue color of the sky, sunrise and sunset are caused by scattering and absorption of light in the atmosphere, more precisely due to the air molecules as well as to aerosols (water drops, dust particles, etc.). On the long and nearly tangential optical path of the light through the layer of air, blue wavelengths are more strongly scattered and absorbed. The remaining blue light, therefore, reaches the observer on the Earth with considerably less intensity as compared with the much less scattered long wavelength red light. The Sun and the sky, therefore, appear reddish. In addition to dependence on daytime, received sunlight changes due to weather conditions, geographical latitude, season, and due to the approximately 11-year sunspot cycle. Accordingly, the color temperature of daylight is subject to substantial variations and takes values in the range of 5,500 K for direct sunlight to more than 14,000 K for blue zenith skylight. Simultaneously, the spectral power distribution changes. This is shown in Fig. 2.3 with curves normalized at the wavelength 555 nm. At this wavelength, the sensitivity of the human eye is at its highest (Section 2.4.6). a Relative spectral energy b 400 c d e 500 600 λ 700 nm Fig. 2.3 Relative spectral energy distribution curves of daylight, normalized at 555 nm: (a) cloud-free zenith skylight, (b) cloud-free north skylight, (c) overcast skylight, (d) medium daylight, and (e) direct sunlight [4] 18 2 Light Sources, Types of Colorants, Observer The daylight variations mentioned above create extra complexities for the unambiguous visual and objective assessment of non-self-luminous colors and their typical properties. A single color sample can produce a completely different color impression simply due to a changing illumination condition. In the practice of color physics, it is necessary to use reproducible artificial light sources which have nearly constant spectral power distributions. These artificial light sources are often referred to as technical sources. This corresponds to a constant color temperature if aging effects are neglected. From an economic point of view, the sources should also have a reliable working life of more than 1,000 operating hours. These standards are fulfilled by most of the technical illuminators of importance in the color industry; in the following section, we turn toward such kinds of sources. 2.1.3 Technical Light Sources For solving coloristical problems of non-self-luminous colors, technical light sources are used exclusively. The main reason for this is the high reproducibility of the generated spectrum. In technical temperature radiators, a metal of high melting point is heated up by an electric energy supply to such an extent that a continuous spectrum is emitted in the visible range; this spectrum is similar to that of a blackbody radiator of the same temperature. A temperature radiator in widespread use is the tungsten filament lamp; its color temperature is essentially dependent on the filament thickness, the applied voltage, and the kind of gas filling of the bulb. The so-called tungsten–halogen bulb contains bromine or iodine which increases the light efficacy, the working life, as well as the color temperature from about 2,800 to 3,000 K. The tungsten filament lamp of color temperature 2,856 K is named standard illuminant A by the CIE. The gradual loss of filament thickness in normal tungsten lamps is slowed down by the included halogen: the vaporized tungsten combines with the halogen, cools down at the surrounded quartz bulb, and reaches – by convection – the hot filament surface; there it dissociates so that tungsten is removed. Tungsten filament lamps typically emit light of yellowish color. The accompanying spectral energy distribution is shown in Fig. 2.4. Furthermore, in a tungsten arc lamp with an argon atmosphere, both tungsten electrodes are heated by an arc discharge in such a way that a radiation distribution is produced similar to that of the tungsten filament lamp; the accompanying color temperature amounts to about 3,100 K. A carbon-arc lamp shows a color temperature of 6,000 K and a very high luminance of about 1.6 Gcd/m2 .1 1 The unit candela (cd) is defined as the luminous flux radiated from 1/60 cm2 of a blackbody with temperature 2.042 K. 2.1 Optical Radiation Sources and Interactions of Light 19 200 Spectral energy distribution S (λ) A 150 D65 100 50 0 300 400 500 600 λ nm Fig. 2.4 Spectral energy distribution of a tungsten filament lamp (CIE standard illuminant A) and a UV-filtered xenon lamp (CIE standard illuminant D65) The term luminescence radiators represents a group of radiators including so-called discharge lamps, as well as photoluminescence radiators [5, 6]. In contrast to temperature radiators, luminescence radiators emit either a line spectrum of discrete wavelengths or a band spectrum of broader wavelength intervals. Line spectra are exclusively generated by gas discharge lamps. The physical mechanisms for generating line spectra are first to accelerate charge carriers by an electric field; during collision with the gas atoms, excitation energy is transferred to the outer electron orbits of these atoms. On the basis of the quantized energy of the electron shells, the electron transition into the ground level results in emission of light with discrete wavelengths λ according to Equation (2.1.2). The actual temperature of luminescence lamps is clearly far lower than the surface temperature of temperature radiators of the same light color. Among the technical gas discharge lamps, only the filtered light of xenon or mercury vapor lamps is of major importance for visual assessment or spectral measurement of colors. The emission of light in gas discharge lamps is based on the same physical mechanisms as in luminescence radiators. At first an electric voltage pulse in a xenon atmosphere causes free charge carriers. In a highpressure xenon lamp under pulsed or constant voltage, the charged particles generate a nearly continuous spectrum in the visible range. This is accompanied by a small amount of UV radiation. The spectral energy distribution shows a flat peak at a wavelength of about 450 nm and the emitted spectrum shows only a 20 2 Light Sources, Types of Colorants, Observer slight decrease in magnitude for longer wavelengths. Therefore, the perceived light appears slightly but insignificantly bluish; this can be seen in Fig. 2.4, curve D65. The radiation distribution is similar to that of diffuse daylight at midday on cloudless north sky, cf. Fig. 2.3, curve d. For these reasons, a UV-filtered xenon lamp of color temperature 6,500 K is used in the color industry to simulate midday light. The spectral energy distribution of this xenon discharge lamp is standardized; it is termed by the CIE as standard illuminant D65. The CIE recommends the use of xenon lamps with color temperatures of 5,000, 5,500, or 7,500 K, if the standard illuminant D65 is not available. The mercury vapor discharge lamp generates a line spectrum with emission wavelengths of 405, 436, 546, 577, and 579 nm, as well as in the UV range of 254, 314, and 365 nm. Because of the energetically high UV amount, this discharge lamp is utilized in a so-called light booth for visual assessment of fluorescence colorants, artificial color fastness tests, and in fluorescence microscopy. A light booth consists of a small one-sided open compartment with one or two small platforms to lay down the color samples to compare, as well as different non-glare light sources which can be individually switched on. The abovementioned emission wavelengths are also used for wavelength-scale calibrations of color measuring instruments. The UV fraction of the mercury spectrum is furthermore applied to stimulate the phosphorus in fluorescent lamps in order to initiate photoluminescence in the visible range. The spectral composition of the resulting band spectrum or the resulting light color depends on the chemical structure and the mixing ratio of the involved phosphorus. For color assessment of special importance, there is the cold white light of the fluorescent lamp CWF (identical with illuminant FL 2) and the light emission of the so-called three-band lamp TL 84 (identical with FL 11); the three-band lamp has radiation maxima at wavelengths of about 440, 550, and 610 nm; see Fig. 2.5. These wavelengths have spectral colors of blue, green, and red and cause trichromatic a neutral white light color. Fluorescent lamps are in widespread use only because of economic reasons: they have a luminous efficacy and a physical life which are about eight times higher than those of tungsten filament lamps, cf. Table 2.2. Light sources of principle importance in the near future are expected to be light emitting diodes (LEDs) and lasers, which greatly ripened technically in the 1960s. The central component part of an LED consists of a p–n semiconductor junction. A voltage between 1 and 15 V in conducting direction and a current of order 50 mA release photons in the p–n region. These photons are generated by an energy surplus from recombining electrons and defect electrons (holes). Available luminescence diodes doped with suited chemical compounds can emit quite monochromatic light with half-widths of 6–25 nm, for example, at wavelengths of 400 nm (gallium-nitride diode), 600 nm (gallium-arsenicnitride diode), and 660 nm (gallium-phosphide-zinc-oxide diode). The benefits of LEDs are the short switching time of about 5 ns, the small spectral 2.1 Optical Radiation Sources and Interactions of Light 21 Spectral energy distribution S(λ) 80 60 FL 11 40 FL 2 20 0 400 500 λ 600 nm Fig. 2.5 Spectral energy distribution of fluorescent lamps: cool white fluorescent CWF (illuminant FL 2) and three-band lamp TL84 (illuminant FL 11) Table 2.2 Properties of five selected illuminants Color Correlated color rendering temperature/K index Light efficacy/ lm/W 2,856 100 12 Tungsten filament lamp CIE standard D65 illuminant D65, middle daylight 6,500 94 35 UV-filtered xenon lamp Cold white daylight FL 2 4,230 64 70 Fluorescent lamp CWF, cool white fluorescent Bluish white daylight FL 7 6,500 90 80 Broadband fluorescent lamp 4,000 83 90 Three-band lamp TL84 CIE CIE illuminant abbreviation CIE standard illuminant A, evening light A White daylight FL 11 CIE simulator 22 2 Light Sources, Types of Colorants, Observer half-width of the emitted intensity, the high degree of optical efficiency, and the long working time. Disadvantages up to now have been the low illumination intensity in comparison to traditional light sources. Improvements in these respects, at the time of this writing, are the subject of ongoing research and development. The term laser is an abbreviation of “light amplification by stimulated emission of radiation.” A laser is, therefore, an optical amplifier which is based on the principle of stimulated emission of light. To initiate stimulated emission of light2 , an irradiating field, in some sense, forces the emission of light in atoms, molecules, or ions of gases, liquids, or solids. The incident field of frequency f has photon energy according to Equation (2.1.2). The primary requirement for stimulated light emission is that this photon energy is at least the natural energy difference of the medium. In such cases, the medium that has some population in an excited state has some return to the ground state. This emitted energy is incorporated into the incident field. In order to obtain an amplification of radiation by stimulated emission, the energetically higher levels or bands of a medium should maintain a state with a greater degree of filling. This greater electron number or population in the upper energy state is usually maintained using an energy supply such as flash lamps, other laser pump sources, currents in semiconductor laser, or atom/electron collisions. Typical classification of lasers is along the lines of the physical state of the gain medium: solid state (crystals), semiconductor, liquid (usually organic dyes), or gas lasers, for example. The ruby laser with emission wavelength of λe = 694.3 nm is a solid-state laser. Semiconductor lasers are, for example, indium-gallium-phosphide (In1-x Gax P) or aluminum-gallium-arsenide lasers (Alx Ga1-x As); the emitted monochromatic wavelength of each usually lies in the range 500 and 1,000 nm depending on the content x of the indicated element. Dye lasers are the dominant class of liquid lasers; typical laser mediums are dyes such as coumarin (460 nm ≤ λe ≤ 560 nm) or rhodamine (535 nm ≤ λe ≤ 630 nm). The most well-known gas lasers are the helium–neon laser (632 nm) and the argon-ion laser (wavelengths of highest intensity 488.0 nm and 514.5 nm). The advantages of lasers are clear, considering the outstanding features of the emitted light: constant frequency, highly monochromatic, spatial and temporal coherence, high beam directivity, and adjustable energy density. In the color industry, lasers have been successfully used for the determination of surface gloss, covering capacity and glittering of effect colorants, as well as size distribution of pigment particles in powders, among other things. In the following section, we concentrate on specific properties of light sources which are of special interest for colorimetric applications. 2 The opposite is absorption, or, more precisely, stimulated absorption. 2.1 Optical Radiation Sources and Interactions of Light 23 2.1.4 Illuminants In the previous section, the physical basics of light emission and the applications in technical light sources have been introduced. Now, we direct our attention toward the special handling of light sources in colorimetry or color matching. Unquestionably, the vast variety of technical light sources complicates the unambiguous visual assessment of colors: colored objects are exposed to changing natural as well as artificial illuminations such as daylight, evening light, or fluorescence light. The change in illumination can alter the visual color impression (see below). The CIE has, therefore, recommended the most representative light sources to use for color assessment applications. For clearness and better communication, four terms should be identified. These terms describe the different kinds of light sources: 1. CIE illuminant: this corresponds to a theoretical source of a tabulated relative spectral power distribution S(λi ); 2. CIE standard illuminant: only two illuminants are standardized by the CIE, illuminant A and illuminant D65; 3. CIE source: corresponds to a technically realized CIE illuminant; 4. CIE simulator: is a technical source which approximately corresponds to the desired CIE illuminant. The first and second terms need some further explanation. The CIE specified several representative illuminants [7], among them are the following: a. three temperature radiators designated D50, D55, D75 with color temperatures of 5,000, 5,500, and 7,500 K, respectively; b. twelve fluorescent lamps designated from FL 1 to FL 12; the illuminants FL 1–6 emit line spectra, FL 7–9 broadband, and FL 10–12 narrowband spectra. Among these, FL 2, FL 7, or FL 11 are preferably used in colorimetry. In Fig. 2.5, only the spectral power distribution of illuminants FL 2 and FL 11 are shown; c. in the end, five high-pressure lamps designated as HP 1–5, of which two are sodium vapor lamps and three metal halide lamps; these are normally not significant in colorimetry but rather in lighting engineering. The two CIE standard illuminants are characterized by the following features: the spectral power distribution S(λi ) of standard illuminant A is given by the Planck law of radiation (2.1.1), whereas that of D65 is given by tabular values [8, 9]. These values correspond to the UV-filtered emission of a high-pressure xenon lamp shown in Fig. 2.4. Standard illuminant A is recommended for simulation of room light in the evening, D65 of midday light of color temperature 6,500 K. 24 2 Light Sources, Types of Colorants, Observer The tabular values of a CIE illuminant are generally used for computation of color values. The corresponding simulation illuminant serves for visual assessment of color patterns. In other words, the real light source which is used to illuminate a color sample is, for the purpose of calculation, substituted by a theoretical simulation source, consisting of discrete wavelengths and power emission. This can clearly be a reason for deviation between the visual assessment and the colorimetric result. A further deviation can result from the so-called CIE standard colorimetric observers. This is not discussed until Section 2.4.6. The five most commonly used illuminants in colorimetry are D65, A, FL 2, FL 7, and FL 11; a selection of their properties is given in Table 2.2. While the standard illuminant A is assigned a true color temperature, the illuminant D65 and the fluorescent radiators have only correlated color temperatures. These are for the luminescence sources FL 2 –11: 4,230, 6,500, and 4,000 K, respectively. In most cases, the change of illumination also results in a change of perceived color. This can be caused either by the colorants themselves or by the light source used. If the spectral power distribution is responsible for color changes, this is attributed to the color rendering of the illuminating source. The yellowish light of the sodium vapor lamp HP 1, for example, bathes each chromatic color in a pale yellow. This is because sodium emits only two closely spaced wavelengths of 589.0 and 589.6 nm in the visible range. The CIE proposed the dimensionless color rendering index Ra to characterize the grade of color rendering of light sources [10–12]. This index takes values in the range 0 ≤ Ra ≤ 100. The sodium vapor lamp HP 1 has an Ra value of 20; this indicates that colors are quite distorted. In contrast, the CIE standard illuminant A takes the highest possible value of 100. An additionally used characteristic, which has a meaning in terms of energy, is the light efficacy of a radiator. This economic quantity is defined as the ratio of emitted luminous flux of a light source to the input power of unit lm/W.3 As can be seen from Table 2.2, the displayed fluorescence lamps show a higher light efficacy than temperature radiators of equal or lower color temperature. From a comparison of the spectral power distributions shown in Figs. 2.4 and 2.5, it is possible to understand how the change of a source alters the color impression. Consider Fig. 2.4: using source A, the color sample appears more yellow and red compared with illumination of a D65 simulator. This is because of the continuously increasing radiation energy characteristic of the source A from yellow to red wavelengths with quite small values at short wavelengths. Consider now Fig. 2.5: the same color sample is rendered bluish white with FL 2 source, or with FL 11 source, redder in comparison to D65 simulator. Colors 3 By definition, the unit lumen (lm) is the luminous flux which a point light source of emissiv- ity 1 cd (candela) emanates evenly in all directions in a solid angle of 1 sr (steradian): 1 lm = 1 cd sr; 1 steradian corresponds to a solid angle Ω – of even circular cone with center point in a sphere of radius 1 m – which cuts an area of 1 m2 out of the sphere surface, cf. Fig. 5.1. 2.1 Optical Radiation Sources and Interactions of Light 25 illuminated with a D65 or FL 7 source are rendered and perceived in a similarly balanced way as under midday light. This is because of the nearly constant and high values of the corresponding emission spectra in the visible range. 2.1.5 Geometric Optical Interactions There are various possible interactions between incident light and atoms, molecules, particles, or crystals. Of these interactions, we are primarily interested in the color appearances that result. In a plane electromagnetic wave, the electric and magnetic vectors E and H are perpendicular to one another, and, in addition, mutually perpendicular to the propagation direction. The so-called wave vector k is oriented in the propagation direction. The electromagnetic wave carries the energy flux density in the direction of k, given by vector S (named as Poynting vector) and relation S = E × H. (2.1.4) Figure 2.6 shows the connection between the three vectors E, H, and S. In the figure, the electric and magnetic vectors are shifted a quarter wavelength in phase with respect to one another. E S H Fig. 2.6 Electric and magnetic field of a stationary wave The amount of energy flux density S carried by such waves, also termed as flux density, or short flux, is the origin of interactions with the molecules or particles of colorants to produce colors. Color production of non-self-luminous colors can be caused by simple or multiple reflection, refraction, absorption, scattering, interference, and/or diffraction. When the wavelength of the light (order 0.4 to about 1 μm) is much smaller than the size of the objects that it interacts with (i.e., macroscopic objects), the light no longer behaves strongly as a wave, but rather propagates in straight lines according to geometrical optics. Reflection, refraction, absorption, or scattering can occur simultaneously if the light is incident on macroscopic boundary surfaces consisting of mediums with different optical densities. The polarization 26 2 Light Sources, Types of Colorants, Observer of light can intensify normal color appearance. This can appear especially for some absorption pigments and liquid crystal pigments. Materials can be illuminated by directional, diffuse, or mixed light. Quite simple, but of great importance, is the directional reflection – also denoted as specular reflection. Directed reflection arises from directional light at smooth, polished, or glossy surfaces, for example at organic binders, synthetic polymers, glasses, metals, as well as colorations with absorption and effect pigments. According to the reflection law, the angles of the incident ϑi and reflected light ϑ r , measured with respect to the normal of the reflecting surface, are equal: ϑi = ϑ r . Additionally, both rays and the normal of the reflecting surface lie in the same plane, that of the paper in Fig. 2.7. It is important to note that for visual assessment of colorations of glossy surfaces one must strictly avoid observations in the direction of the specular angle. For visual inspection of absorption colorations with collimated light, the surface should be illuminated from the side and the observation performed perpendicular to the sample surface. In contrast, the visual assessment of effect colorations requires a sophisticated procedure, cf. Figs. 2.29 and 2.30. ϑi ϑr Fig. 2.7 Depiction of the reflection law with incident and reflected beams, as well as angle of incidence, and specular angle, each from normal to the surface If the medium behind the glossy surface is transparent and of different refractive index than the first medium, the beam is additionally refracted into this medium. The refracted ray deviates from the original direction, see Fig. 2.8a, b, due to the different indices of refraction in the two media. The angle of refraction ϑ 2 depends on the angle of incidence ϑ 1 and the ratio of refractive indices n2 /n1 of the adjoining mediums according to Snell’s law of refraction sin ϑ1 n2 = =n sin ϑ2 n1 (2.1.5) (original W. Snel van Royen, 1621). In general, the refractive indices are also wavelength dependent, this normally results in violet light being refracted at a steeper angle than red light. This property is called dispersion [2] and results in prism effects. 2.1 Optical Radiation Sources and Interactions of Light 27 ϑ1 ϑ2 n1 n1 n2 n2 ϑ2 ϑ1 a) b) Fig. 2.8 Refraction of light at the boundary surface of (a) an optically thinner medium and (b) an optically denser medium The reflected fraction r(μ, n) of the directional beam at the boundary surface follows from the Fresnel equation 1 μn − w 2 μ − nw 2 r(μ,n) = + , (2.1.6) 2 μn + w μ + nw where μ = cos ϑ , w2 = 1 − (1 − μ2 )n2 (2.1.7) [13, 14]. Equation (2.1.6) can be derived from Maxwell equations of electrodynamics [14]. The reversal of light direction does not change the reflected fraction nor the law of refraction. The reversibility of the light path without change of effect is a general principle of geometrical optics [15]; this principle is used in color measuring methods among other things (Section 4.1.2). In the case of light incident perpendicular to the surface, the special reflected fraction is given by n−1 2 . (2.1.8) r(1, n) = n+1 This follows from Equations (2.1.6) and (2.1.7) using μ = 1. For air with refractive index n1 ≈ 1.0, for example, and plastics or binders with a typical value n2 = 1.5, using n = n2 /n1 , the normal incidence reflected fraction is r = 0.04.4 In other words, under these conditions, 4% of the incident light is immediately 4 The cited refractive indices in this book represent values which – as usual – belong to the wavelength of the sodium line of 589.0 nm. 28 2 Light Sources, Types of Colorants, Observer reflected from the surface of a colored sample; this amount is not available for further light interactions in the volume of a color sample. The reflectance of pure metals follows from Maxwell’s equations as well, provided that the complex refractive index n̂ is introduced: n̂ = n(1 + iκ). (2.1.9) The quantity n̂ is divided into the real part n for the refraction and the imaginary part nκ describing the light absorption at the interface. The quantity κ is √ named attenuation coefficient. In Equation (2.1.9), i is the imaginary unit (i = −1). For directional light incident perpendicular to the metal surface, the reflected total amount is given by r(n, κ) = (n − 1)2 + (nκ)2 . (n + 1)2 + (nκ)2 (2.1.10) For κ = 0, this formula reduces to Equation (2.1.8). The product nκ is termed as absorption coefficient; some measured values of n, nκ , and r(n, κ) for metals used for metallic pigments are listed in Table 2.7. A further sort of reflection occurs if a light beam enters an optically thinner medium coming from an optically denser medium. Note that the refracted ray cannot exceed an angle ϑ 2 = 90◦ ; see Fig. 2.9. For a refractive index n = 1.5, the corresponding incidence angle is ϑ 1 = 41.8◦ . In general, from the law of refraction (2.1.5), it follows that rays, with angles of incidence with γcr ≥ arcsin (1/n), are totally reflected back into the optically denser medium. The quantity γcr is called the critical angle of total reflection or in short critical angle. If ϑ2 n1 n2 ϑ1 γcr γcr Fig. 2.9 Critical angle γcr at a boundary surface of different refractive indices 2.1 Optical Radiation Sources and Interactions of Light 29 the total reflected light cannot immediately leave a colored layer, it participates further in the interactions with the color-producing particles until it is absorbed or leaves the layer. Total reflected rays of angles γ ≥γcr are called partly directed in this text. For unpolarized light, a further property follows from the law of refraction with regard to the refracted ray. In the case that the reflected and the refracted rays make a right angle, the light of the reflected ray is linearly polarized, in fact perpendicular to the plane of incidence; see Fig. 2.10. This special angle of incidence is denoted as Brewster angle ϑB and is given from the law of refraction (2.1.5) with ϑ 2 = 90◦ – ϑB : tan ϑB = n. (2.1.11) Fig. 2.10 A reflected beam of Brewster angle ϑB is linearly polarized perpendicular to the plane of incidence ϑB n1 n2 ϑ2 The Brewster angle depends only on the ratio of the refractive indices at both boundary surfaces. For a ratio of n2 /n1 = n = 1.5, the Brewster angle of ϑB = 56.31◦ results. The critical angle γcr and the Brewster angle ϑB are shown in dependence on n in Fig. 2.11. Polarized light produces always more intensive colors than unpolarized light; polarized light is generated in some absorption colorants and especially in liquid crystal pigments. In addition to that from Equation (2.1.6) and the above considerations, the reflection coefficient of directional light depends on the direction of polarization parallel to the plane of incidence. These properties also follow from Fresnel equations [14]. This is shown in Figs. 2.12 and 2.13 for a refractive index value of n = 1.5 in dependence on the angle of incidence ϑi . The outer reflectance coefficient at the boundary of the optically thinner medium begins to differ from one another for the two rectangular linear polarizations already for small angles 30 2 Light Sources, Types of Colorants, Observer 100 Angle / degree 80 60 γcr 40 ϑB 20 0 1.0 1.2 1.4 1.6 Refractive index n 1.8 2.0 Fig. 2.11 Critical angle γcr and Brewster angle ϑB in dependence of refractive index n Outer reflection coefficient 1.0 0.8 Polarisation: parallel normal 0.6 n = 1.5 0.4 0.2 0 0 20 40 60 80 Angle of incidence ϑ1 Fig. 2.12 Outer Fresnel reflection factor as function of angle of incidence for polarization parallel and perpendicular to the plane of incidence of incidence (Fig. 2.12). This difference increases strongly with the angle of incidence. The inner reflection coefficient at the inner boundary of the optically thicker medium shows the same behavior but is compressed into the angle range 0 < ϑ2 < 41.8◦ ; see Fig. 2.13. The high increase of this reflection coefficient is caused by the critical angle of total reflection. Consider now diffuse illumination instead of directional light. This alters the reflection character. The majority of natural and artificial light propagates diffusely. Because of this, it is, perhaps, most reasonable to measure and visually 2.1 Optical Radiation Sources and Interactions of Light 31 Inner reflection coefficient 1.0 Polarisation 0.8 parallel normal 0.6 n = 1.5 0.4 0.2 0 0 20 60 40 Angle of incidence ϑ2 80 Fig. 2.13 Inner Fresnel reflection factor as a function of angle of incidence for polarization parallel and perpendicular to the plane of incidence judge color samples under diffuse illumination. Ideal diffuse light is in the forward direction inside an angle range of ±90◦ and of equal energy over the entire range of these angles. Because of that the radiation power, the optical interactions, and specially the reflection conditions at the boundary surfaces are changed. The reflection coefficients for diffuse radiation follow from energetic considerations leading to the relation 1 − rd∗ n22 = 1 − rd . n21 (2.1.12) The quantity rd∗ denotes the reflection coefficient of diffuse light at the boundary of the optically thinner medium with n1 and rd stands for the reflection coefficient of the optically denser medium. In Fig. 2.14, the reflection coefficients for diffuse light are represented schematically by arrows for simplicity. For diffuse illumination from air of n1 ≈1.0 in a layer of refractive index n2 = 1.5, the appropriate reflection coefficients rd∗ = 0.09178 and rd = 0.59635 come from Fig. 2.14 Reflection coefficients of diffuse radiation at a boundary surface of different refractive indices (schematically) 32 2 Light Sources, Types of Colorants, Observer 1.0 rd Reflection coefficient 0.8 0.6 0.4 rd∗ 0.2 r 0 1.0 1.2 1.4 1.6 Refractive index n 1.8 2.0 Fig. 2.15 Three sorts of reflection coefficients in dependence on refractive index n: r for directional illumination perpendicular to the surface, rd∗ for outer diffuse illumination, and rd for inner diffuse illumination of a material the literature [13]. The reflection coefficients for diffuse light rd∗ and rd as well as for directional light at perpendicular illumination r are shown in Fig. 2.15 in dependence of the refractive index n. The boundary surface reflection certainly complicates the visual and measuring assessment of colored samples: this surface reflection is superimposed on the entire visual impression as well as the spectrometric measuring results. But the essential and interesting parts of color sensation are generated by the light interactions in the volume of a colored layer. For the following, we define the reflection of an optical medium as the amount of incident radiation energy which is backscattered from the volume and this is superimposed by the surface reflection energy. Correspondingly, the transmission is the amount of the incident light energy which overcomes the interactions in the volume and exits the second boundary surface of the optical medium. The accompanying energies are called reflection and transmission energy; these are abbreviated by WR and WT . The electromagnetic field of a light wave can drive vibrations of suitable charge carriers in atoms or molecules of absorption colorants. This additional absorption of energy leads sometimes to emission of secondary radiation; this process is denoted as scattering. The scattering is elastic if the wavelengths of the incoming and scattered light are equal. This is the case especially within non-self-luminous colors but also for Rayleigh and Mie scattering (Sections 2.1.2 and 5.1.3, respectively). Inelastic scattering, however, produces a change of scattered wavelengths such as in Raman and Brillouin scattering [16]. 2.1 Optical Radiation Sources and Interactions of Light 33 In addition to scattering, a part of the incoming light energy is normally absorbed by the charge carriers of the colorant molecules and not scattered. This causes an increased molecular vibration energy and, therefore, a temperature increase of the coloration. The absorption of energy of amount WA is finally absent from the reflected, transmitted or scattered light. In the most colored layers, scattering and absorption occur simultaneously in different amounts, and additionally dependent on wavelength. The three mentioned energy components WR , WT , WA come from the incident energy Wi . Therefore, the energy conservation law, in our case, amounts to Wi = WR + WT + WA . (2.1.13) 1 = R + T + A. (2.1.14) Division by Wi results in The quantities R, T, A are denoted as follows: R = WR Wi reflectance, (2.1.14a) T = WT Wi transmittance, (2.1.14b) A = WA Wi absorption. (2.1.14c) These quotients are, for simplicity, also denoted as reflection, transmission, and absorption but also reflection factor, transmittance factor, and absorption factor, respectively. The law of energy conservation is an axiom of physics and is of fundamental importance; in the above formulation, it plays a central role in the entire radiative transfer of optical systems. The energy conservation law is even valid for each single wavelength, therefore, valid independent of the irradiated spectral power distribution. Furthermore, this law is independent of any specifications concerning the interacting particles of the optical medium. From that follows a basic realization, which is of great importance for the further discussions in this text: The resulting values of reflection, transmission, or absorption are characteristic quantities of the optical medium; in our case, they are essentially caused only by the colorants of the chromatic color. Reflectance and transmittance are determined with suitable color measuring instruments (Sections 4.2.1 and 4.2.2); absorption and scattering are characterized by corresponding optical constants which follow from optical models (Sections 5.1.2 and 5.1.4). Absorption and scattering are generally the most 34 2 Light Sources, Types of Colorants, Observer important quantities of absorption colorants. In effect pigments, however, the dominant processes are wavelength dependent such as interference or diffraction. The basic optical laws responsible for color production of pearlescent, interference, and diffraction pigments are discussed in the next two sections. 2.1.6 Interference of Light The colors produced by absorption colorants and metallic pigments are essentially based on processes such as reflection, absorption, and scattering and are occurring at the surface and in the volume of a colored sample. In contrast to that, impressive color effects are generated by interference of light waves in pigment particles composed of an appropriate sequence of layers. Interference is an effect caused by superposition of suitable waves (of, e.g., liquids, gases, electromagnetic fields, elementary particles). Interference of light is, for example, responsible for the colors of soap lamellas, oil films on water, or coated lenses [17]; the colors of opals, natural pearls, insect wings, or bird feathers are in addition based on interference. The colors of interference pigments result from light waves, which are reflected at the inner and outer layer boundaries and which superimpose with the incoming waves. The produced colors are controlled by the thickness and refractive index of the different layers among other things. The layer thicknesses vary from about 10 nm to 1 μm; see Fig. 2.40 [18]. Interference colors can be distinguished from normal absorption colors by the color change in dependence of the observation angle; this is in some way similar to diffraction colors. A necessary requirement for interference is the existence of coherence. Most of temperature and luminescence radiators emit incoherent waves, because the single atoms of the source oscillate independently from each other, only short wave trains are produced; between the single waves exists no constant phase relationship. Waves are coherent, if the time dependence of their amplitude is the same irrespective of a phase shift. In the case of harmonic waves, this means that the frequencies of the waves have to be the same; however, they can have a constant phase difference. Coherent sine-shaped waves must, therefore, be of equal frequency. Coherent waves can result, for example, from the reflection of a radiative field at a mirror. From this perspective, laser light is of nearly perfect coherence because it is amplified during multiple reflections. Interference pigments normally consist of at least two layers of different refractive indices to produce a suitable reflection at the boundary layer, cf. Equation (2.1.6). In Fig. 2.16, there is a simplified illustration of the reflection and interference of light at a plane parallel layer. The reflected waves of beams R1 and R2 interfere above the layer. The waves of R1 initiated by R1 take a longer way to the surface and, therefore, have an optical path length difference G with regard to the waves of R2 . In view of the different path lengths, the ratio of refractive 2.1 Optical Radiation Sources and Interactions of Light R1 R2 35 R'1 ϑ1 R'2 ϑ1 n1 n2 d ϑ2 n3 Fig. 2.16 Interference at a plane parallel layer of different refractive indices indices n = n2 /n1 , the refraction law (2.1.5), and the phase jump of λ/2 caused by reflection of the waves at the upper layer surface, the difference G is given by G = 2d · λ n2 − sin2 ϑ1 + , 2 (2.1.15) where d stands for the layer thickness and ϑ1 for the angle of incidence. At some locations, the wave amplitude is increased by the so-called constructive interference of the incident and reflected waves. This occurs if G is an evennumbered multiple 2z of λ/2, fulfilling the condition: (2z − 1)λ = 4d · n2 − sin2 ϑz , z = 1, 2, 3, ... . (2.1.16) Destructive interference occurs for G = (2z + 1)λ 2, z = 0, 1, 2, ... . (2.1.17) The positive integer z is called interference order. The amplifying light waves and, therefore, the corresponding colors can be modified according to Equation (2.1.16) by the material quantities d and n; this is used to a great extent for realization of different kinds of pearlescent and interference pigments. For color sensation, the additional change of color impression in dependence on the observation angle ϑz can be quite strange. The quantity ϑz belongs to the different interference orders z instead of the constant angle ϑ1 . Generally, the intensity of the amplified waves decreases strongly with the number of z. 36 2 Light Sources, Types of Colorants, Observer Some special interference features result in the case that light is incident perpendicular to the surface of a layer. Colors of pearlescent and simple interference pigments are visually characterized by observation perpendicular to the colored surface; some important technical applications come out of this. From Equation (2.1.16) with ϑ1 = 0 for the dominant first interference order (z = 1), the simple result d = λ/4n follows. Furthermore, if the interference wavelength λ and the refractive index n are constant, the layer thickness for order z, given by d = (2z − 1)λ 4n, (2.1.18) leads to constructive interference. A stepwise increase of the layer thickness by the quantity d leads to a distance of Δd = λ/2n between two adjacent intensity maxima. The same distance holds for neighboring minima. These considerations are especially used to reduce the reflection of optical systems by destructive interference. With the so-called optical coating, the optical surfaces are coated with an inorganic layer by physical vapor deposition; the refractive index nC of the coating has to satisfy the condition √ (2.1.19) nC = n1 n2 , where n1 and n2 are the refractive indices of air and of the optical material, respectively. Unfortunately, the effectiveness of reflection reduction is limited to a middle visible wavelength. To achieve a nearly regular reduced reflection of wavelengths in the entire visible range, a multi-layered coating on both sides of the optical element is necessary at the most 10 layers which are tuned with each other. This is a type of dielectric coating called an anti-reflection coating. The so-called dielectric mirror coating relies likewise on interference. For this, multi-layer coatings of alternately higher and lower refractive indices nh and n1 are produced; see Fig. 2.17. If each single layer has a constant optical thickness dh = λ/4nh or dl = λ/4nl , then the reflected waves of first order interfere constructively with the incoming light caused by the additional phase jump at the boundary of the optical denser medium. Therefore, a narrowband mirror results; the reflectivity depends on the difference of the refractive indices of the layers [17]. With change of the layer parameters, the width of the wavelength interval can be controlled. These considerations are also used to achieve suitable layer structures in pearlescent and interference pigments to produce a dominant color component. Interference colors can be further improved by multiple reflection of light between two semi-transparent mirrors at distance d, similar to the placement in a so-called Fabry–Pérot interferometer; see Fig. 2.18. One part of the reflected light is transmitted through the second layer. Multiple reflection leads to a great number of partial beams, which interfere behind the second layer. The layer distance d and the refractive index n of the medium between the layers are chosen in such a way that only a small wavelength band is transmitted; this construction 2.1 Optical Radiation Sources and Interactions of Light 37 Fig. 2.17 Layer sequences of a dielectric mirror with high and low refractive indices nh and n1 nh nl nh nl dh = λ 4nh dl = λ 4nl Substrate operates as an interference filter. For fixed distance d, this construction is also called an etalon. The deciding parameters for the interference efficacy are n and d of the intermediate layer. Because adjacent beams have the same geometrical optical path difference, constructive interference is given by zλ = 2nd cos αz , z = ±1, ± 2, ... . (2.1.20) The intensified wavelengths become, therefore, smaller with increasing angle of beam incidence α z . For a layer thickness d = 300 nm and refractive index n = 1.5, the wavelengths of violet and red light (400 and 700 nm) are separated for the first order by an angle difference of about 25◦ . Founded on this principle, d L LQ P Q1 n Q αz Fig. 2.18 Fabry–Pérot interferometer: the partial waves of points Q, Q1 produce interferences of “equal inclination” 38 2 Light Sources, Types of Colorants, Observer in particular, is the angle-dependent color effect of multi-layered interference pigments in liquid crystal structures; see Fig. 2.43. 2.1.7 Diffraction from Transmission and Reflection Gratings When light is incident on objects or boundaries with dimensions on the order of the wavelength of the light, the wave characteristics of light become very important. This is the situation, for example, at a diffraction grating. Upon passing through the grating, some portion of the light is deflected and/or is fanned out depending on the grating geometry and the wavelength. This phenomenon is an example of Fraunhofer diffraction if the light beam is incident nearly perpendicular to the grating [19]. In addition to macroscopic structured materials, diffraction pigments can be impressed with such grating structures. This leads to color effects which are also depending on the angle of observation. A simple macroscopic transmission grating is shown in Fig. 2.19, not to scale. The geometry is simply achieved by scratching or etching of equidistant grooves in a thin plane parallel glass sheet. With recent techniques, diffraction pigments can be impressed with nanostructures. Each constant groove gap d, also called grating period, contains a narrow light-transmitting slit. The reciprocal quantity of the grating period, g = 1/d, is denoted as the grating constant; its units are given in lines per millimeter (l/mm). At each of the slits – which are spaced with typically as much as 5,000 l/mm or more – the incident wave front αz αi d αi G1 αz G2 Fig. 2.19 Diffraction conditions of an optical transmission grating (schematically) 2.1 Optical Radiation Sources and Interactions of Light 39 is diffracted according to the Huygens principle, which means that each point of a wave front is assumed to be the origin of a new elementary wave [19]. Because diffraction occurs at all illuminated grating slits, a pattern of constructively and destructively interfered waves develops behind the grating. The path difference G1 + G2 of waves coming from two neighboring slits follows from Fig. 2.19 as G1 + G2 = d(n1 sin αi + n2 sin αz ), (2.1.21) where n1 and n2 stand for the refractive indices in front and after the grating and α i for the angle of incidence. The diffraction maxima occur for a path difference G1 + G2 equal to an integer multiple z of the wavelength λ. With Equation (2.1.21), the relation zλ = d(n1 sin αi + n2 sin αz ), z = 0, ± 1, ± 2, ..., (2.1.22) follows. The zeroth-order diffraction, equivalent to z = 0, contains all wavelengths of the irradiated light. Higher diffraction orders for z = 0 are generated on both sides of the zeroth order with symmetric intensity maxima and minima. The wavelengths contained in the incident light fan out by the grating in such a manner that the condition in Equation (2.1.22) is fulfilled. The grating deflects large wavelengths stronger than shorter wavelengths; this is the converse of a prism. Moreover, the diffraction spectrum of the first order is of higher intensity compared to that of a prism spectrum. In order to avoid an overlapping of the diffraction maxima of higher order, the incident angle α i and the grating period d can suitably be tuned with each other (see below). In addition to transmission gratings, reflection gratings are also commonly used – these are especially realized in diffraction pigments. These can be formed by vapor coating both sides of a nontransparent grating structure with an additional layer of a reflecting metal, cf. Fig. 2.20; this has the added bonus of a possible improvement in the mechanical stability of the thin plates. The waves reflected from the periodically arranged mirrors interfere with the incoming waves from the opposite direction. Consequently, the diffraction pattern already known from transmission gratings develops in front of the reflection grating. The cross section of the grooves can be produced as rectangular, triangular, or sine shaped. Reflection gratings are used in modern spectrophotometers and optimized diffraction pigments, among other things. Examples of diffraction particles are shown in Figs. 2.54 and 2.55. Concerning the reflection grating in Fig. 2.20, the path difference G1 – G2 of the reflected waves from adjoining grooves follows from the expression G1 − G2 = d( sin αi − sin αz ) . (2.1.23) 40 2 Light Sources, Types of Colorants, Observer Fig. 2.20 Diffraction conditions of an optical reflection grating (schematically) αi G2 αi d αz G1 αz In analogy to the transmission grating, the diffraction maxima are given by zλ = d( sin αi − sin αz ) , z = 0, ± 1, ± 2, ... . (2.1.24) For z = 0, it follows α i = α 0 and the grating operates like a normal flat mirror, that is, the wavelengths are not separated. Generally, the use of gratings results in spectra of higher light intensity in comparison to prisms, but the incident intensity is distributed among all diffraction orders. Among them, is the maximum for z = 0, which is of highest intensity, and also generally not of interest (see Fig. 2.21). This disadvantage can be bypassed using a so-called echelette grating5 ; see Fig. 2.22. On the basis of the special geometry of such a grating, nearly the entire intensity of the diffracted light can be concentrated into a particular diffraction order, as required. To achieve this aim, the cross section of the grooves has to meet the following requirements: 1. The desired diffraction order zB is not zero; the reflecting grating elements should be tilted by an angle α B above the grating base; this angle is called the blaze angle, after the corresponding production method known as the blaze technique. 5 echelette: French, small ladder. 2.1 Optical Radiation Sources and Interactions of Light 41 Δα Δβ Fig. 2.21 Angle differences of diffraction maxima 2. The angle half-width α of the diffraction fringe, caused by this kind of grating element, has to be matched with the angle distance β between two successive diffraction maxima; see Fig. 2.21. In view of the first condition, it is useful to consider the angles from the grating base normal. The blaze angle is, therefore, given by the simple relation αB = (αi − αz ) 2, (2.1.25) where α i and αz are the angle of incidence and the diffraction angle of order z, respectively. In addition, these two angles are combined with Equation (2.1.24), to give zB λB = d · (sin αi − sin αz ) , Grating normal zB = 0, ± 1, ± 2, ... . Face normal αB αi αz b αB d Fig. 2.22 Echelette grating with blaze angle α B (2.1.26) 42 2 Light Sources, Types of Colorants, Observer The quantity λB is called blaze wavelength and zB denotes the blaze order. According to Equation (2.1.25), the blaze angle depends on the incident and the diffraction angles. For this reason, echelette gratings can be realized with different blaze angles. From the last two expressions, the condition zB λB = d · [ sin αi + sin (2αB − αi )] , zB = 0, ± 1, ± 2, ... (2.1.27) follows. It is independent of a diffraction angle. For improved understanding, we differentiate now between two types of light incidence – from which consequently follow different blaze angles. In the first case, we assume an illumination in the direction of the grating normal; see Fig. 2.22. In this case, the angle of incidence is α i = 0 and it follows from Equation (2.1.27): zB λB 1 , zB = 0, ± 1, ± 2, ... . αB = arcsin (2.1.28) 2 d In the second case, the light is incident in the direction of the face normal, the so-called Littrow or autocollimation configuration. In this case, then the incident angle is equal to the blaze angle α i =α B given by zB λB (2.1.29) , zB = 0, ± 1, ± 2, ... . αB = arcsin 2d Note that because an echelette grating of sine-shaped cross section can be approximated by a series of successive isosceles triangles, the outlined considerations are also applicable to that geometry. From the second condition above, some further geometrical conclusions result. With the designations given in Figs. 2.20 and 2.22, the relation cos αz b = d cos (αz − αB ) (2.1.30) can be derived. In other words, the triangle geometry depends on the blaze angle as well as the angle αz of diffraction order z. Additionally, according to Equation (2.1.30), the width b of a step is specified with the groove distance d. If the illumination is carried out parallel to the grating normal, from Fig. 2.22, we have the intermediate result α z = 2α B . The condition b=d· cos 2αB cos αB (2.1.31) therefore follows. On the other hand, for illumination parallel to the face normal, the condition α z = α B is given and the simple formula b = d · cos αB (2.1.32) 2.2 Absorbing Colorants 43 follows from Equation (2.1.30). In this case, the triangle of the echelette grating is right angled. The utilizable wavelength range of such kinds of gratings is roughly limited to the interval 0.7λB ≤ λ ≤ 2λB . Absorption and scattering dissipation reduce the efficiency of a blaze grating to about 70% [20]. Accordingly, the blaze technique enables the focusing of about 70% of the influx into a desired z = 0 diffraction order. Each diffraction pigment is normally optimized with regard to the first diffraction order z = ±1. This diffraction spectrum can be observed symmetrically with respect to the direction of illumination, and is followed by further orders of lower intensity, cf. Section 3.5.5. These principles apply not only to macroscopic gratings but also to diffractive pigment particles; see Figs. 2.55 and 2.56. 2.2 Absorbing Colorants After considering different light sources and basic light interactions in the previous section, the second fundamental component for color producing of non-self-luminous colors is the color sample containing the colorants. Colorants can be divided into two groups, depending on the dominant mechanism of color production: classical absorption colorants and modern effect pigments (cf. Table 1.1). Industrially applied absorption colorants consist mainly of synthesized colors of inorganic and organic compounds, and in some rare cases of modified natural colors. In this section, we characterize dyes and absorption pigments, describe the most important color attributes and the accompanying coloristic properties as well. Some of these properties are correlated with specific spectral features of the corresponding coloration. Additionally, color-order systems will be outlined. In some application cases, such systems offer an overview of the diverse-generated absorption colors. Each of these color order systems is grouped according to preset characteristic criteria. On one such system is based a special CIE color space. It is also shown that the color impression results from light interactions in the volume as well as at the surface of a color pattern. Properties of effect pigments are described in the next section, which show a typical color development in dependence of the angle of observation, a dependence that is absent in absorption colorants. 2.2.1 Types and Attributes of Absorbing Colorants According to a rough classification, colors can be produced by 15 different physical mechanisms [21]. In the case of non-self-luminous colors, these processes are entirely attributable to energetic interactions of electromagnetic waves with the bounded electrons of atoms, molecules, particles, or crystallites of the color-producing material. With regard to absorption colorants, we first outline 44 2 Light Sources, Types of Colorants, Observer some typical phenomenological properties of absorption pigments and afterward those of dyes. The color origin of absorption pigments can be reduced to absorption and scattering processes. Such kinds of light interactions are called selective if they are effective in a narrow range of wavelengths in the visible spectrum. Light is scattered by pigment particles if at least two conditions are met: first, the particle dimensions and the wavelengths of the irradiated light are on the same order of magnitude; second, the colorant molecules show spatially separated electric charge distributions – the so-called multipoles. Details of these are given in Sections 5.1.2 and 5.1.3. Chromatic absorption pigments are also called colored pigments or sometimes merely pigments. They consist of inorganic and organic compounds which, in either case, form crystallites of sometimes different types. The crystallite dimensions are typically of the same order of magnitude lesser as the wavelengths of light. Because of the charge separations in multipoles, the morphological non-uniform crystallites sometimes conglomerate to form differently shaped particles with sizes from 10 nm to as much as 1 μm in size. All sorts of pigments – absorption as well as effect pigments – are insoluble in a binder or any polymer matrix. The pigments are usually uniformly dispersible in such materials although some need a suited additive for that. These colorants are used not only, for example, for mass coloration of plastic materials, fibers, paper but also for coloring of lacquers, pastes, and coatings of solids of quite different surfaces. In synthetic high polymers, the pigments tend to congregate in the amorphous regions and, therefore, additionally change the mechanical, thermal, or even electrical properties of the compound. Of great importance – with regard to color physical applications – are the covering capacity (also called hiding power), color strength, and tinting power. Requirements for optimized incorporation of pigments are sufficient wettability, dispersibility, as well as compatibility of the binding materials used, polymers, or additives, among other things. Inorganic pigments consist of oxides, sulfides, sulfates, silicates, chromates, carbonates, and metal complexes, for example [22]. Compared to organic pigments, they are preferentially used on account of their distinct optical scattering power and the typical high hiding power. In comparison with organic pigments, due to their simple and stable molecular structure, inorganic pigments tend to have better rheological behavior as well as increased weather resistance. Characteristically, inorganic pigments are mostly dull colors with lower color strength but with greater hiding power compared to organic colorants. A multitude of absorbing colorations with desired color properties are, therefore, achieved only with mixtures of inorganic and organic pigments. With regard to the chemical structure, organic pigments are divided into azopigments, polycyclic pigments, and anthraquinone pigments. The outstanding feature of organic pigments is their distinctive colorfulness or chroma in comparison to inorganic pigments. This generally comes with a high color strength. 2.2 Absorbing Colorants 45 Compounds of polycyclic structures, compared to molecules with azo-groups, tend to disperse better in polymer binders, have a lower migration tendency, as well as higher weather durability [23]. Table 2.3 shows the most commonly used modern inorganic and organic absorption pigments, differentiated with regard to the kind of the dominant color production mechanism. White and black pigments assume a special role in industrial color physics. White pigments stand out due to their nearly ideal scattering of light in the visible range. They are preferentially used for pure white, increase in the lightness of any coloration, or covering of a background. On the other hand, the characteristic feature of black pigments is the dominant absorption. These pigments are applied mainly in tiny amounts for black colors and for darkening of absorption colors. With calibration series of white and black pigment mixtures, the calibration of the lightness scale is, therefore, carried out between minimal scattering (pure black pigment) and maximal scattering (pure white pigment). An analog consideration holds for the case of absorption (Section 6.1.1). It is further the case that a really tiny amount of a black pigment improves the interference color of transparent pearlescent or interference pigments; this is because the black amount absorbs the complementary color produced of interference pigments. Table 2.3 lists also fluorescence and phosphorescence pigments. These are summarized by the term luminescence pigments. Both sorts absorb light normally at lower wavelengths in the range of X-rays, UV, or the visible spectrum; they often also absorb energy from electron beams. After some short time, a part of the absorbed quantum energy is reemitted but with longer wavelengths (lower energy) according to Equation (2.1.2). Fluorescence radiation is emitted spontaneously and phosphorous radiation, in particular, has a delay in the reemission. In contrast to phosphorescence (Section 4.2.6), fluorescence emission stops immediately after illumination. Unlike absorption pigments, dyes are completely soluble in a solvent or in a polymeric medium. The coloristic properties are essentially based on absorption. On account of the absence of scattering, dyes are normally transparent – notable exceptions are dark dyes in high concentrations. Dyes consist nearly exclusively of organic chemical structures. Typical groups of atoms with covalent bonds such as >C=C<, >C=O, or –N=N– (ethylene, carboxyl, or azo group, respectively), called chromophores, are typically responsible for the coloration of the organic compounds. The π-electrons6 of these covalent bonds absorb a fraction of the incoming light waves. The incorporation of further molecular groups, the so-called auxochromes, causes a color shift either to 6 In chemical compounds π -electrons form a pair of electrons which belong together to two different atoms. Color production Selective scattering/ selective absorption Pigment Absorption pigment, colored pigment Oxides Iron-II-oxide, iron-III-oxide, chromium-III-oxide, chromium-IV-oxide, chromium-VI-oxide pigments Mixtures with oxide pigments: cobalt blue, cobalt green, zinc iron brown Chromate pigments Chromium yellow, chromium orange, chromium green; chromium titanate, molybdate red, molybdate orange; copper chromate Iron blue pigments Iron cyanide blue Cadmium, bismuth pigments, ultramarine pigments Inorganic Typical examples Table 2.3 Typical modern inorganic and organic absorption pigments Azo pigments Mono-pigment, disazo-pigment, β-naphthole pigment, naphthole AS pigment, benzimidazolon pigment, disazo condensation pigment, metal complex pigment Polycyclic pigments Phthalocyanine, carbazole, quinacridone, perylene, perinone, pyrrolo/pyrrole, thioindigo pigments Anthraquinone pigments Anthrapyrimidine, flavanthrone, pyranthrone, anthanthrone, dioxazine, triarylcarbonium, quinophthalone pigments Organic 46 2 Light Sources, Types of Colorants, Observer Color production Scattering Absorption Selective absorption, emission within 10 ns Selective absorption, emission after 1 ms Pigment White pigment Black pigment Fluorescent pigment Phosphorescent pigment Pure phosphors Alkaline tungsten salts Other phosphors Alkali halogenoids, alkaline earth oxides, alkaline earth sulfides, Barium oxide: doped with Na, Mn, Ce, Sn, Cu, Ag; zinc phosphide, cadmium phosphide, gallium sulfide, zinc sulfide, cadmium selenide, gallium phosphide Fluorite, uranylic salts, salts with metals of rare earths Carbon black, iron oxide black, copper chromate Titanium dioxide (anastas, rutil), zinc sulfide, zinc oxide pigments Inorganic Typical examples Table 2.3 (continued) Pure phosphors Carbazoles Other phosphors Fluorescent organic substances, embedded in crystalline matter Oxinaphthaldazine, disazomethine Aniline black White plastic powders Organic 2.2 Absorbing Colorants 47 48 2 Light Sources, Types of Colorants, Observer higher wavelengths as with –NH2 and –OH groups (amino and hydroxyl groups, respectively) or to lower wavelengths with –NH–CO–CH3 (ethylene-acid-amide group), for example. Dyes are subdivided into natural and synthetic compounds; see Table 2.4. Dyes found in nature are generally known by common names like indigo, crimson, saffron, or alizarin, although they are prepared partial artificially today. For reasons of product constancy, generally only synthetic dyes are applied. Among synthetic dyes are azo-dye, anthraquinone dye, indigo dye, cationic dye, phthalocyanine dye, polymethine dye, triphenylmethane dye, xanthene dye, and fluorescence dye [24, 25]. Owing to their molecular double bond structures, dyes show a poorer fastness to light and weather resistance in comparison to pigments. The basic molecular interactions of fluorescence dyes and pigments are described in the literature [26]. Table 2.4 Typical examples of natural and synthetic dyes Dye Typical examples Natural Indigo, crimson, saffron, alizarin Synthetic Azo-dye, anthraquinone dye, indigo dye, cationic dye, phthalocyanine dye, polymethine dye, triphenylmethane dye, xanthene dye, fluorescence dye 2.2.2 Pigment Mixtures and Light Transmittance The wavelengths of the visible range which are not absorbed by colorants make up a so-called complementary color. This color is the perceived color of the absorbing dye or pigment; see Table 2.5. It can be seen in the table Table 2.5 Spectral range of absorption, light color, and perceived complementary color of absorption colorants Rough spectral range of absorption/nm Light color of the spectral range Perceived complementary color of the colorant 380–440 440–480 480–490 490–500 500–560 Violet Blue Green blue Blue-green Green Yellow-green Yellow Orange Red Crimson 560–580 580–595 595–605 605–750 750–780 Yellow-green Yellow Orange Red Crimson Violet Blue Green blue Blue-green Green 2.2 Absorbing Colorants 49 that the light and complementary colors reverse their roles at a wavelength of about 560 nm. Over and above that, in Table 2.19 are given some pairs and triples of complementary colors; some of them are partly demonstrated in Color plate 1.7 These relationships concerning complementary colors are valid for uniform spectral power distributions of the irradiated light similar to a xenon discharge lamp. Complementary colors are arranged opposite (according to Hering color opponent theory) in a color plane of the CIELAB system; see Color plate 4. As mentioned in the previous section, the realization of a desired color is normally achieved with mixtures of different sorts of colorants. Apart from coloristic aspects, concerns over the compatibility and color fastness of the components are in the forefront. Colorations of lacquers, plastic materials, or textile fibers consist usually of mixtures with three up to six or more different colorants. Mixtures of different fluorescence dyes can be distorted by fluorescence extinction if the quantum emission of one dye in the visible range causes a fluorescence stimulation of a second dye in this range. For the realization of a great number of different color shades, a selection of at least 25 up to about 130 chromatic, white, and black absorbing pigments has to be made and as much as of 110 effect pigments. Among the colored absorption pigments, normally yellow and red should preponderate in comparison to violet, blue, or green shades; additionally, two to four brown colorants are normally taken into consideration. Similar considerations should be taken into account for dyes. The predicted color should match the reference color as exact as possible. In the majority of cases, there are additional properties, such as high color constancy or low metamerism, which need to be fulfilled. It is, therefore, necessary to have a broad experience with the composition of the colorant components and binding materials for mixing in order to achieve the coloristic, processing, or basic performance conditions required with regard to the reference color. Color samples are termed as transparent, translucent, or opaque in dependence on their light transmittance properties. Requirements for transparent colors are not only pure absorption and complete solubility of the used colorants but also the refractive indices of the applied colorant matrix (e.g., solvents, binding agent, or plastic materials) have to agree with those of the used colorants. Transparent optical media are characterized by the wavelength-dependent absorption coefficient. This coefficient follows from the spectrometric measurements of the transmittance and a suitable approximation of radiative transfer in optical media (Section 5.1). A transparent chromatic layer is perceived by way of not only transmitted light but also reflected light. The accompanying reflectance comes merely 7 Color plates are inserted between Chapters 3 and 4. 50 2 Light Sources, Types of Colorants, Observer Table 2.6 Light transmittance and spectral quantities of color samples Measuring quantities Determination quantities Examples Transparent Directed, diffuse reflectance and transmittance Absorption coefficient K Liquids, inorganic, organic glasses Translucent, translucent nonopaque, translucent glimmering Directed, diffuse reflectance and transmittance Absorption coefficient K, scattering coefficient S, phase function p Binders, foils of partially crystalline high polymers, paper, opal glasses Opaque Directed, diffuse reflectance Absorption coefficient K, scattering coefficient S, phase function p Emulsion paints, lacquers, plastics, textiles, ceramics, leather Light transmittance from reflection at the illuminated outer and inner boundary surfaces which is caused by differing refractive indices. The magnitude of the reflected portion follows from Equations (2.1.6), (2.1.7), (2.1.8), (2.1.9), (2.1.10) or (2.1.12). In Table 2.6, three different sorts of color samples with regard to the degree of light transmittance are listed along with some spectral measuring and determination quantities. Translucent color patterns such as turbid films, paper, or opal glass are characterized by selective absorption and simultaneous scattering. Translucent media are only light transmitting on a small scale; nonetheless, a colored background is not completely covered. The light transmittance decreases with increasing layer thickness, this is similar to transparent layers. Some organic pigments of light yellow, orange, or red shade are translucent as are some pearlescent and liquid crystal pigments. The scattering of light occurs at the irregular surfaces or edges of the pigment particles and caused by the electromagnetic interactions with the multipoles of the pigment particles. In general, scattering of translucent colors depends on the pigment sorts used, the chemical structure of the surrounds, the refractive indices, and the structure of the boundary surfaces. Translucent colorations are particularly of interest for such coloristic applications, in which the same hue is to be realized simultaneously in a nearly transparent and almost opaque finish. In addition to reflectance and transmittance, the characteristic quantities of translucent color samples are turbidity and covering capacity (Sections 3.4.3, 3.4.4, and 3.4.5). The theoretical modeling of radiative transfer in translucent systems can actually be quite difficult. These complications are caused by the combined processes of absorption and scattering, where the latter is anisotropic in some 2.2 Absorbing Colorants 51 cases. On the basis of the different optical effects, translucent materials can be subdivided into the following groups: ideal translucent: a directional ray is partly absorbed and diffuse scattered; it exits the medium with lower intensity; translucent diaphanous: the primary ray in the optical medium is surrounded by a halo8 ; the primary ray is more attenuated than in the ideal translucent case; translucent gleaming: the energy of the primary ray is spread out in an intense halo; there is virtually no primary ray remaining at the second boundary surface. These different translucent states are best modeled with a multi-flux approximation. For this, in addition to absorption and scattering coefficients of the optical medium, some additional optical quantities such as the phase function p, for example, need to be taken into consideration (Section 5.1.5). The majority of natural and artificial non-self-luminous colors are opaque; they, therefore, appear impenetrable from the rear – a background is covered completely by this kind of colors. In all opaque systems light scattering is normally the dominant process, and it is accompanied by more or less distinct absorption. Scattering occurs isotropically without a preferred direction or, the other extreme, anisotropic with a specific preferred direction. Increasing scattering lowers the light transmittance and vice versa. The covering capacity of a coloration is, above all, caused by the scattering power of the pigment particles. The single spectrometric measuring quantity of opaque materials is the reflectance. The reflectance, in general, depends on the measuring angle for many kinds of effect pigments. Extreme optical states result in mixtures of absorption and effect pigments with different light transmittance. These are most often implemented in lacquers or plastic materials for consumer goods. 2.2.3 Description of Color Attributes Based on the discussion in the previous sections, it should be clear that the color of absorbing colorants is caused by light interactions such as scattering and absorption. On the other hand, the produced visual color sensation is by no means completely characterized by those. The variety of different combinations of wavelengths as well as the accompanying power distributions reaching the eye results in many colors, which can be described by different color attributes. For better understanding of the context, we use an analogy from acoustics. 8 This is a circular light spot encircling the primary ray; the halo of the Moon, for example, results of light refraction at the ice crystals in the atmosphere. 52 2 Light Sources, Types of Colorants, Observer A pure acoustic tone is unambiguous, physically described by its frequency and amplitude. The same tone, produced from different music instruments, is however surrounded by a typical sound spectrum. In a similar way, each nonself-luminous color is produced not simply by a single light frequency but also from various spectral values of the visible spectrum.9 The different wavelengths simultaneously entering the eye are perceived as a single color impression and not as separate single-colored wavelengths. This entire color impression can be verbally described by characteristic terms. The description or comparison of colors is used in color industry not only from physical or colorimetrical points of view but also according to coloristical attributes [27]. The following enumeration, which is not to be considered complete, gives some conventional terms for characterizing the color impression of non-selfluminous colors. The accompanying definitions and assemblies are, however, not uniformly used in the literature: hue, shade: the color property which is mainly described by adjectives such as red, green, yellow, blue; hue and shade are terms equivalent to color tone, or tint, see below; relative color strength, relative tinting strength: the color economy of an available colorant material relative to an arbitrarily chosen colorant of equal or similar color; color depth, color intensity: the color distinctiveness, which increases with enhancement of the same colorant amount; dullness: a characteristic color feature which can be described by an existing amount of gray or black; it is the converse to brightness. The quantitative determination of relative color strength is standardized based on colorimetric criteria (Section 3.4.2). These instructions underlie the formalism of the CIELAB or DIN99o color spaces. The following terms are also used to denote a color point in color space: lightness: a measure for the reflectance of a non-self-luminous colorant; the reflection ratio of absorption colorants is standardized by the so-called gray scale in which black is assigned to the value of 0 and white to the value 1; fluorescent and effect colorants often have reflectance values greater than 1, caused by the arbitrary fixing of the gray scale; selfluminous sources such as light sources or the sky are characterized by the term brightness rather than lightness; saturation: a quantity describing the colorfulness of colorants which does not change by further increase of the colorant concentration; shade, color tone: this corresponds to hue; equivalent terms are tint or tinge; 9 This metaphor is not to be confused with synesthesia, in which a physiological stimulus induces a further stimulus, for example, colors are associated with music and vice versa. 2.2 Absorbing Colorants 53 chroma: an absorption colorant loses colorfulness with lower saturation; chroma depends on both saturation as well as lightness because a tiny amount of black reduces the colorfulness of a color.10 Common for characterization of color impressions are also adjectives and their comparative forms; their meaning is somewhat equivalent to the terms already given above. Here are listed properties in opposing pairs: colored, chromatic: any color, such as yellow, orange, red, or green; it is analogous to the term hue; uncolored, achromatic: colors like white, gray, or black; light, bright: a color with a high lightness amount; light colors have a high reflectivity; dark: colors of small or even zero reflectance; brilliant, clear, pure: colors of both high hue and high lightness but missing white amount; pale, dirty, dull: colors of both minor hue and minor lightness. A great number of non-self-luminous colors containing absorption colorants can be directly manufactured with properties in the ranges of the last 12 listed extreme color states. Some of the cited characteristics correlate also with typical special features of the corresponding spectral reflection or transmission curve traces. The measured spectrum can sometimes be interpreted as a kind of “finger print” of the accompanying color. Some of these properties can be visualized by characteristic spectral reflection curves of absorption pigments, for example, in Figs. 2.23–2.27. Some of these features can also be found by the angle-dependent spectral reflection of effect pigments. The spectral reflectance of a chromatic absorption color is generally characterized by either a significant maximum (e.g., violet, blue, green) or a steep rise to higher wavelengths (e.g., yellow, orange, red) in the wavelength range of the complementary color or rather natural color; see Fig. 2.23. The highest absorption exists in a wavelength range of a distinct reflection minimum; backscattering, however, dominates in the range of maximal reflection or the plateau region of the relevant pigment. In contrast, an achromatic color shows a nearly constant spectral reflectance; see Fig. 2.24. Ideally scattering white is represented in the visible range by a constant reflection of 1.0 and ideal black of 0.0; gray takes intermediate values depending on the content of white or black. The decrease of spectral reflection for white or gray with shorter wavelengths is due to the tail of the UV absorption of the underlying TiO2 pigment. The impression of white results exclusively 10 These four color terms can be visualized by geometrical quantities in both mentioned color spaces and further ones; see Sections 3.1.3 and 3.1.4. 54 2 Light Sources, Types of Colorants, Observer R(λ) c 0.8 d e 0.6 b a 0.4 0.2 0 400 500 600 λ 700 nm Fig. 2.23 Spectral reflectance curves of chromatic pigments: (a) blue, (b) green, (c) yellow, (d) orange, and (e) red R(λ) a 0.8 0.6 b 0.4 0.2 c 0 400 500 600 700 λ nm Fig. 2.24 Spectral reflectance curves of achromatic colors: (a) white, (b) gray, and (c) black 2.2 Absorbing Colorants 55 R(λ) 2bt 0.8 2dk 1bt 0.6 0.4 1dk 0.2 0 400 500 600 700 λ nm Fig. 2.25 Spectral reflectance of bright and dark pigments: 1bt bright blue, 1dk dark blue, 2bt bright yellow, and 2dk dark yellow R(λ) 0.8 a 0.6 b 0.4 c 0.2 0 400 500 600 700 λ nm Fig. 2.26 Spectral reflectance of different gray colors: (a) light gray, (b) middle gray, and (c) dark gray 56 2 Light Sources, Types of Colorants, Observer R(λ) 2br 0.8 2du 1br 0.6 0.4 1du 0.2 0 400 500 600 700 λ nm Fig. 2.27 Spectral reflectance of brilliant and dull pigments: 1br brilliant blue, 1du dull blue, 2br brilliant yellow, and 2du dull yellow from regular light scattering over the entire visible range. This is the case for examples such as water vapor, clouds, or snow. Ideal black, on the other hand, is caused by absorption of entire visible wavelengths. Light (or dark) colors stand out either due to a high (low) reflection maximum or a widened (narrowed) plateau region; a light (dark) gray shows a shift of the reflection level to white (black); see Figs. 2.24 and 2.26. Most of the color-order systems and the colored calibration samples for recipe prediction are based on colored pigment mixtures with white and black colorants. It is remarkable that the human eye provided by nature is more sensitive to color differences between dark colors (violet, blue, green) in comparison to light colors (yellow, orange, red). This is correlated with a low maximum respective high reflectance plateau range. The higher and steeper the rise of the curve to the plateau region or the smaller the half-width of the reflection maximum, the more the color is perceived as brilliant, clear, or pure. Conversely, pale, dirty, or dull colors possess a spectral reflection characterized by a lower and broader maximum or overlapping maxima, compare in Fig. 2.27 curve 1br with 1du for a blue pigment. The spectral reflectance of a dull yellow, for example, shows a more flat peak profile and a lower plateau range compared to a brilliant yellow, cf. curves 2br, 2du in Fig. 2.27. The terms outlined up to now are merely used to describe some typical coloristical properties of classical absorption colors or colorants. This vocabulary 2.2 Absorbing Colorants 57 cannot be directly carried over to effect pigments. Rather than absorption and scattering, effect pigments produce new sorts of colors on account of different optical mechanisms; identical terms have, therefore, different meanings for effect pigments than for absorption colorants. Metallic pigments, for example, produce a characteristic metallic lightness, brilliance, or hue extinction. This ambiguity is discussed in Sections 2.3.3 and 3.5.1. 2.2.4 Color-Order Systems It is quite remarkable that the color sense of humans is capable of distinguishing about 10 millions of colors. It is further important to note that, in addition to the astonishing number of colors, a color can have different attributes; therefore, it seems essential to have systematic classifications for such a tremendous diversity of colors. Such classification systems serve not only as an overview but also as an improved communication about non-self-luminous colors, particularly for their use in difficult applications. From each of the established color-order systems, series of color samples exist for visualization. The antiquated color classifications are certainly not ordered after uniform criteria [28, 29]. The chronologically first systems were arranged based on features, which included the actual knowledge about colors. Among the contemporarily used color-order systems are to differentiate roughly two groups: systems on coloristic and on colorimetric basis. In the following, we sketch the common four representative examples of both groups. The most important coloristic-order system is that of Munsell, established in 1905. It is simultaneously comprised of various companion features such as, for example, precise nomenclature or systematic extension capability for additional colors [30]. The corresponding color patterns are ordered according to the three properties hue H, value V, and chroma C in three dimensions in a cylindrical coordinate system. The true significance of this collection are the colored patterns which display a nearly constant color difference between neighboring colorations. This was developed without any colorimetric background – an amazing for the beginning of the 20th century. In spite of the visually nearly equal color steps, this color-order system was not accepted until 1976 as a basis of the CIELAB system. Experience with the Munsell system has brought out critical disadvantages. Particularly unfavorable are the non-uniform perceived color differences of bright and dark colors. In remedy of these shortcomings, the Munsell system was supplemented by an additional color pattern in 1990. The natural color system (NCS) was worked out in Sweden and is standardized there; it is based on the opponent color theory of Hering and is arranged in pairs of the four chromatic colors red, green yellow, and blue as well as the achromatic colors white and black [31]. The patterns are organized in color 58 2 Light Sources, Types of Colorants, Observer spectra and color triangles after the three criteria blackness s, colorfulness c, and shade Φ. They are grouped in the form of an atlas of 1,741 color patterns. In spite of this great number, the NCS system is restricted in its applicability. It incompletely covers the color space, and additionally, colors with glossy surface are inapplicably marked. Moreover, the arrangement pattern is visually non-uniform. Without a measuring device, this color system is, therefore, only suited for rough orientation in color space. The so-called color index (C.I.) is suited for identification of colorants but represents no real color-order system as in the discussion above. It simply consists of a list with unsystematically assembled dyes and absorption pigments. These are partially denoted according to the origin (generic names) and according to the chemical constitution with natural numbers (constitution numbers) [32]. This listing offers a certain aid only in a few cases, if, for example, some of the colorants listed in the C.I. are to exchange with one another. Strictly speaking, the widely distributed color registry RAL 840 HR in Germany is also not a color-order system in a broader sense. This registry was created to ensure that industrial colors are classified uniformly with defined names and numbers for better communication between public agencies and producers of consumer goods. The color patterns were originally vaguely arranged in view of coloristic criteria; in the meantime, a modification was undertaken using the so-called DIN color chart, see below. It should be added that contemporary color systems also consist of patterns which change uniformly by a suitable technical parameter such as the concentration of the used colorants, for example. The corresponding inconstant changes of hue, lightness, or chroma certainly make color perception and color comparison more difficult. A visual ascertainment of color differences is not ensured by such systems. In contrast to the order arrangements above, the DIN color chart is a colorimetric-based color system [33]. It comes from the CIE chromaticity diagram; see Section 3.1.2 and Color plate 2. The color patterns are arranged with regard to three properties, similar to the Munsell system. These color properties are denoted as darkness D, hue T, and saturation S. They correspond to the ∗ , and chroma C∗ of the CIELAB system (Section 3.1.3). lightness L∗ , hue Hab ab The OSA-UCS system (Optical Society of America Uniform Color Scales) is principally used in the USA. It consists of a total of 588 color patterns, from which 12 colors at a time are positioned in the corners and one in the center of a cubic octahedron [34]. With this system, a multitude of visual equidistant color scales can be established; visually equidistant means that adjacent color patterns always show the same visually perceived color difference independent of color point in color space. This system cannot be directly transformed into the CIELAB system; the same holds for the Munsell system, NCS system, and the DIN color chart. A reliable determination of color differences is impossible on the basis of the OSA-UCS system. 2.2 Absorbing Colorants 59 Accordingly, it is advantageous to fall back on a universal applicable colororder system, which, for chromatic as well as achromatic colors, has the implicit metric of a color space. The RAL design system is organized on such considerations. It is based on the structure of the CIELAB system. The RAL design system enables, with good approximation, the visual determination of color differences. The corresponding color collection is established as RAL design atlas [35]. There exists also a collection of 70 RAL effect colors, which cannot be classified as a definite color-order system. 2.2.5 Surface Phenomenon The color attributes assembled in the next to last section are more or less an expression of a subjective color perception. As already mentioned in Section 2.1.5, the entire color impression is certainly composed of at least two components: the light interactions in the volume and at the boundary surface of a colored sample. In other words, the reflection or transmission from the volume is superimposed on the boundary surface reflection. This reflection is caused by different refractive indices at the boundary surface. Such kinds of boundary surfaces are present in paints, coatings, plastic materials, emulsion paints, or ceramics. This distinction cannot be made for undefined surfaces such as of textiles, uncoated papers, plasters, or suede leather. The kind of surface reflection is also influenced by the structure of the surface. A given color can exhibit a surface structure between two extremes: matt: appears a rough (or structured) surface; this appearance is caused by completely (or partly) diffuse surface reflection; high-glossy: appears a very smooth reflecting surface; such a surface induces only directed reflection, which is called specular reflection, specular gloss, or simply gloss. This behavior is described by the reflection law. Both the above surface properties should generally be interpreted as color attributes. For the illumination of a (color) pattern with directional light, the transition between matt, half-matt, glossy, or high-glossy surfaces can be characterized by the resultant diffuse or directed reflection with the aid of the reflection indicatrix. This is a plane polar diagram which represents the angle-dependent intensity distribution of the light reflected from the surface. In reality, an indicatrix is in three dimensions. Four different indicatrices are shown schematically in Fig. 2.28, each caused by a different sort of surface reflection. The diffuse and directional reflection amounts are given by the shape of the envelope curve and enveloping surface of the intensity distribution. 60 2 Light Sources, Types of Colorants, Observer Fig. 2.28 Reflection indicatrices of different surfaces: (a) matt: purely diffuse reflection, (b) half-matt: dominant diffuse, minor directed reflection, (c) glossy: predominant directed and minor diffuse reflection, and (d) high glossy: exclusive specular reflection A diffuse reflecting surface of high roughness is achieved by various treatments, for example, with the help of suited polymer matrices or ceramics or pigment crystallites standing out non-uniformly from the boundary surface. In addition, the use of embossing dies is possible with regular geometrical surface forms such as micro-spheres and micro-prisms or irregular linen and other fabric structures. Further methods are sanding, etching, or physical vapor deposition (PVD). Certainly, the realization of ideal matt surfaces is exceedingly difficult. A matt surface appears normally somewhat lighter than a high-glossy surface of the same material. This is caused by the higher reflection coefficient for diffuse light in comparison to that of directional and perpendicular incident light, cf. Equations (2.1.8) and (2.1.12). The higher diffuse reflection is nearly independent of the absorption colorant sort. In the case of directional illumination, however, the reflection is only influenced by the degree of surface roughness. The matt surface of brilliant but dark-colored samples sometimes causes a minimal color shift. This phenomenon comes from the superimposed scattering of pigments near the surface. The entire diffuse reflection at the surface of a colored layer can, therefore, be composed of three components: – immediate reflection at the boundary surface; – scattering from particles near the surface; – anisotropic or isotropic scattering from the volume. The most of color physical problems are associated with the color component originated from the volume because this shows the interesting light interactions with the contained colorants. The result of a color measurement is, of course, composed of the volume and surface components. This result must, therefore, be corrected with regard to the surface boundary effect. This is achieved through the implementation of the various theoretical concepts detailed in Sections 5.3, 5.4, and 5.5, among other things. If the boundary surface contains no colorant particles, then the reflection is given by the refractive index of the binder. The pigments can, however, be 2.2 Absorbing Colorants 61 located in or near the surface, for example, by high pigment volume concentration (PVC), blooming, or flooding. In such cases, the arithmetic mean of the refractive indices of the involved materials is to be used. Such a surface boundary can have further color features, due to the fact that the refractive index of most colorants is dispersive. This effect is named bronzing; it can be present in printing inks, lacquers, plastic materials, or textiles, and can be avoided by appropriate measures. For unambiguous coloristic assessment of matt to high-glossy samples, it is absolutely necessary to avoid the glare caused by specular reflection. Therefore, the sample containing absorption colorants is always illuminated laterally at an angle of 45◦ and viewed perpendicular to the surface; see Fig. 2.29a. The reversed arrangement is also possible, but rarely used. In commercial light booths with lamps of different illuminants (normally D65, A, FL 2, FL 11 simulators), the light sources are arranged laterally and glare-free as shown in the mentioned figure. The color sample should be surrounded directly by a middle gray and the assessment should be performed by keeping the so-called CIE reference conditions, cf. Section 3.2.2. In contrast, the visual evaluation of the surface gloss is achieved with a fixed light source and constant line of vision by tilting of the sample over a specular Light source Observer Specular reflection a) Color pattern > 60° b) Fig. 2.29 Two different configurations of the three factors for color impression of absorption colors: (a) for coloristical assessment and (b) for evaluation of surface gloss 62 2 Light Sources, Types of Colorants, Observer reflection angle range; see Fig. 2.29b. A light booth should, therefore, possibly have a tiltable support with angle scaling. The quantitative determination of surface reflection is carried out separately using a gloss meter; the reflected intensity is registered at several variable angles between normal to the surface and greater than 60◦ . In the case of curved substrate surfaces, for instance, car body components, cans, bottles, or tubes, it is possible to pursue simultaneously gloss, color blending, and change of gloss in dependence of the observation angle. To achieve comparable results, the radius of curvature of the substrate and the thickness of the coating have to be the same for all color samples of a collection. In contrast, coated curved substrate surfaces are absolutely unsuited for instrumental color measurements. The evaluation of the surface reflection of colorations containing effect pigments is particularly critical. The optical properties of a metallic paint coating, for example, are essentially caused by specular reflection at the flake-shaped metal particles. The flakes are primarily arranged parallel to the substrate surface. Therefore, specular reflection dominates, but it is superimposed by diffuse reflection coming partly from the rough particle edges. For metallic pigments, the angular distribution of the reflection depends also on the illumination angle as well as the angle of observation. As already explained in Sections 2.1.6 and 2.1.7, the color physical properties of effect pigments are also extremely angle dependent. Compared to absorption colorations, the visual assessment of such colorations needs a much more sophisticated procedure, cf. Fig. 2.30. The observation for effect pigments is also normally performed using a fixed light source, but the classical method needs two identical colorations, one kept horizontal and the other rotated by an angle < 45◦ from this position; see Fig. 2.30a. This procedure allows for the observation of the angle-dependent change of lightness intensity. For flake-shaped metallic pigments, this angledependent change in reflected intensity is typical; it is the so-called lightness flop. The color changes of interference and diffraction pigments between the two extreme observation angles is, however, termed as color flop. Figure 2.30b shows the modern arrangement for visual evaluation of effect colorations. In this configuration, the light source and the observer are fixed. Vertical movement of a color sample simultaneously changes both the angle of illumination and angle of observation. Therefore, the observation of the color flop, for example, needs only one color pattern and is carried out at the same surface spot. We have arrived thematically at the transition from absorption to effect pigments. These colorants have been used industrially since about 1970 and to an increasing extent. In the following sections, we discuss the structure, morphology, and the spectral properties of the most important sorts of these modern colorants. 2.3 Effect Pigments 63 Light source Observer a) Effect Color pattern b) Fig. 2.30 Two different configurations for assessment of colorations containing effect pigments with fixed observer: (a) classical method (tilting): lightness flop and (b) modern method (vertical movement): color flop 2.3 Effect Pigments Effect pigments have broken new ground in color physics, especially with regard to industrial-scale research, development, and application. The color production of effect colorants is predominantly caused by anisotropic processes like single or multiple reflection, interference, or diffraction. These processes are unrealized in absorption colorants. The generic term “effect pigment” is inadequate because colors generated by absorbing colorants are also based on an optical “effect”. However, flake-shaped pigment or shorter flake pigment is an accurate expression for this sort of colorants. The generated color impression of effect pigments is extremely angle dependent. This is a function of both the illumination and the observation direction. Effect pigments result in quite strange color 64 2 Light Sources, Types of Colorants, Observer sensations for human color sense because our sense has evolved to perceive only colors from absorption colorations. In a practical sense, effect colorants need more extravagant manufacture methods in comparison to absorption pigments and also a more extensive characterization, measuring techniques, application, and processing. All types of effect pigments consist of flake-shaped particles with a large range of typical lateral dimensions between 1 μm and 1 mm. This is more than 10 – 1000 times larger than that of absorption pigments. The flake thickness has values between 10 nm and 1 μm. On account of the flake form, the resultant color effect is increasingly distinct with a more uniform morphology and the more the particles are oriented in the binder parallel to the substrate or surface. Like absorption pigments, effect colorants can be of inorganic as well as organic nature. With regard to the processes of color production, they are divided into four groups (cf. Table 1.1). For historical reasons, they are named: – metallic pigment; – pearlescent pigment; – interference pigment; – diffraction pigment. In the literature, pearl luster pigments are often subsumed to the interference pigment classification [36]. The laws used to describe the optical properties of metallic pigments are essentially geometrical optics; all other sorts of effect pigments are generally described by wave optics. Metallic pigments consist normally of a metal or an alloy of metals. The typical metallic gloss is increasingly brilliant the more uniformly the flakes are oriented parallel to the boundary surfaces of a coating. The so-called metallic effect is mainly a consequence of the directional and diffuse reflection at the surface and the edges of the flakes. In contrast, pearlescent pigments consist of two or more layers with a high index of refraction difference; the values normally range from 1.5 to 2.9. The mostly used substrate is mica, but also metals or metal oxides are often applied. The specific pearl luster depends on the permutation of the layers. This luster originates from single or multiple reflections at the layer boundaries followed by interference of the light waves. Differing optical layers are behind the general function of interference pigments; this does not require the use of a mica substrate. An interference pigment subgroup is the so-called optically variable interference pigments. The high ratio of refractive indices, in conjunction with different layer thicknesses, fans out the first or more interference orders in such a way that a variety of interference colors are to observe angle dependence. 2.3 Effect Pigments 65 The grating structure of diffraction pigments deflects the incoming light. The resulting color effect can be attributed also to the wave nature of light. The substrate consists of a highly reflecting or even ferromagnetic substance. The substrate is vapor-coated symmetrically on both sides with several materials known from nanotechnology. The ferromagnetic particles can be oriented with an external magnetic field before the crosslinking of a binder. The produced unusual but often impressive colors require that effect pigments undergo a more subtle and closer examination and handling compared with absorption colorants. 2.3.1 Types of Metallic Pigments Metallic pigments, generally consisting of metal flakes, are employed mainly on account of the metallic reflection from the flake-shaped particles. This kind of reflection consists of superimposed specular and diffuse components which produce unusual color effects compared with absorbing pigments. Conventional metal flakes have mean lateral dimensions ranging from about 5 μm to nearly 50 μm, whereas the thickness varies between roughly 100 nm and 1 μm. In some extreme cases, the particles have dimensions which are up to 10 times higher. The ratio of thickness to diameter of the particle is called the form factor and it extends from 1:50 to about 1:500. Metal flakes are used in paints, lacquers, plastic materials, and inks; they are also employed in chemical products and for sinter metals, building materials, explosives, or pyrotechnics, for instance, as functional or chemically reactive particles. In this text, we are mainly interested in the metallic reflection. This property is caused, in simplified physical terms, by the fact that individual metal atoms can easily release the bonding electrons. In lattice arrangements, the metal atoms completely loose the valency electrons. These electrons form the electron gas which is distributed among the remaining ions so that each ion is fixed on a corresponding lattice position. On account of its interaction with the electrons, an external light wave from a normal source cannot penetrate the very dense electron gas. The majority of the light is rather reflected and the remaining part is absorbed within a very small penetration depth. Reflection and absorption produce the typical metallic brilliance and characteristic natural color of metals [14]. The change in electron gas density at the metal surface results in light dispersion in the visible range, among other things. This causes a light-, gray-, or low-colored metallic effect. The theoretical reflectivity of metals is given by Equation (2.1.10). In Table 2.7, the indices of refraction n, absorption nκ, reflection r(n,κ), and the melting temperature Tm are shown; these are for metals that are most commonly used for metal pigments. In this listing, the metals are arranged according to decreasing reflectivity. The given optical 66 2 Light Sources, Types of Colorants, Observer Table 2.7 Reflectivity, refractive index, absorption index for perpendicular incident light at wavelength of λ = 589.3 nm and T = 293 K as well as melting point of metals used for metallic pigments [37] Metal Reflectivity r (n, κ) Refractive index (n) Absorption index (nκ) Melting point Tm /K Ag Al Au Cu Zn Ni Fe Mo Ti W 0.99 0.912 0.888 0.804 0.768 0.664 0.586 0.575 0.565 0.524 0.052 1.181 0.280 0.493 2.74 1.71 2.91 3.40 2.09 2.83 3.91 6.99 2.91 2.80 5.77 3.61 3.58 3.56 3.11 3.02 1,235 933 1,336 1,356 693 1,726 1,809 2,890 1,933 3,683 quantities are for the middle of the visible Na wavelength of λ = 589.3 nm; they will generally have different values for other wavelengths. The melting temperatures of the given metals are higher than those of the highest flow temperature of normal polymer melts. The refractive index is also subject to dispersion; in cases of Ag, Au, and Cu it is valued n < 1. The phase velocity cp is, on account of cp = c/n, inside these three metals higher than the velocity of light c in vacuum; this is not in contradiction to the special theory of relativity because only the group velocity – with which energy or signals propagate – cannot exceed the velocity of light c. Clearly, the actual reflectivity is lower than the theoretical one. The real reflectivity depends on the details of morphology of the particles, especially the – surface grade and edge roughness; – particle size and particle size distribution; – flake thickness; – pigment orientation in the material of application. In the context of metallic pigments, it is useful to emphasize the fact that historical laxness in naming remains an issue. Terms such as aluminum bronze or silver bronze instead of aluminum pigments, gold bronze or even the more general metal bronzes, are still in widespread use today by pigment manufacturers, colorists, and even in modern literature [38–40]. Actually, aluminum bronze consists of copper alloyed at most 12% aluminum; silver bronze is an alloy of silver and tin; gold bronze is a solid blend of suitable amounts of copper and zinc; genuine bronze, however, consists of copper alloyed with tin. 2.3 Effect Pigments 67 Apart from dispersion and particle size, the character of the metallic color impression is influenced by further details. Among them are the chosen metal or alloy, the manufacturing and processing method of the flakes, and the wettability in binders. In the following, we give a survey of the influence of these parameters with regard to the visual perceived metallic effect. First of all, the chosen metal is responsible for the brilliance of the natural metallic pigment. The metallic colors change from light white (Ag, Ni), white (Al – as a substitute for Ag), bluish white (Zn), orange-yellow (Au), and reddish (Cu) to gray (Fe, Mo, Ti, W). These color attributes relate only to the metal gloss and, therefore, have a different meaning from that which was outlined for absorption pigments in Section 2.2.2. Additional natural metallic colors can be realized using mixtures of metallic pigments: Ni flakes lighten and Fe particles gray the metallic effect. Also alloys such as brass (alloy of Cu and Zn) are suited for gold-yellowish to reddish color, for example. Metallic pigments are manufactured with mixtures or alloys only if the required metallic effect is not achievable using only conventional metal flakes. The most commonly used metallic pigments from modern point of view are given in Table 2.8. Uncoated metal flakes based on natural metals have the most diversity. Particles with especially even surfaces can be manufactured using the PVD method. For this, a polymer foil is vapor coated in vacuum with a metal and afterward crushed at temperatures far below the glass transition temperature of the polymeric material. These flakes are termed as crushed PVD films. Due to modern developments, even colored metallic flakes can be manufactured. In these cases, a colored component is superimposed on the Table 2.8 Classification of metallic pigments Metallic pigment Typical examples Uncoated metal flakes Aluminum (“aluminum bronze”, “silver bronze”), copper, zinc, copper/zinc alloys (70/30, 85/15, 90/10: “gold bronzes”), copper/aluminum alloys (4–12% Al: aluminum bronze), iron (austenitic steel, max. 11% Cr), nickel, tin, silver, gold, titanium Crushed PVD films Foils of polyethylene terephthalate, polystyrene, or polypropylene: vapor coated with aluminum, chrome, magnesium, copper, silver, gold (PVD procedure) Flakes coated with absorption pigments Inorganic or organic pigments in silicon dioxide or acrylate coating fixed on aluminum or “gold bronze” flakes as substrate (CVD procedure) Partially oxidized and oxide-coated metal flakes Partially oxidized from the surface aluminum flakes, copper flakes, zinc/copper flakes (“fire colors”); coated aluminum flakes: iron-III-oxide, tin oxide, zirconium oxide, iron titanate, cobalt titanate 68 2 Light Sources, Types of Colorants, Observer metallic effect. There are two different methods for manufacturing. In the first, absorption pigments are suitably fixed at the surface of the flakes by chemical vapor deposition (CVD) [38, 39]. The second method is based on metal flakes which are partly oxidized from the surface, or coated with metal oxides. Such metal flakes produce an intense color effect, sometimes called “fire colors.” These intense colors are caused by multiple reflections at the transparent outer layers with varying refractive indices; the multiple reflected waves then interfere. Technically, such colorants are not metallic pigments in the strict sense, rather just a multi-layered interference pigment on top of a metal substrate. In most cases, the original metallic brilliance of the metal substrate is lost. It must be noted that the chosen manufacturing method is of great influence to the resultant coloristical properties of metallic pigments. For shaping of natural particles, the melt is pressed through a narrow nozzle of suitable geometry with high pressure. Due to high flow velocities in the nozzle channel, often up to 400 m/s, the velocity gradient leads to an atomizing of the melt into round and contracting tiny droplets outside of the nozzle tip. After cooling, they are transformed into flake-shaped particles; these are the resulting metal flakes. The grinding of the solid particles is performed by two different processes. The wet milling method of Hall uses white mineral thinner for liquid phase. This simultaneously has the benefit of preventing dust explosions. In order to prevent clumping or welding of the particles, long-chained fatty acids are often added, typically 3–6% oleic or stearic acid. The dry milling method of Hametag, however, works in a N2 atmosphere containing at most 5% O2 . For this method, 4–6% palmitinic acid or stearic acid is often used as separators. The mentioned long-chained fatty acids, on the other hand, coat the entire surface of the resulting flakes; this certainly changes their wettability especially against binding materials. Because the end groups of the fatty acids are dependent of surface tension and behave either hydrophilic or hydrophobic, the metal flakes flood or disperse uniformly in the binding agent. Figure 2.31 gives an Metal flakes Coating Substrate a) Leafing b) Non–leafing Fig. 2.31 Two different distributions of metallic particles in a painted layer: (a) leafing near the surface and (b) non-leafing or nearly uniform distribution 2.3 Effect Pigments 69 illustration of two flake arrangements in a binder, the first is called leafing and the second non-leafing. The tendency to form the leafing arrangement is stronger with the lowering of the wetting with the surrounding polymer. Leafing flakes result from coating with stearic or palmitinic acid; non-leafing particles are usually obtained with oleic acid, for example. It is worth mentioning that the sort of wetting is generally correctable afterward with suitable additives. If the flakes are dispersed in the melt state of plastic materials, the leafing is generally avoided due to the high structural viscosity of the melt.11 A measurement method for determining the leafing behavior is detailed in the literature [41]. Leafing pigments incorporated in transparent binding agents show high brilliance due to a uniform and constant reflection. The abrasion resistance of the surface film is often reduced and, therefore, an additional top coat is usually applied. In contrast, the parallel and compact flake arrangement often behaves like an optical or mechanical barrier: in addition to visible wavelengths, it reflects UV and IR radiation and can also inhibit the diffusion of gases or vapors. Leafing flakes are, therefore, often used for reflection of UV and IR radiation as well as corrosion prevention pigments. Further non-colored applications of metallic pigments are given in Appendix 7.1.1. 2.3.2 Morphology of Metallic Particles As already mentioned, the metallic character is especially influenced by the morphology of the flakes. The wet milling procedure of Hall predominantly produces particles of irregular and uneven surfaces along with high edge errors – they are, therefore, quite accurately called cornflakes. Typical aluminum cornflakes are shown in Fig. 2.32. The picture was taken with a scanning electron microscope (SEM). The irregular particle edges result from fracture from other flakes during the milling process within the ball mill. The uneven surfaces are caused by abrasion of the coarse edges of colliding and pressed particles. At the particle surfaces shown in Fig. 2.32, it is possible to discern some remains of broken edge zones and indentation traces of striking balls. Both the uneven surface structure and the rugged particle edges are responsible for the typically increased diffuse light scattering of cornflakes. The light reflected from such flakes is composed of a directional and a superimposed scattering component. The accompanying indicatrix corresponds to that of Fig. 2.28c. The amount of diffuse reflected light is increased, therefore, with more uneven particle surfaces and rugged flake edges. With increasing particle scattering, there is a reduction of brilliance, that is, “it turns gray.” 11 Structural viscosity means that the viscosity has a nonlinear dependence on shear velocity; this is in contrast to constant Newtonian viscosity. 70 2 Light Sources, Types of Colorants, Observer Fig. 2.32 SEM picture of typical cornflake particles of aluminum (source: Eckart Werke GmbH, Velden, Germany) Sophisticated grinding techniques with metal brushings or polishing pastes have been used since about 1980 to reduce this brilliance loss. These techniques allow for the manufacture of thicker metal flakes with relatively plane surfaces as well as even or rounded edges. Particles of this kind are often called silver dollars, of which an example is shown in Fig. 2.33. These sorts of flakes reflect light with a dominant directional component accompanied by a considerably lower scattering. A paint film with silver dollars and clear top coat is, therefore, lighter and more brilliant than the one with cornflakes of the same metal and identical particle size distribution. Silver dollar pigments are preferentially employed in high-quality systems such as automotive coatings, the so-called metallics. They are also used in high polymer materials and printing inks. Shear stable flakes of upward 10 times the particle thickness of cornflakes can be realized in order to withstand processing techniques of high pressure or high shearing stress (e.g., ring main pumps, injection molding, blow molding, or extrusion). Particles with nearly plane surfaces and high brilliance can also be manufactured by PVD coating of thin polymer foils. They do, however, exhibit an undefined breaking edge. A representative example is shown in Fig. 2.34. In addition, it is possible to produce metallic pigments of constant thickness and of geometric regular shapes. These sorts of particles are called glitter flakes. To describe the glitter effect, the terms sparkle and glittering are also used. Both expressions are often utilized simultaneously, although they have somewhat different meanings. 2.3 Effect Pigments 71 Fig. 2.33 SEM picture of silver dollar pigments of aluminum (source: Eckart Werke GmbH, Velden, Germany) Fig. 2.34 Metallic pigments of PVD metal coated and broken polymer films (source: Eckart Werke GmbH, Velden, Germany) 72 2 Light Sources, Types of Colorants, Observer Sparkle is the property that single flake particles are directly recognized visually due to their expanded planar reflection surfaces. This is typically the case for mean particle sizes of about 30 μm and larger. The metal flakes are perceived separately on account of the surface reflection contrasting to the darker surroundings. They behave as isolated microscopic mirrors. In contrast to glittering, see below, neither the morphology nor the lateral dimensions of sparkle particles are necessarily uniform. The phenomenon of sparkle (also referred to as sparkling, optical roughness, micro-brightness, glint, or diamonds) is present in quite an assortment of effect pigments and is particularly observable with directional light; see also Section 3.5.1. In contrast, glittering is exclusively due to particles of uniform and regular geometry. These particles are manufactured in the form of squares, rectangles, rhombs, or circles by cutting or punching-out from metal foils or metallized polymer foils. In Fig. 2.35 an example of nearly quadratic aluminum glitter flakes cut from ribbons with a band knife is shown. Glitter flakes are of nearly uniform lateral dimension compared with conventional manufactured metallic pigments in ball mills. They are produced with sizes of 50 μm up to as much as 2 mm. They are generally at least 10 times thicker than usual cornflake or silver dollar particles. With regard to quadratic and rectangular glitter flakes, often specifications such as “2 × 2” or “2 × 4” are used. These can be interpreted as follows: Fig. 2.35 Almost quadratic glitter flakes cut with a band knife from foil strips of aluminum [38] (source: Rapra Technology Ltd, Shawbury, UK) 2.3 Effect Pigments 73 multiplication of each of these numbers with one thousandth inch (2.54 × 10–3 cm) gives the middle lateral extension of the corresponding particles. This means, for the given examples, that the glitter flakes have dimensions of 50 × 50 μm and 50 × 100 μm, respectively. It is also worth noting that with extreme process control in the Hall technique, it is also possible to produce spherical pigment particles with diameters as large as 700 μm. Such particles have, however, not the appearance of glitter flakes [38]. Colored metallic pigments offer an exceptional optical enlargement of usual metal pigments. These consist either of metal flakes covered by absorption pigments or metal flakes partially oxidized from the surface or oxide-coated metal particles. In the first case, the metal particles are coated with silicon dioxide or a polyacrylate containing inorganic or organic absorption pigments. In Fig. 2.36, there is an SEM photograph of aluminum flakes with a silicon dioxide coating of embedded inorganic pigment particles. This picture shows not only the coarse surface structure of the flakes but also the size proportion of the absorption pigments having only a few nanometers to the around two orders of magnitude larger sized metal flakes. From this difference in size, the typically higher scattering power of absorption pigments compared to effect pigments is also understandable. Colored metal effect pigments consist also of partially oxidized or oxidecoated flakes, which are manufactured using the CVD procedure. Partially Fig. 2.36 Aluminum flakes coated with silicon dioxide and embedded inorganic pigment particles (source: Eckart Werke GmbH, Velden, Germany) 74 2 Light Sources, Types of Colorants, Observer 20 100 10 50 Cumulative frequency curve Relative frequency % oxidized flakes of aluminum, copper, or zinc/copper are generally preferred. Iron-III-oxide-coated aluminum flakes are also common. All of these pigments produce particularly impressive reddish colors – and are, therefore, also called fire colors. These unusually striking colors are due to the combination of three effects: first, absorption and scattering of copper, zinc, or iron-III-oxide; second, interference caused by the layer construction; third, metallic reflection of the particles. Already the concept of the glitter flakes suggests that the character of the metallic effect is particularly dependent on the particle size. All particles, however, are not of the same size; therefore, the metallic effect is in general influenced by the particle size distribution. On the other hand, the size distribution can be controlled partly by the milling and sieving process; from these manufacturing steps, an asymmetrical particle size distribution with respect to the mean results. This distribution has a higher amount of smaller particles, cf. Figs. 2.37 and 2.38. The mean, in this context, is usually denoted by the quantity d50 or D[v; 0.5]. This quantity, for example, d50 = 25 μm, indicates that 50% volume of all particles are higher or lower in size than this near center value. The subtle properties of the metallic character even depend on the width of the distribution. In addition to the use of scanning electron microscopy, the laser granulometry method has proven quite useful for the determination of the mean particle size of effect pigments and the accompanying size distribution. The laser method is founded on scattering and diffraction of the particles suspended in a suitable liquid. This so-called laser granulometrical operation is suited only as a relative method, this is, not as an absolute method. d50 0 10–1 0 100 101 102 d /μm Fig. 2.37 Curves of particle size distribution and of cumulated frequency of an aluminum cornflake pigment with same value of d50 ≈ 20 μm as in Fig. 2.38 2.3 Effect Pigments 75 20 100 10 50 Cumulative frequency curve Relative frequency % The size distribution of effect pigments is characterized by the so-called width W, which is given by the quotient W = (d90 − d10 )/d50 > 1. The quantities d10 and d90 mean that 10 and 90% volume, respectively, of the particles have lateral dimensions of Φ ≤ d10 and Φ ≤ d90 . A narrow distribution with low W produces a more brilliant metallic effect in comparison to a broader distribution of equal d50 value; see Figs. 2.37 and 2.38. The concentration of small particles is lower in a narrow distribution than in a broad distribution. However, the greater the number of small-sized particles present, the more gray and paler the metallic effect appears. Of course, with smaller flakes edge scattering preponderates, and in addition, the parallel configuration of the flakes is more distorted than with larger sized particles. The metallic reflection of typically narrowly distributed silver dollar pigments is consequently more distinct than that of traditional cornflakes. Cornflakes show a significantly broader particle size distribution. Among modern metallic pigments, silver dollar flakes of aluminum are the most light and most brilliant particles. According to Figs. 2.37 and 2.38, there is always an elevated number of particles smaller than 5 μm.12 This increased content of fine particles is unavoidably caused by the grinding process and is quite typical for the manufactured metal powders. The fine particles give rise to a scattering component which reduces the metallic brilliance. Finally, the production of the metallic effect is also influenced by the orientation of the particles in the polymeric surrounding medium. The particle d50 0 10–1 100 101 102 0 d /μm Fig. 2.38 Curves of particle size distribution and of cumulated frequency of an aluminum silver dollar pigment with same value of d50 as in Figs. 2.37 12 Particles smaller than 5 μm contribute to particulate (dusty) matter. 76 2 Light Sources, Types of Colorants, Observer alignment is primarily determined by the processing techniques used. The maximum possible metallic reflection is achieved by complete flake parallelism to the bounding faces of a plane parallel layer; this is equivalent to a mirror. Local perturbations of particle alignment parallel to the paint coating can be caused by turbulent motion of the solvent during evaporation; such kinds of heterogeneity lead to mottling or flocculation. Both kinds of visible non-uniformities are also known from coatings with absorption pigments. Lacquers with low solid-state content display a more distinctive metallic effect than systems with higher solidstate content (so-called high solids). This is because the lower viscosity makes the orientation of the flakes easier. During processing of metallic or other flake-shaped pigments in printing inks, the absorbability of the stock can influence the parallel orientation of the flakes. But the slower the diffusion rate of the solvent, the more time available for parallel alignment of the particles. In high polymer materials, the flake pigments orient themselves according to the prevailing flow conditions. The alignment of the particles direct after surface formation is nearly maintained during cooling time and concurrent volume contraction. The collision of two melt fronts causes a flow line, at which the particles orient – visibly – parallel to the flow fronts. Flow lines can be avoided generally with suitable manipulation of the fusion in the mold [38]. 2.3.3 Coloristic Properties of Metallic Pigments The geometry, morphology, and reflection of metallic pigments produce a variety of unusual color effects which need to be described in detail. The most important coloristic characteristics of metallic pigments are given in Table 2.9. From this apparent arbitrary division it is possible to discern two groups: in the first group, the indicated effect properties increase with expanding lateral dimension of the particles and for the second group, they decrease. This inverse behavior and the complex color attributes of metallic pigments demand a closer examination in comparison to the more simple properties of absorption pigments. First, the five special features of the first group will be discussed. The metallic character or metallic gloss depends on the ratio of the directional to the diffuse reflection. Both components are directly proportional to the quotient of the surface to the edge length of the metallic flakes. The higher this ratio, the more distinctly developed the metallic character. Small particles normally give rise to a higher edge scattering and, therefore, produce a poor and gray metallic effect. Conversely, flakes with a lateral dimension greater than 30 μm show a striking metallic character. In general, the narrower the particle size distribution, the more distinct the metallic luster. 2.3 Effect Pigments 77 Table 2.9 Correlation between particle size and coloristical properties of metallic pigments (other used terms in brackets) Assessment of characteristic particle diameter d50 , non-leafing pigments Characteristic of metallic pigment ≤10 μm: fine pigments Cornflakes ≥30 μm: coarse pigments Silver dollars, glitter flakes Metallic character (metallic gloss) Brightness (brilliance) Reflection brightness (whiteness) Sparkle, glittering (optical roughness) Graininess (coarseness, texture) Insignificant, matt, gray Quite distinct, brightened Low Minor High Enhanced Invisible Visually noticeable Low Visible Lightness flop (flop, flip, travel, two-tone) Hue extinction Covering capacity (hiding power, opacity) Distinctiveness of image (DOI) Light Dark Enhanced Enhanced Low Low High Minor The brilliance of metallic pigments is, in essence, caused by the directional reflection component. Metallic flakes, therefore, appear all the more brilliant the higher the directional reflected light amount and the lower the diffuse reflection component. The brilliance, and consequently the directional reflected component, is reduced with smaller and more uneven surfaces of the pigments, with broader particle size distributions and with greater irregularities in particle orientation in the surrounding polymer material. The reflection brightness or whiteness characterizes the lightness of the metallic effect. This property is a measure of the total reflected light and is composed of the directional and diffuse components. Consequently, reflection brightness differs from lightness of absorption pigments, which is due to scattering and absorption. In connection with effect pigments, the term reflection brightness has, therefore, a quite different meaning from the lightness of absorption colorants (although both quantities are determined with the same measuring and evaluation system). In fact, the spectral reflection of metallic pigments behaves similar to that of white/black mixtures of absorption pigments. Metallic pigments certainly show a key difference: the spectral reflection depends on the angle of illumination and direction of observation. This angle dependence is shown clearly, for example, by the reflectance of an aluminum cornflake pigment in Fig. 2.39. In this illustration, the reflectance 78 2 Light Sources, Types of Colorants, Observer R (%) 150 100 15 25 50 45 75 110 0 400 500 600 λ /nm μas /degree Fig. 2.39 Spectral reflectance of a cornflake aluminum pigment in dependence of the wavelength λ measured at aspecular angles of μas = 15º, 25◦ , 45◦ , 75◦ , 110◦ ; illumination angle β = 45◦ R is plotted in dependence of wavelength λ for five standardized aspecular measuring angles μas and an illumination angle of β = 45◦ .13 With increasing measuring angle, the reflectance behaves similar to that of light white and middle or dark gray, cf. Figs. 2.24 and 2.26. For angles steeper than μas ≈ 75◦ , the reflectance remains at a low level, the metallic effect appears dark gray [42, 43]. On the other hand, the reflectance increases exponentially for the aspecular angle of μas = 0◦ . This drastic change in brightness in dependence on the observation angle is characteristic for metallic flakes; it is termed as lightness flop or short flop (see below). The reflectance increase near the specular angle can be further raised, within limits, with a narrower particle size distribution or altogether larger sized flakes. Measured reflectance values higher than 100% are absolutely usual and produce no inconsistency with conservation of energy. Because of the lack of suited and corrosion-resistant metallic standards, the reflectance scale is based on the reflectance of a white (scattering) standard which is interpreted as a reflectance of 100% (Sections 2.2.3 and 4.1.2). Real effect pigments can have reflectance values up to about R = 800%. 13 For nomenclature and counting of angles, see Section 4.1.2, Figs. 4.5 and 4.6. 2.3 Effect Pigments 79 Metallic pigments of irregular lateral dimension greater than about 30 μm produce a phenomenon termed as sparkle in the last section. This effect is also called sparkling or optical roughness. For particle dimensions of this size or larger, the naked eye can distinguish single flakes of nearly equal orientation at the surface of a coating or plastic material. This is caused by the increased intensity of directionally reflected light at the larger particle surfaces (similar to parallelized crystals of an illuminated snow surface). As a consequence of the distorted orientation of the flakes, sparkling changes in dependence on both the illumination and observation angle. Leafing flakes develop no sparkling in dependence of the particle size because nearly all flakes have an alignment parallel to the surface of the coating or the plastic material. Sparkle is not restricted to metallic pigments and can be present in other sorts of flake-shaped pigments. This striking feature depends, e.g., on the size, the sort, the surface curvature, and the content of the effect pigment in a coloration. If the illumination is switched from directional to diffuse, the sparkling disappears completely and turns into a kind of graininess of the particles. Under this lighting condition, only a kind of fixed snowing picture is observable near the surface of the coating. This phenomenon is also called coarseness, texture, or vivid “salt and pepper” and is independent of observation angle. The impression of graininess depends on the size and type of the flakes, orientation irregularities, or clustering of the pigments during processing. Now, consider the second group of properties listed in Table 2.9. The abovementioned lightness flop (also light to dark flop, flop, flip, travel, two-tone) can be regarded as the most important and visually most striking property of metallic pigments. This term characterizes the decrease in lightness that a metallic coloration shows under diffuse illumination between two extreme angles of observation, especially at angles for perpendicular observation and an angle greater than 60◦ with regard to the normal of the surface (cf. Fig. 2.30a).14 The lightness flop is influenced by three primary factors: first, the flakeshaped pigment morphology, second, the surface and edge formation, and third, how well the flakes are ordered parallel to the surface boundaries of a layer. During observation perpendicular to the surface, the light enters directly the eye after interactions with the flakes. The observer registers the reference lightness. Now, for angles nearly parallel to the surface, the light path through the layer is longer. For this reason more interactions can take place with the particles of the layer, that is, at the surface or edges of the flakes. Due to this, light is increasingly scattered or reflected out of the line of observation and, therefore, only a small amount of the interacting light reaches the eye. This results in a registering of a reduction of lightness in comparison to the perpendicular observation. 14 Perpendicular observation means, in practice, that observation angles of β = ±20◦ , ν referred to the vertical, are permitted. 80 2 Light Sources, Types of Colorants, Observer This flop is termed as light if only a small lightness difference is observed between both extreme observation angles. It is, however, called dark if a large lightness difference is registered. For finer and irregularly shaped flakes (e.g., cornflakes), for broader accompanying particle size distribution, and for greater particle disorder in the layer, the flop is lighter. Conversely, the flop is the more dark, for greater evenness of the particle surfaces, for more rounded flake edges (silver dollar flakes), for narrower size distributions, and for more consistent parallel orientation of the particles to the surface boundary of the layer. The lightness flop can be altered afterward to some degree by adding inorganic or organic absorption pigments (see Table 2.10). Table 2.10 Lightness and color flop of effect colorations Flop kind Flop character Effect pigment/ absorption pigment Lightness flop Light Metallic pigment Metallic pigment and absorption pigment Dark Metallic pigment Metallic pigment and absorption pigment Color flop Colored Absorption pigment Absorption and pearlescent pigment Interference pigment Diffraction pigment Typical examples Fine non-leafing cornflakes, eventually with orientation distortion medium Scattering, inorganic, and organic; for example, titanium dioxide, chromium titanate Coarse non-leafing silver dollar flakes, normal silver dollar flakes, PVD flakes Transparent, inorganic, and organic Blue with green flop: phthalocyanine pigments of neutral color flop; blue with red flop: α/-phthalocyanine pigments Combination of hiding absorption and transparent pearlescent pigments, nano-titanium dioxide Interference pigments with extreme color flop: LCP, flakes coated with silicon dioxide, aluminum oxide, iron-III-oxide, magnesium fluoride Aluminum or nickel substrate PVD coated with chromium/magnesium fluoride or magnesium fluoride/silicon dioxide 2.3 Effect Pigments 81 The phenomenon of lightness flop can be examined quantitatively by a gloss meter. The usual measuring angles μν = 20◦ , 60◦ , 85◦ with regard to the normal of the surface are certainly not sufficient. This is already clear from the angle-dependent reflectance measurements in Fig. 2.39. A reliable characteristic value describing the lightness flop of a single-layered metallic formulation is the so-called flop index; however, for clear-over-base paints, the so-called metallic value is used (Section 3.5.1). As mentioned, some metallic systems are mixed with absorption pigments for coloring or covering of the background. These systems have a more or less colored flop; see Table 2.10. Mixtures with absorption pigments always result in a lighter flop compared to the natural metallic pigment. This effect is generally called color flop. Mixtures of pearlescent and metallic pigments normally produce a lighter flop than the corresponding single natural pigments. However, the brilliance is usually raised at perpendicular observation. This behavior can be reversed with suitable pigment combinations. The color flop of interference and diffraction pigments is generally accompanied by a distinct color change. This change is mainly due to the interference or diffraction maximum of first order (Sections 3.5.3 and 3.5.5). A particular kind of color flop is given by a mixture of a metallic flakes with titanium dioxide, provided that nanoparticles of the rutil modification are used. The observable minor color shift caused by the nanoparticles is generated by the selective scattering of waves in the region of blue wavelengths; this special phenomenon is called frost effect [44]. Such a layer has a yellowish color at top view but for a flat angle of observation, a bluish color impression results. Accordingly, the shorter blue wavelengths are more scattered than the other longer wavelengths, in agreement with Rayleigh’s law (2.1.3). This comparatively low effect is also observed with other absorption or pearlescent pigments of lateral dimensions in the nanometer range. Altogether, the color flop of a formulation can be controlled within limits by adding small amounts of nanoparticles. Certainly, the frost effect lowers the entire brightness of the relevant coloration. The next property of interest in Table 2.9 is the hue extinction. This feature characterizes the capability of a metallic pigment to change or to cover completely the natural color of an absorption pigment incorporated into a formulation. In the literature [39], this ability is called “hue saturation,” which is again misleading, because this term implies a saturation of the relevant absorption colorant. The extent of the hue extinction is related to the covering capacity of the metallic particles. In this case, for metallic particles this term has the same meaning as it does for absorption pigments (Section 3.4.3). Both the hue extinction and the hiding power are improved with smaller cross sections of the particles, broader particle size distributions, larger flake thicknesses, and denser packing of the flakes. 82 2 Light Sources, Types of Colorants, Observer Finally, there is the so-called distinctiveness of image (DOI). In addition to lightness flop and hue extinction, this property lists among the central characteristics of single as well as clear-over-base paints of metallic coatings. The DOI value represents the uniformity of the observable metallic reflection. It depends mainly on the particle size and orientation of the flakes in a layer. The distinctiveness of image is again improved by smaller particles and more highly parallelized grade of the flakes. The DOI value of large-sized flakes nearly correlates with the glittering effect. The determination of the DOI value by measurements is outlined in Section 3.5.1. 2.3.4 Sorts of Pearlescent and Interference Colorants The color production of pearlescent and interference pigments is essentially based on constructive interference. Pearlescent pigments imitate the nacre luster of natural pearls. The brilliant colors and unique luster are due to superimposed light interactions such as absorption and multiple reflection at different boundary surfaces of the particles. Interference pigments generate substantially more brilliant colors than pearl luster pigments. The terms pearlescent and interference pigments are often wrongly used as synonyms for both pigment sorts, although only pearlescent pigments have the typical luster of natural pearls coming from the depths to the surface. The particles of pearl luster and interference pigments consist of layers with different refractive indices. The layer thicknesses are on the order of magnitude of visible wavelengths. The entire flake thickness varies from about 30 nm to 1 μm and the mean lateral dimension of the transparent to opaque pigments extends – similar to metallic flakes – from about 5 to 300 μm. Pearlescent, interference, and diffraction pigments can also exhibit sparkling. This sizedependent phenomenon is, in this case, generally darker than the sparkle of metallic pigments because the reflection is caused only by the difference of refractive indices instead of metallic reflection. The color-producing properties of pearlescent, interference, or diffraction pigments are dependent on the particle geometry, especially on the interfering light interactions, and the color physical conditions in the particle surrounding. According to Equations (2.1.15), (2.1.16), (2.1.17), (2.1.18), (2.1.19), and (2.1.20), the interference laws are functions of the wavelength λ, the refractive index n at the interface, the thickness d of each single layer, and the observation or interference angle α z . These parameters can be tuned in such a way that only the first interference order (z = 1) occurs in the range of normal observation angles. In this case, the higher orders can be neglected or are simply not to observe. The incoming light waves are partly reflected at each boundary surface of a particle, cf. Fig. 2.16. The constructive interference of the waves 2.3 Effect Pigments 83 produces the matt to high brilliant color appearance. The interference color is observed at the specular angle on the illumination surface and the complementary color is transmitted by transparent flakes. Each single pigment, therefore, behaves as an interference filter, which the incoming light waves split up into a reflected interference component and a complementary transmitted or absorbed component. As a result of the different refractive indices at the interfaces as well as the morphology of the particles, the following light interactions together contribute to the color appearance of pearl luster and interference pigments: – constructive interference produces the sometimes intense colors which change in dependence of the angle of observation; the different colors and the angle dependence are given by the refractive indices, the thicknesses, and the number of layers; – single reflection at interfaces causes part of the glossiness; – multiple reflection at the different interfaces of the transparent or translucent layers causes the typical luster “from the depths” of pearlescent pigments; – scattering at the edges or rough surfaces of the particles leads to matt interference colors; – absorption reduces the brilliance; it depends on the layer material. Table 2.11 shows the customary substances from which pearlescent and interference pigments are composed. The materials are ordered according to increasing values of refractive index nD . In comparison, air at a pressure of 1.0 bar at room temperature T = 298 K has a refractive index of only n = 1.000272. The pigment particles consist of at least three different Table 2.11 Refractive index n of substances used for pearlescent and interference pigments; λ = 589.3 nm, T = 298 K [40, 45, 46] Substance Special terms Refractive index n Synthetic high polymers MgF2 Proteins SiO2 Alumina silicate CaCO3 Al2 O3 Guanine, hypoxanthine Pb(OH)2 2PbCO3 BiOCl Fe3 O4 TiO2 α-Fe2 O3 Organic materials Magnesium fluoride Proteins Inorganic glasses Mica, muscovite Aragonite Aluminum oxide Natural pearl essence Basic lead carbonate Bismuth-oxide chloride Magnetite Anastas/rutil Hematite 1.35–1.70 1.384 1.40 1.458 1.50 1.68 1.768 1.85 2.00 2.15 2.42 2.5/2.7 2.88 · 84 2 Light Sources, Types of Colorants, Observer materials. Because the relevant substances are anisotropic crystalline, the indicated n values represent a mean. The refractive indices of the substances given in Table 2.11 are subject to dispersion. Table 2.12 is arranged by pigment classes: pearl luster, interference, and diffraction pigments. In other literature, these are often gathered arbitrarily under the collective name: special effect pigments [18, 40]. Our further discussion relates to the pigment classification and terms given in Table 2.12. This fixes a unified nomenclature for all sorts of pearlescent, interference, and diffraction pigments. Pearlescent pigments of the simplest structure are substrate free and form flake-shaped single crystals. The flakes consist of natural fish scales (75–95% Table 2.12 Effect pigments producing colors founded on wave properties of the light: pearlescent, interference, and diffraction pigments Sort of effect pigment Unsystematic names Pearlescent pigment Platelet-like single crystals Mica-based pearlescent pigments Interference pigment Special interference pigments Liquid crystal pigments (LCP) Optical variable interference pigments (OVIP) Extended interference films Diffraction pigment Grating pigments Typical examples Natural pearl essence, basic lead carbonate, bismuth-oxide chloride, α-iron-III-oxide, titanium dioxide, mixed-phase pigments of aluminum oxide, manganese-iron-III-oxide Substrates: natural or synthetic muscovite layers: titanium dioxide (rutil or anastas), iron-III-oxide, chromium-III-oxide, silicon dioxide (multi-layer principle) Substrates: aluminum oxide, silicon dioxide, iron-III-oxide chromium, silicon–aluminum–boron silicate; Layers of iron-II-oxide-hydroxide, iron-III-oxide, chromium-III-oxide, titanium dioxide, chromium phosphate; chromium, iron-II-/iron-III-oxide, iron titanate, silver, gold, molybdenum Polysiloxanes in cholesteric phase, cross-linked in layers Substrates: aluminum, aluminum oxide, iron-III-oxide, silicon dioxide, glass flakes; Layers: aluminum, chromium, iron-III-oxide, magnesium fluoride, silicon dioxide, titanium dioxide Multi-layer film consisting of polyacrylates, polypropylene with polyethylene terephthalate, polystyrene, or polycarbonate Al substrate with symmetrical PVD layers of MgF2 or Cr/MgF2 Ferromagnetic: Ni substrate with symmetrical PVD layers of MgF2 /Al or Cr/MgF2 /Al 2.3 Effect Pigments 85 guanine, 5–25% hypoxanthine), basic lead carbonate, bismuth-oxide chloride, or α-iron-III-oxide, as well as mixed phases of aluminum oxide or manganeseiron-III-oxide. On account of the lack of a mechanically stabilizing substrate, these pearl pigments will not easily survive shear and pressure flow of technical processing. They are similar to ground shells and are, therefore, limited to a small range of applications [40]. However, for the most part, the flake-shaped pearl and interference pigments consist of a symmetrically coated substrate of at least one additional layer. The most used substrates are natural or synthetic mica, aluminum, aluminum oxide, chromium, iron-III-oxide, or synthetic silicon dioxide. The lamellate center should have a great difference in refractive index compared to that of the coated layers. Pearlescent pigments are mostly based on mica substrate. This is a native depositing layer silicate, named muscovite, with total molecular formula KAl2 [(OH, F)2 AlSi3 O10 ]. Instead of natural muscovite, also synthetic mica is increasingly being used. The synthesized material shows a more uniformlayered structure and produces, therefore, more brilliant interference colors. Apart from metal oxides, further coating substances are fluorides or silicon dioxide, also cobalt and iron titanate, chromium phosphate, silver, gold, molybdenum, or chromium [18, 46–48]. The symmetric permutation of layers of the flakes is achieved by normal chemical procedures or vacuum evaporation coating by the PVD or CVD method [49, 50]. Examples of pearl luster pigments based on natural muscovite are shown in Color plates 7 and 8. 2.3.5 Interference Pigments Consisting of Multiple Layers Flake-shaped pigments based on muscovite or other substrates can be modified to produce a variety of further impressive colors. Intensified interference colors and simultaneously selective absorption, analogous to colored pigments, can be achieved by coating mica with two or more metal oxides of different refractive indices. Such kinds of flakes are also called combination pigments. Compared to single-coated mica pigments, they show more brilliant and brighter interference colors, as well as a more distinct color flop. The color flop is called distinct if a variety of interference colors are to observe. Conversely, the color flop is less distinct if only few interference colors are angle dependent to perceive. The color flop is again more distinct than with a mixture of the natural pearlescent and absorption pigments. Because of the underlying two different color production mechanisms, combination pigments are also termed as two-color pigments or color-flop pigments.15 In dependence on the observation angle, 15 Not only combination pigments produce a color flop but rather interference pigments with other layer combinations as well as diffraction pigments, cf. Table 2.10., Section 2.3.3. 86 2 Light Sources, Types of Colorants, Observer Fig. 2.40 Cross section of a symmetrical multi-layer pigment; permutation of layers from the centered mica substrate: titanium dioxide, silicon dioxide, titanium dioxide; overall layer thickness about 500 nm (source: Merck KGaA, Darmstadt, Germany) either the gloss is composed of the absorption and interference color or the non-self-luminous color of the absorption pigment is dominant. The most important combination pigments are TiO2 -coated mica flakes vapor-coated with further oxides such as α-Fe2 O3 (hematite modification), Fe3 O4 , or Cr2 O3 . As shown in Fig. 2.40, the muscovite substrate can be covered with two different oxide layers of TiO2 and SiO2 . On account of the six boundary layers with different refractive indices, 15 interference combinations are possible. These produce extreme interference colors which are superimposed by the absorption colors of both oxides. Mica pigments vapor-coated with TiO2 and top-coated with other metal oxides such as TiO2–x , TiOx Ny , FeTiO3 , or nanocarbon particles embedded in TiO2 generate silver gray or black pigments of improved compatibility with colored pigments. Transparent mica pigments can be produced in form of nano-sized particles by a suitable precipitation method of oxides or oxide hydrates; these colorants are called transparent colors. Moreover, modified process engineering allows for the manufacture of pigments of minor gloss [41]. The top-coat of an interference pigment can also consist of a pure metal. A substrate of a metal (Al or Cr) or metal oxide (Al2 O3 , Fe2 O3 , SiO2 ) is coated with a glassy layer of another refractive index (TiO2 , MgF2 ), as well as an evaporated semitransparent metal top-coat (Cr, Ni, or Al). The inner and outer reflecting layers form together a Fabry–Pérot etalon, cf. Fig. 2.18. This structure causes increased interference intensities and a sharp color flop by multiple reflection. An interference pigment showing a distinct color flop is generally named as optical variable interference pigment (OVIP). An example of such an OVIP of layer composition MgF2 /Al/MgF2 is shown in Fig. 2.41. In this SEM picture, it is particularly interesting to see the quite 2.3 Effect Pigments 87 Fig. 2.41 SEM photograph of an optical variable interference pigment with symmetrical layer composition of MgF2 /Al/MgF2 ; cf. Color plate 9 (source: Flex Products Inc, Santa Rosa, CA, USA) even surfaces and the sharp edges of the pigment particles. The even surfaces indicate also internally even surface boundaries and, therefore, brilliant interference colors followed by a distinct color flop. The sharp edges indicate that the flakes are broken at low temperatures and sifted out. The particles shown in Fig. 2.41 have a mean lateral dimension of d50 ∼ = 20 μm and a thickness of about 100 nm. An impression of the color flop produced by this pigment is given by comparing the two pictures of Color plate 9. Both photos show the same image field of a light microscope in bright- and dark-field illumination; bright field means illumination from the top of the surface and dark field means interference from the side of the color sample. In this case, the colored flop changes from green to violet (see also Section 3.5.3). Interference pigments of special shish-kebab layer structures and consisting of organic polymers are termed as liquid crystal pigments (LCP). A liquid crystal state is arranged without exception of rod- or elliptical-shaped polymer molecules consisting of suitable dipole moments or polarizing groups. The corresponding textures are optically anisotropic and are, for example, used in seven segment displays for more than four decades. The accompanying texture is called liquid crystalline or mesomeric phase because the molecular conformation corresponds neither to a random liquid nor to an ordered crystalline state. 88 2 Light Sources, Types of Colorants, Observer There exist altogether three different liquid crystalline textures. The corresponding molecular configurations are termed as nematic, smectic, and cholesteric: – nematic: the molecules are aligned parallel to their longitudinal axes, are arbitrary slidable in the axial direction, and are rotatable around the longitudinal axes independent of one another; – smectic: the molecules are oriented with their long axis perpendicular to each monomolecular sheet; the movement of the molecules is restricted to rotations around the longitudinal axes; – cholesteric: the molecules are arranged parallel to one another and grouped in layers; the layers are systematically turned toward each other by a specific angle; the mobility of the molecules is the same as in the nematic phase. These molecular configurations are schematically sketched in two dimensions in Fig. 2.42, but are to interpret as three-dimensional textures. Nematic Smectic Cholesteric Fig. 2.42 Schematic representation of rod-shaped polymer molecules in nematic, smectic, and cholesteric phase The manufacture of liquid crystalline pigments of suitably layered structures normally starts with polymer molecules in the nematic phase. This state is converted into layers of cholesteric texture – for example, with silicones – at higher temperatures in the presence of a chiral additive. The single parallel layers are then cross-linked and fixed using UV radiation; see Fig. 2.43. Each layer is twisted by a constant angle relative to the adjacent layer. The nearly identical molecular conformation with regard to the initial layer is attained after passing the so-called pitch height p of about 100 nm. On account of the systematically twisted molecular conformation inside the pitch, the transmitted light is circularly polarized by this structure. The pigment particles have thicknesses 2.3 Effect Pigments 89 Fig. 2.43 Parallel and cross-linked layers of polysiloxane molecules in cholesteric texture forming a half pitch of a liquid crystal pigment (schematically) of about 5 μm, the lateral dimension normally ranges from about 7 to 90 μm. Liquid crystalline sparkling pigments can be realized up to about 500 μm. An entire pitch works optically like a Fabry–Pérot etalon [51]. The partial reflection at the pitch surfaces and the rotated molecular arrangement causes several optical effects which greatly affect the interference behavior of these pigments: – a kind of gloss coming from the depths, which is attenuated in pearl luster pigments because the light must pass through various pitches and layers; – on account of reflections between adjacent pitch surfaces, the interference wavelength λ changes according to Equation (2.1.20) for z = 1 and p = 2d; the wavelength decreases with increasing angle of observation from the vertical; an example of transparent liquid crystal pigments is shown in Color plate 10; – caused by a low pitch value, only one single interference order is observable within ±90◦ ; it is accompanied by a distinct color flop; – the reflected polarized light increases the brilliance of the interference color; – because the particles are transparent, the total color impression can be influenced by the background color or mixed absorption pigments. Furthermore, modern developments use even pure metals, metal alloys, metal oxides, or borosilicate glass for substrates of interference pigments; see Table 2.13. An example of an uncoated glass substrate and coated with TiO2 is shown in Fig. 2.44. The differences in refractive indices at the interfaces cause not only unusual brilliant and pure interference colors but also sparkle effects which are even colored. Pigments of other compositions, thicknesses, and permutation of layers cause impressive color flops. These occur nearly throughout the entire visible spectrum (see Section 3.5.3). Finally, there are the so-called extended interference films (cf. Table 2.12, previous section). The manufacturing is carried out by co-extrusion of transparent polymer foils with different refractive indices (1.48 ≤ n ≤ 1.60). The films are partly colored with absorption pigments. The original low interface reflectivity is improved by semitransparent silvering of some internal foils. The full foil sequence has a thickness of up to 400 μm and contains a maximum 90 2 Light Sources, Types of Colorants, Observer Table 2.13 Some optical variable interference pigments Substrate Coating Peculiarities Al2 O3 Depending on coating thickness d TiO2 Fe2 O3 Lateral dimension 5 μm ≤ φ ≤ 30 μm Colors: “Silver,” yellow over blue-green until blue; “Bronze,”, “Copper,” red interference colors; sparkle pigments for φ ≥ 30 μm Ca–Al borosilicate TiO2 , Fe2 O3 , SiO2 : SiO2 /TiO2 in multi-layers: d ≤ 1 μm, 20 μm ≤ φ ≤ 200 μm Substrate of high transparency, “pure” interference colors without scattering, multicolored sparkle effect SiO2 TiO2 Colored flop: “gold-silvery” to greenish, green-blue to dark-blue; more distinct with rutil compared to anastas Fe2 O3 Layer configuration: Fe2 O3 /SiO2 /Fe2 O3 / SiO2 /Fe2 O3 Colored flop: violet to orange-“gold”; top coating of Fe2 O3 , corrosion resistant Metals and metal alloys Mono-layers: Al, Zn, Cu–Zn alloys; SiO2 /Al/SiO2 , α-Fe2 O3 /Al/α-Fe2 O3 Multi-layers: From the surface partially oxidized and oxides of metal flakes Fabry–Pérot etalons; cf. Table 2.8 Fig. 2.44 (a) Uncoated borosilicate substrate, (b) coated with titanium dioxide layers; total flake thickness of about 300 nm (source: Merck KGaA, Darmstadt, Germany) of 70 films. The multi-layer films are crushed at temperatures below the lowest glass transition temperature of the polymers used and are sieved in different fractions. 2.3 Effect Pigments 91 2.3.6 Spectral Behavior of Pearlescent and Interference Colorants Pearl luster and interference pigments are either nearly transparent or opaque. The most important representatives of both groups are shown in Table 2.14. In this section, we limit ourselves to describing only transparent particles because these colorants have more interesting color shades. First, we discuss the dependence of the color impression on the background color; thereafter, we explore methods for covering coatings. As already mentioned, the interference color appears in the direction of the specular angle; this corresponds to the interference angle of first order. The complementary color is transmitted by the transparent particles and absorbed by opaque flakes. Table 2.14 Examples of nearly transparent and opaque pearlescent and interference pigments Light transmittance Examples Nearly transparent TiO2 pigment, Fe2 O3 combination pigments on mica substrate; Fe2 O3 coating of Al2 O3 substrate; coated SiO2 flakes; liquid crystalline polysiloxanes Opaque Reduced TiO2 on white mica; multi-layer pigments: Al flakes coated with SiO2 , Fe2 O3 ; Al or Cr platelets vapor coated with MgF2 , Cr, or Ni The total color impression of transparent interference pigments is strongly influenced by the chosen background; this is clearly shown in connection with Fig. 2.45. Because a black background absorbs the complementary color, only the interference color is observed above the coating. The interference color corresponds to the mass tone of the pigment. On account of the additional light scattering, which is generated to a greater or lesser degree by the corners or edges of the pigment particles, the surface of such coatings appears in fact dark, but rarely absolute black. On the contrary, a white background scatters, to a large extent, the transmitted complementary color and is only slightly absorbed. The interference color is then superimposed upon by the scattered amount of the complementary color in direction of the specular angle. In all other directions, only the scattered complementary color is observed. Consequently, over a black background, the natural colors of an interference pigment are observed and over a white background, the covering capacity. These uncolored background surfaces allow also for the determination of the reflectance and transmittance of a transparent or translucent layer from reflection measurements (Sections 3.4.3 and 4.2.4). In the case of a colored background, the interference color is clearly superimposed upon by that color. Because the interference and absorption colors can 92 2 Light Sources, Types of Colorants, Observer Interference color Complementary color Black White Colored Fig. 2.45 The color impression of colorations with transparent interference pigments is affected by the chosen absorbing or scattering background be either identical or different, a variety of color flops are possible. At curved surfaces (which are always to be avoided for color measurements), the interference and the absorption color can be observed simultaneously. Transparent interference pigments mixed with colorants of complementary mass tone result in a white color according to the laws of additive color mixing. Mixtures of transparent interference pigments with other pigments of similar color produce more dull colors like the single colorants. As an alternative to a white background, a scattering silver-colored metallic or pearlescent pigment of d50 value less than 10 μm can be used. Such parameters for the pearlescent pigment normally ensure a high DOI value. Preferred bright silvery pigments for this purpose are mica flakes coated with TiO2 or aluminum cornflakes. For light gray layers FeTiO3 -mica pigments are suitable. On the basis of the scattering contribution or broad particle size distribution, the gloss is reduced. Aluminum pigments have also the tendency to reduce the chroma of pearlescent and interference pigments. This is in analogy to white in mixtures of colored absorption pigments. In the following, we consider in more detail the color systematic and the corresponding spectral reflection which result from thickness changes and composition of the layers. For this, we restrict ourselves to the pigments with layer compositions which were already discussed in the previous section, among other things. They are as follows: – titanium dioxide evaporated mica particles; – mica flakes coated with iron-III-oxide; 2.3 Effect Pigments 93 – two mica-based combination pigments of titanium dioxide in rutil modification: top coated with iron-III-oxide or with chromium-III-oxide; – liquid crystal pigments consisting of polysiloxanes. These pigments are typical representatives of other pearlescent and interference pigments. This goes especially for the accompanying colorimetric behavior of these pigments which show astonishing colorimetric parallels (Section 3.5.3). 2.3.6.1 Titanium Dioxide Evaporated on Mica Substrate An example of a pearlescent pigment on a mica substrate coated with rutil is shown in the upper half of Color plate 7. This picture was taken under bright field illumination. From the top view, the particles produce a yellow color impression over a black background. The non-uniform colors of the particles are caused by different layer thicknesses and by flakes tilted with regard to the image plane. This is further elucidated with the example of the red pearl luster pigment in Color plate 8. In this case, the particles in the same field are recorded in using bright and dark field illumination. The comparatively high-valued refractive index of titanium dioxide (n = 2.5 or 2.7) together with the low value of muscovite (n = 1.5) offers suitable conditions for developing neatly ordered interference colors. However, if the mica substrate is already flake shaped, TiO2 crystallizes in a thin film which is only suited for interference. Among the three possible crystal modifications of titanium oxide – rutil, anastas, and brookit – the rutil structure is preferred in this case. The dependency of the interference color on the titanium-dioxide-layer thickness is given in Table 2.15 (cf. Table 2.5). Each color impression over black background changes with increasing layer thickness from metallic “silver” over copper-red to green. These are no spectral colors because the accompanying colors are, in each case, composed of several adjoining interference wavelengths. The different wavelengths are selected by varied layer thicknesses of the metal oxide and by particles tilted differently toward the image plane (see Color plates 7 and 8). Under diffuse illumination, these pearl luster pigments produce the spectral reflectance over black background shown in Fig. 2.46. With increasing layer thickness, the peak shifts to longer wavelengths and simultaneously broadens. In the figure, this begins in the violet region. The reflectance minimum also moves to longer wavelengths, in the figure starting from the yellow range. The spectral reflectance of the “silver” pigment corresponds to that of a light gray hue or to that of aluminum cornflake pigments. This suggests the substitution of the metallic aluminum pigment by the cheaper pearlescent pigment in suitable cases. 94 2 Light Sources, Types of Colorants, Observer Table 2.15 Interference colors depending on layer thickness of titanium dioxide on mica substrate (cf. Table 2.5) Layer thickness titanium dioxide/nm Platelet thickness/nm Interference color – inherent color over black background Transmitted complementary color 40–60 60–80 80–100 90–110 120–130 100–140 120–160 120–140 140–160 230–250 250–270 280–300 310–320 370–390 “Silver” Yellow Red Copper-red Violet Blue Green “Silver” Blue Green Blue-green Yellow-green Yellow Red Now, assume that the peaks in Fig. 2.46 can be interpreted as interference wavelengths of first order. Clearly, this is not exact, but sufficient for the following estimations. If we use the values of the relevant refractive indices of Table 2.11 and assume perpendicular observation, then Equation (2.1.18) delivers an approximate value for the thickness of the titanium oxide layer. For the R (%) Layerthickness in nm 80 a: 40 – 60 b: 60 – 80 c: 80 – 100 d: 120 – 130 e: 100 – 140 f : 120 – 160 60 40 b a c d 20 e f 0 400 500 600 λ nm Fig. 2.46 Spectral diffuse reflectance of mica pigments of different TiO2 coating thicknesses; measurements over black background, de:8 geometry16 16 The corresponding de:8 measuring geometry (see Section 4.1.2) simulates diffuse illumination conditions in closed rooms. 2.3 Effect Pigments 95 last five flakes indicated in Table 2.15, this approximate calculation results in values which are in the given thicknesses intervals. The systematic changes in spectral reflectance are characteristic features of the basis pigment series: the spectral reflectance curves measured under diffuse illumination are “fingerprints” of the relevant pearl pigments. This is an analog to absorption colorants. These fingerprints are sometimes utilized for analyzing mixtures with further pigments. Using directional illumination and angle-dependent reflectance measurements, particularly important information about the properties of the relevant interference pigments can be obtained. For the moment, we restrict the discussion to only one illumination angle although the colors of pearlescent, interference, and diffraction pigments depend on the illumination as well as the observation angle. The five spectral reflectance curves in Fig. 2.47 were measured with the green pearlescent pigment, which has a peak at 507 nm in Fig. 2.46, curve (f). The film of pearl luster pigments over a black background is illuminated at an angle β = 45◦ and the spectral reflectance is measured at aspecular angles μas = 15◦ , 25◦ , 45◦ , 75◦ , and 110◦ . As can be seen, the peak reflectance reduces dramatically with increasing measurement angle and it shifts to slightly shorter wavelengths. For observations near the specular angle, the reflectance exceeds values higher than 1.0 or 100%. The chosen five measuring angles are by no means sufficient to gather the entire color dynamics of pearlescent and interference pigments [52, 53]. 2.3.6.2 Iron-III-Oxide on Mica Substrate Crystalline α-Fe2 O3 has the highest refractive index of n = 2.88 among the substances listed in Table 2.11. As mentioned in the previous section, the total color impression of the layer composition with mica results from superposition of the layer-dependent interference color and the absorption color of the hematite. Iron-III-oxide produces a red to reddish-brown absorption color which is further modified by the thickness of the outer layer, see lower picture of Color plate 7. The color impression changes with increasing layer thickness from bronze colored to copper to purple or even reddish-green at the highest layer thickness. This is clear from the spectral reflectance curves shown in Fig. 2.48. In the cases of bronze, copper, and red, the reddish-brown absorption color is even amplified by the corresponding, nearly equal interference color like yellow, copper, and red. We return to the hue dependence of the layer thickness in Section 3.5.3. The superposition of interference and absorption leads to brilliant colors in the vicinity of the specular angle. Near this angle, the purple and reddish-green pearlescent pigments have a violet or green interference color caused by the relative high layer thickness of the hematite. With regard to comparable outer 96 2 Light Sources, Types of Colorants, Observer 150 R (%) 100 μas = 15° 50 25° 45° 0 400 75° 500 600 110° λ nm Fig. 2.47 Spectral reflectance of the green interference pigment from Fig. 2.46 at five aspecular measuring angles μas ; measurement over black background, illumination angle β = 45◦ layer thickness, the TiO2 -mica pigments produce a broader variety of interference colors, whereas the iron-III-oxide produces diverse types of red hues. The distinct brilliance of the α-Fe2 O3 pigments comes from the slightly higher refractive index of the hematite in comparison to that of titanium dioxide. The increased covering capacity is again a consequence of the typically increased scattering of the inorganic oxide. 2.3 Effect Pigments 97 R (%) a: Bronce b: Red-golden c: Copper d: Purple e: Red-green 80 Fe2O3Layer thickness 60 a b c 40 d e 20 0 400 500 600 λ nm Fig. 2.48 Diffuse spectral reflectance of mica pigments coated with Fe2 O3 of different layer thicknesses; measurement over black background, measuring geometry de:8 2.3.6.3 Combination Pigments Interference with more brilliant colors and higher absorption is generated by coating the substrate with two or more different metal oxides. A multitude of combination pigments are based on titanium dioxide-mica flakes, where the flakes are additionally vapor coated with Fe2 O3 or Cr2 O3 . These sorts of combination pigments show, in comparison to the original single-coated mica pigments, higher brilliance and a more distinct color flop. In the following, we consider the reflection behavior of mica combination pigments composed of layers of titanium dioxide in rutil modification coated with iron-III-oxide. The optical interactions between both metal oxides lead to many brilliant golden colors reaching from pale yellow-gold to rich red-gold to green-gold. With the addition of an oxide layer, a clear color extension with regard to the simple Fe2 O3 -mica particles is achieved. Furthermore, the change of the layer thicknesses of the two metal oxides generates a wealth of superimposed interference and absorption colors. The thicknesses of all three layers can be tuned with each other in such a way that the interaction of the interference and absorption components leads to a demanded coloristical effect, within limits. Similar features result from the substitution of the outer Fe2 O3 layer by Cr2 O3 . The combination of Cr2 O3 with TiO2 in anastas modification results in 98 2 Light Sources, Types of Colorants, Observer R (%) Fe2O3 TiO2 Rutil 80 60 Fe2O3 TiO2 Rutil 40 Cr2O3 TiO2 Anastas Cr2O3 20 TiO2 Anastas 0 400 500 600 λ nm Fig. 2.49 Diffuse spectral reflectance of two combination pigments Fe2 O3 /TiO2 (rutil), Cr2 O3 /TiO2 (anastas) on mica substrate of different layer thicknesses; measurement over black background, measuring geometry de:8; the curves of Fe2 O3 /TiO2 are shifted 20 units toward higher reflectance values for better overview high-luster blue-greenish to moss-green colors. Figure 2.49 shows the spectral reflectance curves measured under diffuse illumination of Fe2 O3 /TiO2 pigment and Cr2 O3 /TiO2 -mica pigment. Each has two different outer layer thicknesses, but the total coating thickness is constant in each case. The greater thickness of the outer oxide layer reduces the reflection. This is clearly caused by increased absorption due to greater layer thickness. In the case of a higher layer thickness of Cr2 O3 , this pigment additionally develops a clear peak in comparison to the quite broad peak belonging to the thinner outer layer. The increased influence of the Cr2 O3 layer on the interference development can be ascertained from the reflectance curve (f) in Fig. 2.46 for the green pearlescent pigment together with the two lower curves in Fig. 2.49. Altogether, titanium dioxide is responsible for the brilliance of the colors and the outer layer thickness for the interference color. The included absorption colors of iron oxide or chromium oxide exist otherwise under all observation angles. Nearly equal-colored oxide layers create a pearl luster effect of intensive colors which, at nearly all observation angles, show a noticeable color shift. However, if the color of an absorption colorant corresponds to that of the complementary color of the interference pigment, then a distinct two-colored effect is achieved, especially in the oxide combination of Cr2 O3 /TiO2 . Further inorganic absorption pigments such as Prussian blue, cobalt blue, Fe3 O4 , or carbon 2.3 Effect Pigments 99 black generate, in combination with titanium oxide on mica substrate, unusual color effects as well. 2.3.6.4 Liquid Crystal Pigments The color flop of liquid crystal pigments consisting of polysiloxane depends on the pitch height p and causes, for example, the color pairs violet/blue, blue/turquoise, blue/green, green-blue/gold, and green/copper-red. Flakes with blue/green-flop are shown in Color plate 10 at bright and dark field illumination over black background. The noticeable sparkle particle there is already green from the top view because of the higher pitch height compared to the other flakes. To the present day, mixtures of the transparent particles with absorption or other effect pigments produce unequaled and extremely brilliant colors. As mentioned at the beginning of the section, further shades can be obtained with a suitable background color. With regard to liquid crystal pigments, this concept is underlined by the example in Fig. 2.50. The reflectance curves correspond to background colors of white, red, and black as well as each top coated with a transparent film of the same liquid crystal pigment. The reflectance peak over black at 512 nm corresponds to the green color impression from the top view. The red background leads to a minimal blue-tinged red and the R (%) Background alone White 80 Layer over background Red 60 40 20 Black 0 400 500 600 λ nm Fig. 2.50 Spectral reflectance of a transparent liquid crystal pigment with d50 = 30 μm over white, red, and black background, as well as backgrounds alone; wavelengths of maximum reflectance over background: 512 nm (red), 531 nm (black); measuring geometry de:8 100 2 Light Sources, Types of Colorants, Observer white background creates a very light pink. The flat maximum of the white background at a wavelength of 490 nm is caused by fluorescence emission of the contained optical brightening agent (Section 4.2.6). Figure 2.51 shows the directional reflectance over a black background for illumination angle β = 45◦ and aspecular observation angles μas = 15◦ , 25◦ , 45◦ , 75◦ , 110◦ . With increasing measuring angle, the wavelength of the peak shifts from 483 to 520 nm. Simultaneously, the peak height decreases from R = 108% to about R = 2%. The angle dependence of the interference wavelength corresponds to the cosine function in Equation (2.1.20). R (%) μas = 15° β = 45° d50 = 30 μm 100 25° 50 45° 75° 0 400 500 λ nm 110° 600 Fig. 2.51 Spectral reflectance of a liquid crystal pigment with d50 = 30 μm for five aspecular measuring angles; measurements over black background, illumination angle β = 45◦ The brilliance of liquid crystalline pigments depends also on the average lateral dimension of the flake particles. This can be seen from the reflectance maxima in Fig. 2.52. The reflectance curves are measured for three different particle size distributions over the same black background and at constant illumination and aspecular angle of β = 45◦ and μas = 15◦ , respectively. The flakes have size distributions which correspond to the ratios of d50 /d99 = 30/90, 23/60, and 18/50 μm/μm. The reflectance maxima in Fig. 2.52 correspond to the ratios 30:23:18 of accompanying d50 values. In addition, this result is confirmed by measurements over red and blue background. The height of the reflectance maximum of liquid crystal pigments is, therefore, directly proportional to the mean flake size. Clearly, large-sized LCPs orient better to the background surface, in analogy to metallic flakes. These larger particles then show increased brilliance 2.3 Effect Pigments 101 R (%) β = 45° μas = 15° d50 = 30 μm 100 23 μm 50 0 400 18 μm 500 λ 600 nm Fig. 2.52 Directional reflectance at constant aspecular measuring angle μas = 15◦ of a liquid crystal pigment in dependence on particle size d50 ; measurements over black background, illumination angle β = 45◦ compared to smaller sized flakes. The colorimetric properties of the most important pearl luster and interference pigments are outlined in Sections 3.5.3 and 3.5.4. 2.3.7 Opaque Films Containing Absorbing and Effect Pigments From discussions up until now, it is clear that the creation of new colorations by mixtures or films consisting of modern effect and classical absorption pigments represents quite a challenge. Especially needed to meet this challenge are hiding layers which consist of transparent effect pigments and covering absorption pigments. A coating is called covering or hiding, if any colored background can no longer be observed from above the film (Section 3.4.3). Covering layers with coarse metallic, transparent pearlescent, interference, or even diffraction pigments are produced by mixtures of colorants which generate suited scattering or absorption. It is also important to consider the change of the originally desired color effect with the addition of further colorants and also the compatibility with the pure effect pigment. Experience shows that covering coatings with effect pigments can, in the most cases, be manufactured with three different colorants: carbon black, suitable absorption pigments, and fine metallic pigments [54]. 102 2 Light Sources, Types of Colorants, Observer A small amount of carbon black turns out to be quite effective for this. The resulting dark and sometimes even intense colors are caused by absorption of the complementary color with carbon black already inside the layer. Only a small volume amount < 1.0% of carbon black is normally sufficient. For larger concentrations, the interference color often appears too dark and the color travel (respectively, color flop) is too small or suppressed. The selective absorption and scattering of mixed in absorption pigments also result in covering layers of additionally impressive colors. Small amounts cause mostly brilliant interference colors. Larger amounts, however, can obliterate the pearl luster and interference effect: on the one hand, the interference intensity is increasingly masked and on the other hand, the complementary and part of the interference color are absorbed depending on the chroma of the absorption pigment. Finally, in the third method, the transparent pearl or interference pigment is mixed with a small amount of a special fine and, therefore, strongly scattering metallic pigment. In this case, the covering formulation is, however, accompanied by reduced brilliance, color saturation, and gloss. In all three mentioned cases, it is important to pay attention to the compatibility of the added components. Furthermore, the added amounts should be as small as possible in order to result in a coloristic effect changed only slightly. Altogether, the level of pigmentation of effect pigments in recipes depends on the desired color effect, the spreading rate of the pigment, and the molecular surroundings. For a few applications the pigment volume content is shown in Table 2.16. Apart from the application, the processability, the light, temperature, or weathering resistance, etc., additionally determine the total pigment amount of a coloration; see also Section 3.4.6. Table 2.16 Pigmentation level of effect pigments in various fields Pigment level % Employment Metallic pigments Pearlescent, interference pigments Lacquers, emulsion paints Thermoplastics, thermosets Printing inks Cosmetics Toiletries 0.5–2 0.5–3 1–45 1–15 0.05–1 0.5–20 0.5–2 1–30 1–50 0.05–1 From color physical point of view, mixtures of effect pigments together or with absorption colorants obey the laws of additive or subtractive color mixing (Section 2.4.3). Mixtures or layers of effect pigments show additive color mixing if the colors of the single pigments are based on the superposition of wavelengths; see Table 2.17. But, as soon as the light interacts only with one 2.3 Effect Pigments 103 Table 2.17 Additive and subtractive color mixing of effect and absorption pigments Pigment combination Color mixing Cause Interference pigment mixed with interference pigment Interference pigment mixed with diffraction pigment Additive Interference pigment on absorption pigment Additive and subtractive Interference pigment mixed with absorption pigment Subtractive Absorption pigment mixed with absorption pigment Subtractive Superposition of reflected interference and transmitted complementary color Superposition of interference, diffraction, and transmitted complementary color Superposition interference color, absorption of complementary color and selective absorption of the colored pigment Colored pigment absorbs parts of the complementary and natural color of the interference pigment Each colored pigment absorbs parts of the influx light Additive absorption pigment together with any further pigment sort, the resulting color impression is based on subtractive color mixing; see also the literature [54, 55]. Additive color mixing is fundamental in the human color sense and the based on colorimetry of versatile industrial applications. Finally, we return to optical properties of interference pigments which depend on the particle size and morphology. Smaller particles show a reduced pearl luster effect in comparison with those of larger sized. This is because the higher edge scattering reduces the luster. In the case of dominant scattering, the pearl luster and gloss of interference pigments can even disappear completely. An increasing lateral size dimension up to 200 μm improves not only the brilliance but also the sparkle of the pearlescent and interference pigments; furthermore the color travel passes more wavelengths. However, with increasing flake geometry, the hiding power and DOI are reduced. The pigment properties shown in Table 2.18 correlate with related properties of metallic pigments listed in Table 2.9. In other words, comparable color properties of metallic, pearlescent, and interference pigments change in the same direction depending on the flake size. We have, thus far, still neglected opaque multi-layered pigments (Table 2.13). A considerable part of their color physical properties correspond to those of transparent effect pigments. An advantage of these pigments is the fact that the color effect is not distorted by additional colorants, but the absorption and selfscattering of the particles softens the original color. Further similarities between different effect pigment sorts are uncovered in Section 3.5.3. 104 2 Light Sources, Types of Colorants, Observer Table 2.18 Assessment of some properties of pearlescent and interference pigments in dependence of the particle size Particle size Φ/μm Property Φ<5 5 ≤ Φ ≤ 25 10 ≤ Φ ≤ 60 30 ≤ Φ ≤ 200 Brilliance Color flop Covering capacity DOI Low Reduced Excellent Very good Silky Low Very good Good Very well Striking Good Low Sparkling Distinct Low Very low 2.3.8 Colors of Diffraction Pigments Although the diffraction of light waves has been known since the beginning of the 19th century, this phenomenon has only been used in color physics for a few years [56]. Waves are diffracted, analogous to interference, when they interact with structures of dimensions on the same order of magnitude as the wavelengths. Polychromatic light is split up by diffraction into the spectral components. Reflective diffraction pigments are the sorts that is of interest in industrial color physics. These consist of a metal substrate with a grating of embossed periodic grooves. In addition, the substrate is coated with inorganic substances; see Table 2.12. Each particle works as a reflection grating. The nano-engineering method of interference lithography can be used to produce periodic grating structures on surfaces. This method is based on the interference of two laser beams; see Fig. 2.53. With the two coherent waves from the same source, each of wavelength λL , an interference fringe pattern of parallel fringes of distance d results (Michelson configuration). This distance is given by the relation d = λL · sin ϑ, λL (2.3.1) d 2ϑ λL Fig. 2.53 Generation of parallel structures with two coherent light rays using the Michelson configuration (schematically) 2.3 Effect Pigments 105 where ϑ denotes the half of the divergence angle. The periodic laser fringe pattern is directed onto a metallized thermoplastic film or photoresist film so that this pattern is transferred into the film as an exposure. After removing the organic backing layer by thermal or chemical procedures, the remaining metal foil of projected groove geometry is evaporated in vacuum with further substances which are also used in nanotechniques. The substrate is coated symmetrically so that the diffraction always develops at the illuminated surface of the reflection grating. The films of up to 1 μm in thickness can be broken up into particles with lateral dimensions between 10 and 300 μm using ultrasound. The resulting flakes can be sifted by pigment size. Flakes with mean diameters of d50 = 20±2 μm are preferably used for print media and coatings [56]. The regular grating patterns consist not only of parallel but also rectangular, diagonal, or hexagonal lines. Presently, diffraction pigments are manufactured with 100 up to 5,000 equidistant parallel lines per millimeter (l/mm). The cross section of the grooves can be chosen in such a way that the first diffraction order corresponds to the geometrical direction of reflection (blaze techniques, Section 2.1.7). The diffraction particles shown in Fig. 2.54 have a grating constant of 1,000 l/mm. The substrate consists of highly reflective aluminum of about 80 nm thickness and periodic folding. Using PVD techniques, the metal film is coated on both sides with MgF2 of about 450 nm thickness; see cross section at fracture in Fig. 2.55. Diffraction pigments have been produced industrially since 2002, although symmetric grating cross sections have been used in technical optics since about 1980. The spectral reflectance of diffraction pigments with three different grating constants measured by diffuse illumination and de:8 geometry is shown in Fig. 2.56. For pigments with 1,400, 2,000, or 3,000 l/mm, the reflectance Fig. 2.54 Diffraction pigments with periodic grating dividing of parallel lines; grating constant 1,000 l/mm (source: Flex Products Inc, Santa Rosa, CA, USA) 106 2 Light Sources, Types of Colorants, Observer Fig. 2.55 Cross section at fracture of a diffraction particle with periodic grating dividing; the surfaces of the aluminum substrate are vapor coated with MgF2 (source: Merck KGaA, Darmstadt, Germany) R (%) 3,000 l/mm 80 70 60 2,000 l/mm 50 1,400 l/mm 40 30 400 500 600 λ nm Fig. 2.56 Spectral reflectance of diffraction pigments of magnesium fluoride/aluminum of three different grating constants; the middle and upper curves are shifted 5, respectively 10 units toward higher scale values is between R = 0.4 and R = 0.7. This quantity depends on the reflectivity of the metal layer, the number and thickness of the non-metallic vapor-deposited films, the accompanying refractive indices, as well as the mean particle size. The pigment with 1,400 l/mm produces a silver metallic color impression at observation perpendicular to the coating surface. The nearly flat spectral reflectance 2.3 Effect Pigments 107 shown in Fig. 2.56 is known from silver-colored metallic or pearlescent pigments. Under diffuse illumination, particles of grating constant 2,000 l/mm appear bluish and those of 3,000 l/mm produce a yellow-orange color impression. The almost equal form of the reflectance curves in Fig. 2.57 indicates that the thickness of the aluminum substrate between 80 and 240 nm is, as to expect, of no influence with regard to the color impression. For a fixed grating constant of 1,400 l/mm, the height of the reflectance – and, therefore, the brightness – is only slightly increased with aluminum thickness. With substrate thicknesses greater than 240 nm, the surface roughness increases and, therefore, also the interface scattering. This scattering reduces, however, the intensity of diffraction. R (%) 240 nm 70 160 nm 80 nm 60 50 400 500 600 λ nm Fig. 2.57 Spectral reflectance of MgF2 /Al pigments with aluminum layer thicknesses of 80, 160, and 240 nm; grating constant 1,400 l/mm; the middle and upper curves are shifted 10 units toward higher scale values Reflective diffraction pigments consisting of a ferromagnetic substrate allow for the orientation of the particles according to an external magnetic field. Preferred ferromagnetic materials are nickel, iron, cobalt, but also elements of the lanthanide series. For better understanding of the orientation of ferromagnetic particles in an external magnetic field, it is useful to make a short excursion into magnetostatics. The ferromagnetic state in solids is caused by non-compensated electron spins of the unsaturated 3d- and 4f-electron shells of metal ions. The unbalanced 108 2 Light Sources, Types of Colorants, Observer angular momentums of the electrons behave, therefore, like magnetic elementary dipoles which, in the crystal state, respond to two different forces. The first, the anisotropic force causes an alignment of the dipoles parallel to an external bounding face and the second, the exchange force forces the dipoles to parallelize to each other in the volume. In a magnetic material, anisotropic and exchange forces produce zones of equal magnetization direction. These zones have linear extensions between 1 μm and 1 mm which are called domains or Weiss areas, after their discoverer P.E. Weiss. An external magnetic field can drive two geometrical processes in the domains: a change of the threedimensional extension as well as a rotation from the original position at constant volume. Both effects are represented schematically in Figs. 2.58a–c. Figure 2.58a represents the original position of four domains in a ferromagnetic substance. A weak external magnetic field causes a shift of the domain walls; see Fig. 2.58b. An even higher external magnetic field strength turns the molecular magnets more into the direction of the external field, accompanied by a further extension of the domain volume, Fig. 2.58c. In general, domain wall shifts occur at moderate magnetic field strengths and domain rotations only at higher strengths. The basic driving mechanism for the orientation of ferromagnetic domains or particles parallel to an external field is the tendency of such systems to seek a state of minimal total energy. This is achieved by an internal demagnetization field which counteracts the external field. A sufficiently high external magnetic field strength causes a total rotation of the domains. If the lateral dimensions of free particles are on the order of magnitude of the domains, then the rotation into magnetic field direction is performed by the entire particle. This effect is H a) b) H c) Fig. 2.58 Schematic representation of Weiss domains in a ferromagnetic material: (a) without external magnetic field, (b) with weak magnetic field, and (c) with strong external magnetic field H 2.4 Observer 109 known from iron filings, which align along the lines of an external magnetic field. Also ferromagnetic diffraction pigments are subject to such rotations. With the help of an external magnetic field, a nearly uniform orientation of diffraction pigments of ferromagnetic substrate can, therefore, be fixed before and during crosslinking of a binder. The both diffraction pigments given in the last line of Table 2.12 are ferromagnetic. With an additional Ni layer for the substrate, their composition corresponds to the two- and three-layered diffraction pigments one line higher in the table. The ferromagnetic particles consisting of the three different layers MgF2 /Al/Ni and grating constants of 1,400, 2,000, or 3,000 l/mm produce, under diffuse illumination, a nearly uniform silver-colored impression. A further PVD coating with chromium causes a gold-yellow color. The spectral reflectance curves of ferromagnetic diffraction pigments are of the same shape as the curves of non-ferromagnetic particles with grating constants of 1,400 and 2,000 l/mm; see Fig. 2.56. Certainly, on account of the particle orientation in a magnetic field, an angle-dependent colorimetrical behavior results, one which had not been observed before (Section 3.5.5). After a detailed description of the optical operation modes of industrially used colorants, we can conclude: between the rock and cave paintings of natural colors and the modern produced and applied colors there was, without doubt, an impressive historical development. This is accompanied by broad research as well as process and application technology in color industry. In spite of this, all presently known and also newly developed or modified colorants are merely orientated toward the color perception of humans. The human color sense is, therefore, discussed in some detail in the next section. 2.4 Observer In addition to the importance of the light source and the color pattern, the most important and final crucial factor for the emergence of color perception is the observer. His/her subjective color sensation comes from the remaining light waves that reach the retina of the eye after source light interacts with the colorants. Nearly all efforts in processing and applying natural, modified, and synthesized colorants are oriented toward the capability of human color sensation. Long ago, Newton emphasized the fact that color production is ultimately based on neural processes. This means that outside the visual cortex, colors do not exist, but only electromagnetic waves. In the following, we give a brief overview of the modern physiological and neurological understanding of color sensation [57, 58]. These connections lead directly to the fundamental Grassmann laws of additive mixing of colors. The standardized CIE color values of the years 1931 and 1976 as well as the broad color physical and colorimetrical applications are based on these laws. 110 2 Light Sources, Types of Colorants, Observer 2.4.1 Color Perception and Color Theories As already mentioned in the introduction of this text, color perception is produced by psychophysical and neural processes. Color sensation is, therefore, not directly measurable with normal physical methods. The first important element contributing to overall color perception is the eye. The essential optical components of the human eye for image formation are shown in Fig. 2.59. The cornea is only 0.5 mm thick and of fixed focal length of 25 mm, the iris has a lightness-dependent aperture ratio of 28:1, and the crystalline lens is of variable focal length. This focal length amounts about 50 mm for the resting eye when relaxed for distant vision. For an eye of normal vision, these optical elements provide a clear and focused image on the retina in the area of the fovea. In the retina are located two types of photosensitive receptors: first, the rods responsible for dusk vision and achromatic colors for luminance less than 0.01 cd/m2 (scotopic vision); second, the cones for color vision for luminance higher than 10 cd/m2 (photopic vision).17 If the eye is fully adapted to darkness, just nine photons are required before a light stimulus is detected. In cases of middle illumination for luminance in the range of 0.01 and 10 cd/m2 , rods and cones are simultaneously active (mesopic vision). The retina of the human eye contains altogether about 125 million visual cells, but only 5% consist of cones. In the small area of the fovea for visual angles of about ±0.5◦ , there are only cones present. Here they are of maximum density and enable focused vision only at this spot of the retina. The majority of lris Crystalline lens Cornea Fovea Macula Optic axis Blind Spot { Optic nerves Retina Fig. 2.59 Horizontal section of the human eye 17 For definition of unit cd (candela) see footnote 1 in Section 2.1.3. 2.4 Observer 111 the rods are, however, distributed outside of the macula in an area of visual angle greater than ±5◦ (for visual angle, see Fig. 2.65). At the place of the blind spot of missing visual cells, the cord of the optic nerves continues to the brain.18 The different density distributions of rods and cones in the human retina are shown in Fig. 2.60. Four different photosensitive pigments are contained within the outer zones of the visual cells: one pigment in the rods and three pigments in the cones. The photosensitive pigments consist of a protein molecule denoted as opsin to which a derivative of vitamin A1 molecule is bound. This chromophoric group is common to the four pigments. The absorption spectrum of a photosensitive pigment depends on the kind of protein as shown in the normalized representation in Fig. 2.61. The pigment in the rods, called rhodopsin, shows an absorption maximum at the wavelength of 498 nm, the tails of the maximum project into the spectral absorption ranges of the cones. The absorption maxima of the three cone pigments occur at wavelengths 437, 533, and 564 nm. These wavelengths are perceived as blue, green, and red and the corresponding cones are, therefore, called blue, green, and red receptors. In the English-speaking medical literature they are denoted as S-, M-, and L-cones, indicating the selective sensitivity at short, middle, and long wavelengths of the visible spectrum. The three cone types are not equally distributed throughout the retina. The relative distribution for blue:green:red is about 1:20:40. From the similar shapes of absorption Number of retinal receptors × 103/mm2 Blind spot Rods Cones 150 100 50 0 –80° –40° 0° Angle from fovea center 40° Fig. 2.60 Density distribution of rod and cone receptors across the human retina 18 In modern neurology, the retina is interpreted as a part of the brain. 80° 112 2 Light Sources, Types of Colorants, Observer λ max 437 498 533 564 nm Relative absorption 1.0 0.5 Cones Rods 0 400 500 600 λ nm Fig. 2.61 Normalized spectral absorption of the four different photo receptor types in the human retina [57] curves in Fig. 2.61, it is possible to conclude that the spectral absorption mechanisms of the three cone types are basically identical, although the curves seem to be shifted along the wavelength axis. Up until now, we have assumed normal color perception, called trichromacy on account of the three different cone receptors. Some sort of color vision deficiency with at least one defective color receptor occurs in about 0.5% females and about 7% males [58–60]. Although some animal species show an evolutionary caused tetrachromacy [61], this property has almost disappeared completely of human beings. In only extremely rare cases of women a fourth color receptor was proven; such a receptor shows a maximum sensitivity in the range of yellow wavelengths [62]. The unusually varying description of defective color vision in the literature is a consequence of the fact that previous generations of researchers used the constrained color perception for indications of the neural color sensation. The following kinds of anomalous color vision can be distinguished: – color asthenopy: fast onset of tiredness during color vision; – color amblyopy: selectively reduced ability to distinguish colors; – color anomaly: caused of defective or missing color receptors. The color anomaly can be divided further into: – anomalous trichromasy: the characteristic feature is a reduced perception of one color during simultaneous observation of several varied colors. In this 2.4 Observer 113 case, there are three color receptors available but one does not work normally. More concretely, there are red-, green-, and blue-yellow weakness; – dichromasy: is present if a certain color is not perceived at all; dichromasies are the most frequent anomalies in humans and can be passed on gender specifically. Dichromates have only two color receptors, leaving red-, green-, and blue-yellow blindness; – achromatopsy: this term is a synonym for complete color blindness. Affected people do not possess any of the three well-operating color receptors; such people can only differentiate lightness levels. Although the after retinal occurring neural processes are only vaguely understood for normal color vision – and surely will remain for a long time at this level understanding – we follow at least roughly the path of the neural signals in the brain. This discussion is also carried out here to indicate to the reader how difficult the search of an adequate color vision theory is. About 50 ms after photon absorption in the photo pigments, retinal signals reach the optic nerve behind the eye. Each left and right half of the retina of both eyes form a nerve fiber; see Fig. 2.62. At the position of the optic nerves crossing over, the so-called chiasma or optic chiasma, each nerve fiber coming from the left and right half of both retinas is shared to the related brain lope. In the optic chiasma, however, there is no mixing of the incoming neural signals from both eyes. The subsequent optic tract ends at the region of the so-called lateral geniculate nucleus, where Lateral geniculate nucleus Optic radiations Optic tract Visual cortex Chiasma Optic nerve Fig. 2.62 Top view of the head to the human brain with indicated path of neural signals between the two retinas and the visual cortex; the visual cortex is in no way a sharp restricted region of both brain lopes, but individually different expanded 114 2 Light Sources, Types of Colorants, Observer the separate incoming neural impulses from both eyes are united into groups. Along several optic radiators, the transformed signals directly reach the region at the back of the brain lopes. This is the location of the center of our visual perception, called the visual cortex. In one special zone of the visual cortex, the actual color perception is produced, just about 100 until 150 ms after photon absorption in the retina. On the basis of this incomplete knowledge, it is necessary to have at least an adequate theory of human color perception. Although the trichromatic color theory of Young–Helmholtz and the opponent color theory of Hering have been shown to be true on physiological basis, neither theory can concretely explain the mechanism in the visual cortex for producing color perception (cf. Chapter 1). Likewise the modern retinex theory of Land, based on studies of color constancy, delivers no usable ideas about the emergence of color impression in the visual cortex. According to the zone theory, proposed by Müller [63] and Judd [64], the first zone contains the three independent S-, M-, and L-color receptors of the trichromatic theory. In the second zone, the generated nerve impulses are transformed according to Hering’s theory into an achromatic signal and two opponent chromatic signals. The visual cortex represents the third zone. The arriving neural signals initiate the color impression including the memory. Accordingly, the zone theory merely brings together the verified and accepted basics of both theories mentioned above. On the basis of current knowledge, it is possible to distinguish 30 different zones of the brain responsible for vision. Merely five of them are assigned to the color sense, of these only one dominates for color perception. The neural processes between photon absorption in the retina and induced color impression in the visual cortex remain unclear. It is not surprising, therefore, that only the physiological confirmed theories of Young–Helmholtz and Hering lead to scientific color applications such as colorimetry. The lacking of a theory which accurately describes the human color sense turns out to be disadvantageous, in particular for quantification of visually perceived color differences. As shown in Sections 3.1 and 3.2, only empirical formulas are given to express a color difference numerically. This unsatisfactory situation has existed since the beginnings of colorimetry. 2.4.2 Color Perception Phenomenon In the previous section, we have roughly outlined how humans perceive color. Now we direct our attention at some remarkable color phenomena of the complex processes of color sensation. Among these are the so-called simultaneous contrast, negative, or positive after-images or phosphene perception. These effects are important in different color applications and need to be taken into 2.4 Observer 115 consideration during color assessment. These are, therefore, considered briefly here. The term simultaneous contrast describes the phenomenon that the lightness and the color of the surroundings influence the color impression. We should differentiate between simultaneous lightness contrast and simultaneous color contrast. A middle gray, for example, appears darker in a white neighborhood than in a black one; this is lightness contrast. In a similar manner, differences between dark chromatic colors are resolved worse with bright-surround field than with dark-surround field; this is color contrast. For visual assessment of color differences, it is, therefore, necessary to always use the same achromatic surrounding color (Section 3.2.2). Phenomenon of simultaneous color contrast is more varied than simultaneous lightness contrast. In both cases, the contrast is amplified just at the edges of color areas. The so-called lateral inhibition is responsible for the altered color perception. This term means that the neural signals in adjacent receptors within the retina interact with one another. Changes that are caused by lightness or color alone are, therefore, felt lesser strongly; contrasts, on the other hand, are perceived amplified. An additional quite remarkable ability of human color sense is the fact that many object colors are unchanged in spite of illuminant change. For example, a blue color is still perceived as the same blue, although the spectral energy distribution of the illuminant is varied. Another property of the visual sense is combined with the so-called afterimage. This after-effect occurs, if a single-colored area of high color saturation is seen with fixed eyes during about 1 min, and without movement of the eyes or head. If the eyes are afterward adapted to a white area, the color impression remains for some time. This negative after-image is produced in the complementary color. The reason for this is that the most of the corresponding receptors are desensitized during the fixing of the chromatic surface; the remaining sensitized receptors continue to have a reinforced effect during the white impression. The contrary phenomenon becomes apparent if the eyes are closed for some minutes, and then for a short time directed toward a contrasting object and then closed again. The resulting positive after-image shows that the color sensation actually lasts longer than the original action of the light. A longer continuing involuntary persistence occurs on chromatic adaption. After-images are in particular of importance for colorists if color shades are to be judged after a bright lighting phase with monochromatic sources. Therefore, before assessment of critical hues, for example, is important to look at a large, plane, and achromatic area for several minutes in order to avoid influences of after-images. A further time-dependent characteristic of color perception is associated with a short viewing of a color stimulus. For a viewing time of less than 0.1 s, most hues appear progressively desaturated. In the case of very short stimuli of about 3 ms duration, monochromatic light in the range from 490 to 520 nm appears 116 2 Light Sources, Types of Colorants, Observer achromatic white or gray. These effects are attributed to the property that the response time of the receptors is clearly shorter for achromatic colors than for chromatic colors. Colors can be perceived, quite astonishingly, also without an outside stimulus; this phenomenon is called phosphene. After the eyes are accommodated to darkness for a sufficient time, it is normal to observe light or colored spots. The effect of outside pressure on one or both eyes results in time-dependent changing light areas or colored schlieren. Phosphene occurs in addition without dark adaption by sudden pressure or electric current. In these cases, the influence from outside the closed eyes evokes disturbances in circulation and neural transmission. There are further phenomena of color perception which depend on spatial conditions or movement of the colored object. These are not of interest to color physics and are beyond the scope of this book. With exception of phosphene, the above outlined effects enable us to perceive a world of stable colors and lightness, although we are surrounded by an even greater variety of electromagnetic waves of different frequencies and changing intensities. But these electromagnetic waves are responsible for further color effects such as additive color mixing, which is effective especially in the human eye, or subtractive color mixing which, for example, is present in absorption colorants. Both phenomena are subjects of the following section. 2.4.3 Subtractive and Additive Mixing of Colors A deeper insight into the human color sense has been obscured as a consequence of subjective color judgment and, up to now, the inability to detect directly the chromatic signals at each position from the retina to the visual cortex by objective measurements. Therefore, Grassmann tried an indirect way to come closer to the human color sense [65]. In order to describe color impressions quantitatively, he avoided some of the briefly mentioned problems by using three monochromatic light sources of different wavelengths; see Fig. 2.63. Consequently, color stimuli are generated under defined conditions and color effects can be observed and registered. Non-self-luminescent colors are unsuited for such investigations, because the colors of these light sources are required to be produced quite simply, reproducible, and additionally, they need to be mixed trouble-free with one another. For better understanding of the results achieved by Grassmann, it is useful to go into details of subtractive and additive color mixing, both of which are basic properties of color physics. Subtractive color mixing is present, for example, after polychromatic light has passed through an optical selective filter: one part of the incident light is absorbed by the filter, and, therefore, denoted as subtracted. In Table 2.19, some 2.4 Observer 117 Red Green Blue White screen Observer Black partition Incandescent lamp Fig. 2.63 Configuration for producing light colors for additive color mixing examples of subtractive color mixing are listed, cf. also Color plate 1, overlapping upper colors. In the case of several simultaneously used filters, the resulting transmitted color is independent of the order of the filter. Subtractive color mixing dominates in all sorts of absorption colorants and their mixtures; the color result of a colorant mixture is, therefore, independent of addition sequence. Subtraction of light waves occurs also in special cases of mixtures with effect pigments, as well as during developing of color pictures, among other things. In contrast, additive color mixing occurs by superposition of colored lights. The likely most important example is the human color perception. Additive color mixing is subject to photons of visible light, provided they enter the retina at the same time. Superimposed, the waves or photons are denoted as added. If the retinal photo pigments are stimulated simultaneously by polychromatic light, merely one single color stimulus is induced. In this context the synonymous term “additive color mixing of light” is correct. Further examples of additive color mixture are computer or television screens. For such screens, addressable groups of closely packed red, green, and blue pixels of diameter less than 0.1 mm (of phosphorus, liquid crystals, or inert gas cells) are stimulated simultaneously to produce color points. Color pixels of such small lateral dimension cannot be perceived separately by the eye at sufficient distance; therefore, only a single color stimulus is produced. A macroscopic example is shown in Color plate 1, lower overlapping colors, cf. Table 2.19. 118 2 Light Sources, Types of Colorants, Observer Table 2.19 Examples of subtractive and additive mixing of colors; cf. Color plate 1, overlapping color segments Subtractive mixing of colors Additive mixing of colors Initial colors Mixed color Initial colors Mixed color Magenta, yellow Yellow, cyan Cyan, magenta Magenta, yellow, cyan Red Green Blue Black Green, blue Blue, red Red, green Green, blue, red Cyan Magenta Yellow White From the position and shape of the curves in Fig. 2.61, it is clear that the light absorption of the red, green, and blue color receptors occurs in different and partially overlapping spectral regions, although only one color stimulus is evoked in the retina. The color stimulus Φ clearly depends on wavelength λ. If the photons of the source directly reach the retina, the color stimulus Φ(λ) equals the spectral energy distribution S(λ) of the source. For non-self-luminous colors, Φ(λ) is given by the product of S(λ) and the reflection R(λ) or transmission T(λ) of the illuminated layer: Φ(λ) = S(λ) · T(λ), (2.4.1) Φ(λ) = S(λ) · T(λ). (2.4.2) Using several illumination sources simultaneously, each individual color stimulus is summed up to form an aggregate stimulus, exactly the same procedure as in the retina or in screens. All further color physical themes dealt within this book, such as color vision, colorimetry, color measurement, or color recipe prediction, are based on the fundamental empirical laws of additive color mixing formulated by Grassmann in 1853. As briefly mentioned at the beginning of this section, for his investigations, Grassmann used three monochromatic light sources emitting constant red, green, and blue wavelengths, respectively. With a similar configuration to that shown in Fig. 2.63, but without the incandescent lamp, a new light color is mixed on a white field by superposition of these three wavelengths. The experimental results show that any additive color mixing is characterized by three arbitrarily chosen primaries R, G, B, in this case lights, which are given by the corresponding color values R, G, B. They correspond to the relative luminance of the light sources used. Of importance is that each of the three color values R, G, B is not necessarily restricted to a fixed wavelength in the red, green, or blue range; they are optional. The three color values R, G, B are combined in the so-called color 2.4 Observer 119 stimulus specification C, which is written as a vector in three dimensions19 C = (R, G, B)T . (2.4.3) Furthermore, the primaries R, G, B can be interpreted as the unit vectors of a three-dimensional space R = (1, 0, 0)T , G = (0, 1, 0)T , B = (0, 0, 1)T . (2.4.4) Using terms such as color values, color stimulus specification, and primaries, Grassmann summarized his results in the following three empirical laws of additive color mixture: 1. For identification of a color stimulus specification, three independent primaries, which cannot be matched by additive mixture of the other stimuli, are necessary and sufficient. 2. The result of an additive color mixture is influenced only by the color stimulus specifications, not by their spectral compositions. 3. All producible color mixing series change continuously. Now, we consider the consequences of the Grassmann laws. According to his first law, each color stimulus specification C is represented by an equation of the form C = RR + GG + BB. (2.4.5) It is called the color equation. Equation (2.4.5) is of central significance to all of color physics. It is valid for arbitrarily selected primaries R, G, B. The three color values R, G, B provide the contributions of the three primaries to the color stimulus specification C. In other words, the color values describe the entire color impression. This is synonymous with the statement that every color impression is given in quantitative form by three color values R, G, B. The numerical quantities of R, G, B are, therefore, representatives of a color impression. The second law of additive color mixing turns out, for example, to be applicable to all cases of color matching; it is the basis of color recipe prediction. For any color impression, it is irrelevant of which individual colorant components the corresponding coloration is composed. The same holds for the mixture of lights of different spectral distributions. If, for example, two arbitrarily given color stimulus specifications C1 and C2 are matched by three primaries R, G, B, then from the first Grassmann law, it follows 19 The exponent T symbolizes a transposed vector. 120 2 Light Sources, Types of Colorants, Observer C1 = R1 R + G1 G + B1 B , (2.4.6) C2 = R2 R + G2 G + B2 B. (2.4.7) According to the second law, the additive mixture of both color stimulus specifications is given by the sum of the corresponding individual color values C = C1 + C2 = (R1 + R2 )R + (G1 + G2 )G + (B1 + B2 )B. (2.4.8) The additive color mixing produces a new color stimulus specification C, from which is not possible to discern whether or not it consists of several individual color components (i.e., color values). The third law of additive color mixing implies that if one or more components of the mixture are gradually changed, then the resulting color values also change gradually, that is, as opposed to changing in a discontinuous fashion. Therefore, if we assign the color stimulus specification to a point in three-dimensional space, all additively mixed color stimuli generate an own continuous and coherent color solid, the color space. Grassmann has formulated originally four laws, which in modern literature are summarized to the three given above. In the next section, we pursue the industrially important question, how we can use color values to treat color impressions objectively? 2.4.4 Tristimulus Color-Matching Experiments According to the laws of additive color mixing, a given color is characterized by three color values R, G, B. For handling of these laws, it is useful to establish the optional primaries R, G, B in such a way that at least the requirements that follow are fulfilled. The primaries should – be definite, reproducible, and computable from color measurements; – have always a positive sign; – correspond to photopic vision; – achieve numerical color differences corresponding to the visually perceived color differences. The system introduced from the CIE in 1931 meets, to a large extent, the listed first three criteria [7]. The final listed requirement is as yet not satisfactorily solved (see, e.g., Section 3.2). The CIE 1931 system rests on the results of tristimulus color-matching investigations of Wright [66] and Guild [67], which used ten and seven people, respectively. For these experiments, the complete configuration used is shown in Fig. 2.63. With a source of nearly monochromatic 2.4 Observer 121 light, a test stimulus of ±2.5 nm wavelength accuracy was generated by illuminating a bipartite white screen which was shielded against the other half. On this second field, the additive mixture of three primaries was projected. These were the matching stimuli of the three monochromatic lights. By using adjustable light controllers, the observer subjectively adjusted the light flux of the three primaries to obtain a color match between the two separated fields. Wright and Guild used three monochromatic light sources of wavelengths 700.0, 564.1, and 435.8 nm. In the case of a match, the test stimulus was characterized by the three luminance values of the primaries. Before the actual matching experiments were performed, the intensities of the three primaries were adjusted to obtain an additive mixture of achromatic white. This procedure is termed as white balance; an example is shown in Color plate 1, see lower overlapping color circles. The color values are, therefore, normalized with regard to the radiant energy density of the primaries for white balance: the accompanying color equations are valid for the so-called equienergy spectrum. Colors differing only in their lightness belong to the same chromaticity. The color stimulus specification of the test stimulus at wavelength λi is termed as Ci . The matching color values of the three primaries are called colormatching values and are assigned by ri , gi , bi ; they are valid especially for the chosen primaries R, G, B [68, 69]. Due to the subjectively different color sensation of the observers, the ri , gi , bi values fluctuate. Their mean values are denoted by r̄i , ḡi , b̄i . In the case of match, the color equation Ci = r̄i R + ḡi G + b̄i B (2.4.9) is fulfilled according to the first Grassmann law. However, the matching procedures certainly show that not every given spectral color can be matched with the preset primaries. For example, a blue-green color of wavelength 490 nm does not match by mixing the blue or green primaries alone. In this case, the color match of equally saturated color fields is only achieved if an amount r̄io of the primary R is directly added to the given test stimulus specification Ci . This procedure is called outer mixture and is represented by the color equation Ci + r̄io R = ḡi G + b̄i B. (2.4.10) By adding the quantity −r̄io R to each side of color equation (2.4.10), an equation analogous to Equation (2.4.9), but with negative amount −r̄io on the right-hand side, results. This is a less than satisfactory situation to which we return in the next section. For continuous wavelengths λ, the mean color-matching values r̄i , ḡi , b̄i turn into the color-matching functions (CMFs), which are assigned to r̄(λ), 122 2 Light Sources, Types of Colorants, Observer Color matching function 0.4 – r (λ) – b (λ) 0.3 g–(λ) 0.2 0.1 0 546.1 435.8 700.0 –0.1 400 500 600 λ nm Fig. 2.64 Color-matching functions r̄(λ), ḡ(λ), b̄(λ) of the equienergy spectrum using wavelengths of 700.0, 546.1, and 435.8 nm for primaries R, G, B 2° 10° 50 1.8 9.1 Fig. 2.65 Visual angles of 2◦ and 10◦ ḡ(λ), b̄(λ), and shown in Fig. 2.64. The color match on both color fields is carried out with a visual angle of 2◦ by the observer; see Fig. 2.65. Under this observation angle and at normal viewing distance of 50 cm, a circle area of 1.8 cm in diameter is perceived. In the same angular range, the fovea of the retina contains only cones (Fig. 2.60). An observer, which fulfills these conditions, is called 2◦ standard observer, abbreviated 2◦ observer, and is represented by the three CMFs r̄(λ), ḡ(λ), b̄(λ). As shown in Fig. 2.64, the CMFs have unequal peak heights. This represents the different sensitivities of the corresponding three retinal color receptors. Among the CMFs, only the function r̄(λ) has a negative amount with the dip minimum at about 522 nm. The negative proportion is a consequence of the outer mixture. If the reference color stimulus specification corresponds to the 2.4 Observer 123 wavelength of a primary, the other two primaries are not required and their corresponding CMFs are zero. This can be taken from Fig. 2.64 for wavelengths of 435.8, 546.1, and 700.0 nm. Finally, it needs to be pointed out that the trichromatic matching experiments were achieved only with few people, under photopic vision with an observation angle of 2◦ and dark surroundings. Insights for scotopic or mesopic vision, bright surroundings, or large colored fields have, up to now, not been performed. 2.4.5 Determination of Tristimulus Values In view of color measuring methods and colorimetric applications, we will use discrete wavelengths λi in the following. A trichromatic stimulus is induced, according to the explanations in Section 2.4.3, by additive mixture of all monochromatic color stimuli Φ i = Φ(λi ). In the case of non-self-luminous colors, the color stimulus Φ i follows, according to Equations (2.4.1) and (2.4.2), from Φi = S(λi ) · R(λi ) (2.4.11) Φi = S(λi ) · T(λi ), (2.4.12) or because a non-self-luminous color is to illuminate with a source of spectral power distribution S(λi ). Each retinal color stimulus Φ i is represented by a corresponding color stimulus specification Ci . If there are simultaneously i = 1, 2, . . . , N stimuli Ci , the total color stimulus specification is given by additive mixture: C= N Ci . (2.4.13) i=1 Applying Equation (2.4.8) with N ≥ 2, C= N i=1 Ci = N i=1 Ri R + N Gi G + i=1 N Bi B (2.4.14) i=1 follows. The color values Ri , Gi , Bi correspond, on the other hand, to the product of the color stimulus Φ i , one of the respective CMFs r̄i , ḡi , b̄i , and the technically given wavelength interval width Δλ of the used illuminant. From this, it is possible to write the equations for the color values: Ri = Φi r̄i Δλ, (2.4.15) 124 2 Light Sources, Types of Colorants, Observer Gi = Φi ḡi Δλ, (2.4.16) Bi = Φi b̄i Δλ . (2.4.17) If we insert these relations into Equation (2.4.14) and compare the new equation with Equation (2.4.5), finally the color values R, G, B of a non-self-luminous color follow from expressions: R= N Φi r̄i Δλ, (2.4.18) Φi ḡi Δλ, (2.4.19) Φi b̄i Δλ. (2.4.20) i=1 G= N i=1 B= N i=1 If the emitted wavelengths are quite closely spaced together so that infinitesimally small wavelength intervals dλ can be assumed, the discrete color stimuli Φ i can be written as the color stimulus function Φ(λ). Then, the color-matching values r̄i , ḡi , b̄i also become the CMFs r̄(λ), ḡ(λ), b̄(λ). Accordingly, the sums in Equations (2.4.13), (2.4.14) and (2.4.18), (2.4.19), (2.4.20) should be substituted by integrals and the integration limits correspond to the lower and upper cutoff wavelengths of the visible range. In this text, the sum notation is generally preferred. Two straightforward reasons for this preference are as follows: first, the spectral power distribution S(λi ) of the most used illuminants in color industry and the CMFs of the 2◦ standard observer are tabulated for interval widths Δλ of 5, 10, and 20 nm [70–72] and second, all industrial spectrophotometers are designed to measure in one of these wavelength interval widths. Therefore, the color values R, G, B of a given color sample can be calculated from Equations (2.4.18), (2.4.19), and (2.4.20) if the accompanying reflection or transmission is known from measurement. To summarize, we emphasize that owing to additive color mixture, a given color can be described by three corresponding numerical color values R, G, B. These are merely representatives of the corresponding color and are by no means absolute values. On the basis of the experimental connections, they can be interpreted as the red, green, and blue components of a color shade. In the following section these results are finally modified for practical applications in colorimetry. 2.4 Observer 125 2.4.6 CIE 1931 and CIE 1964 Standard Colorimetric Observers Among the indicated color values, the red component R of a color shade has a region of negative values of the CMF r̄(λ) shown in Fig. 2.64: this is extremely unreasonable. Depending on color stimulus Φ i , the color value R can show, according to Equation (2.4.18), a positive or negative sign and, therefore, cannot be clearly interpreted in a coloristic sense. More confusing is, for example, a red coloration with a color value of R = 0. The occurrence of negative color values is due to the choice of the three real primaries R, G, B. Negative color values cannot be altogether avoided with the spectral energy distribution of technical light sources. In order to achieve only positive or zero CMFs and color values, respectively, the CIE introduced in the year 1931 – after the conclusions of Wright [66] and Guild [67] – the so-called virtual primaries X, Y, Z. These follow from a suitable numerical transformation of the previous real primaries R, G, B [7]. The virtual primaries X, Y, Z are chosen in such a way that the following criteria are fulfilled: – X, Y, Z are by definition independent of each another, and are, therefore, not producible by mixing (the same requirement as for the real primaries R, G, B); – the new CMFs x̄(λ), ȳ(λ), z̄(λ) always take values ≥ 0 and follow from the previous CMFs by an appropriate transformation (see below); – the virtual primaries X, Y, Z are adjusted in such a way that the corresponding tristimulus values X, Y, Z are equally valued for the chromaticity of the equienergy spectrum: X = Y = Z; – the two virtual primaries X and Z are chosen in such a way that only the color value Y is proportional to the lightness of a color. The new color quantities X, Y, Z are called standard color values. The new CMFs x̄(λ), ȳ(λ), z̄(λ) are named standard color-matching functions (SCMFs) and are given with the previous CMFs r̄(λ), ḡ(λ), b̄(λ) by the empirical matrix equation ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ r̄(λ) x̄(λ) 2.768892 1.751748 1.130160 ⎝ ȳ(λ) ⎠ = ⎝ 1 4.590700 0.060100 ⎠ · ⎝ ḡ(λ) ⎠ . z̄(λ) 0 0.056508 5.594292 b̄(λ) (2.4.21) These SCMFs belong to the 2◦ observer, called CIE 1931 observer; the corresponding graphs are shown in Fig. 2.66 [7]. Discrete values of these functions are used to calculate the standard color values X, Y, Z, see below. 126 2 Light Sources, Types of Colorants, Observer In practice, all color samples for visual assessment have a larger sized colored area compared with the 2◦ field at the normal vision range of 50 cm (Fig. 2.65). A considerable reason for such small-sized samples is that an observation angle of 2◦ covers only the area of the fovea. Although there is the highest cone density, the induced color stimulus from this spot is insufficient for an adequate color assessment. Because of that, the CIE introduced in 1964 the so-called 10◦ observer, also termed as CIE 1964 observer, based on investigations of Stiles and Burch as well as Speranskaja with 49 and 27 people, respectively [73–75]. Recent tabular values of the SCMFs for the 10◦ observer have been given in the literature [70–72]. Whereas the primaries of the 2◦ observer are related to the wavelengths 700.0, 546.1, and 435.8 nm and the primaries of the 10◦ observer have the corresponding wavelengths 645.2, 526.3, and 444.4 nm. For the normal vision distance of 50 cm, the visual angle of 10◦ covers a circle area of 8.8 cm in diameter, cf. Fig. 2.65. In this area, the retina certainly contains rods. For this reason, the SCMFs were corrected to eliminate the influence of the rods [7]. The CIE recommended the 2◦ observer for visual angles between 1◦ and 4◦ , and the 10◦ observer for visual angles > 4 ◦ . The 4◦ limit was arbitrarily established although there exists no discontinuity of color perception at this angle. The SCMFs of the 10◦ observer x̄10 (λ), ȳ10 (λ), z̄10 (λ) are distinguished from those of the 2◦ observer by the subscript 10. The values follow from a transformation similar to Equation (2.4.21) using the corresponding CMFs r̄10 (λ), ḡ10 (λ), b̄10 (λ) according to the equation ⎞ ⎛ ⎞ ⎞ ⎛ r̄10 (λ) 0.341080 0.189145 0.387529 x̄10 (λ) ⎝ ȳ10 (λ) ⎠ = ⎝ 0.139058 0.837460 0.073160 ⎠ · ⎝ ḡ10 (λ) ⎠ . z̄10 (λ) 0 0.039553 1.026200 b̄10 (λ) ⎛ (2.4.22) The numerical values of the components of the matrices in Equations (2.4.21) and (2.4.22) are unequal because they belong to different primaries and different observer fields. The SCMFs of both observers are together represented in Fig. 2.66. The maxima of the functions ȳ(λ) and ȳ10 (λ) are normalized at λ = 555 nm to 1.0. Due to the different visual field of the observers, the corresponding curves do not match perfectly. For one and the same color, the standard color values corresponding to each observer are also not identical. From the nonlinear wavelength dependence of both CMFs follows that the corresponding standard color values cannot be converted into one another. Although the 10◦ observer is used to an increasing extent in color industry, in order to avoid ambiguity, the observer must be clearly indicated with the results. For the last adjustment criterion of the four listed above, it should be stated that the graph of the function ȳ10 (λ) agrees with the measured luminous efficiency V(λ) of the human eye 2.4 Observer 127 2° 10° Standard color matching function 2.0 z (λ) 1.5 x (λ) y (λ) 1.0 x (λ) 0.5 0 400 500 600 700 λ nm Fig. 2.66 Color-matching functions of the 2◦ and 10◦ standard observers (CIE 1931 and CIE 1964 observers, respectively) ȳ10 (λ) = V(λ), (2.4.23) see Fig. 2.67.20 The standard color value Y is, on account of this adjustment, a measure for the lightness of a coloration. The curves of V (λ) and V(λ) in Fig. 2.67 correspond to the sensitivity of the eye for scotopic and photopic adaption, respectively. The curves are shifted with respect one another by about 40 nm. This is described by the so-called Purkinje effect. From the half-widths of 150 nm, it follows that the middle wavelengths of the visible spectrum are perceived with particular sensitivity under both adaption conditions. Now, the CIE standard color values X, Y, Z are simply given from the previous quantities R, G, B by substituting the discrete color-matching values r̄i , ḡi , b̄i of the 2◦ observer in Equations (2.4.18), (2.4.19), and (2.4.20) by the corresponding quantities x̄i , ȳi , z̄i : 20 Since V(λ). 2005, the CIE’s altered recommendation [71]; since 1931 it was accepted ȳ(λ) = 128 2 Light Sources, Types of Colorants, Observer V(λ) Relative luminous efficiency V '(λ) 1.0 0.5 0 400 500 600 700 λ nm Fig. 2.67 Relative luminous efficiency of the human eye in scotopic adaption V (λ) and photopic adaption V(λ) X= N Φi x̄i Δλ, (2.4.24) Φi ȳi Δλ, (2.4.25) Φi z̄i Δλ. (2.4.26) i=1 Y= N i=1 Z= N i=1 The standard color values for the 10◦ observer follow from the same considerations using x̄10, i , ȳ10, i , z̄10, i instead of x̄i , ȳi , z̄i and are denoted by X10 , Y10 , Z10 . According to the last three relations, the standard color values of a coloration can be explicitly calculated if the retinal color stimuli Φ i are known from Equation (2.4.11) or (2.4.12). The spectral power distribution S(λi ) of the light source used is known from CIE tables. This means that the spectral power distribution of the real source is substituted by a corresponding artificial source for the determination of color values. The same is the case with regard to the observer: the individual observer is substituted by one of the standard observers. In addition, the measured reflection or transmission of a given color sample can differ in different color measuring devices. The retinal color stimulus values above are, therefore, idealized quantities and it is, therefore, not astonishing that color values can differ from the individual visual assessment. Nevertheless, a given coloration is unambiguously characterized by three corresponding numerical standard color values. 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