Light Sources, Types of Colorants, Observer

Chapter 2Light 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 isultimately due to three independent components: the light source, the colorantsof the color pattern, and the observer. The color perception depends, therefore,on the specific properties of these factors. Factors of particular importance areas 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 interfer-ence 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 colorassessment and the most simple light interactions of colorants. The composi-tion and the typical spectral properties of industrially applied colorant sorts aredescribed in detail. The explanation of color sensation of the observer seemsinitially to be out of scope; however, this theme is necessary to consider for atleast two reasons: first, some phenomena of the human color sense really standout. These have to be taken into account during color assessment. Second, colorperception is affected by the law of additive color mixing, upon which the entirecolorimetry and the corresponding applications of industrial color physics arefounded.

2.1 Optical Radiation Sources and Interactions of Light

Without light there exists no color. The concept of color is bound to visiblewavelengths. Therefore, we turn at first toward the typical properties of natural

11G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154,DOI 10.1007/978-1-4419-1197-1_2, C© Springer Science+Business Media, LLC 2010

12 2 Light Sources, Types of Colorants, Observer

and man-made light sources because the spectral power distribution of anilluminant affects the color impression. Due to ever-present changes in natu-ral daylight, such a source is unsuited for producing a consistent color sensationwith an unchanging non-self-luminous color. On account of this uncertainty,we are forced to rely on man-made sources of constant and reproducible lightemission – normally in the visible range. For a reliable assessment of colorsin industry, the spectral power distributions of two commonly used man-madelight sources have been standardized. The actual physical processes producingcolor appearances can be described by elements of simple geometrical optics aswell as some effects of wave and quantum optics. In this section, these interac-tions are described in so far as they are significant for better understanding ofthe 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) forcosmic radiation to λ ≈ 10 km for radio waves, therefore a range of around 19orders of magnitude; see Fig. 2.1. On the other hand, the visible range of humansis only a small part of the spectrum of electromagnetic waves. Merely wave-lengths in the very small interval from 380 to 780 nm are normally perceivedby humans as visible light. Wavelengths at the left end of the range between

10–15

1021 1018 1015 1012 109 106

10–12

1

2

3

45

Violet Green OrangeRedYellowBlue

380 nm 780 nm

6

7

8

9

10

10–9 10–6 10–3 1031 mλ

Hzf

Fig. 2.1 Spectrum of electromagnetic waves: 1 cosmic radiation, 2 gamma radiation, 3 X-ray radiation, 4 ultraviolet radiation, 5 near-ultraviolet radiation; 6 infrared radiation, 7 radarwaves, 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 colorimpression changes to blue, green, yellow, orange, and finally red. Red is per-ceived at wavelengths above 600 nm. The associated wavelengths are subject toindividual variations in color perception.

The so-called spectral colors are the purest producible colors. They are char-acterized by a wavelength width of less than 1 nm (i.e., with a laser). Onthe other hand, if the radiation contains nearly all wavelengths of the visiblespectrum 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 and780 nm to be perceived, there must be sufficiently high intensity. Under normalillumination conditions, the wavelength interval that can be seen by humans isrestricted to between about 400 and 700 nm. Many modern color measuringinstruments work in this limited range [1].

Apart from its wave character, light also exhibits simultaneously particle-like properties. To this day, perhaps, this dualism is not understood in termsof everyday human experience. The corresponding particles of electromagneticradiation, and therefore of visible light, are the so-called photons. Photons in thevisible range carry a sufficient amount of energy for selective stimulation of thephotosensitive pigments in the retina of the eye to initiate color impression.

The eyes should, however, be protected from dangerous ultraviolet (UV) orinfrared (IR) radiation. However, radiation of wavelengths near the visible rangewhich cannot be directly perceived by humans can, in conjunction with suitablecolorants, cause different physical effects. Luminescence colorants, for exam-ple, absorb energy at UV wavelengths and then emit most of this energy atlonger wavelengths – usually within the visible or IR range. The needed tran-sitions from energetic steady states occur either spontaneously by fluorescenceor delayed by phosphorescence. The energy surplus is converted into molecu-lar vibration energy and leads macroscopically to a temperature increase. Theenergy absorption of normal absorption colorants in the visible or IR rangeis also transformed into molecular vibration energy. If this energy conver-sion is accompanied by a color change, such kinds of colorants are denotedas thermochromic. Moreover, colorants are termed as phototropic, if the colorchange is only caused by energy absorption at visible wavelengths. On the otherhand, excessively high UV or IR radiation energy is sometimes able to initiateirreversible molecular changes, which result in bleaching or total loss of color.

In contrast to the above-mentioned colorants, overall the greatest percent-age of industrially used colorants contain absorption and effect colorants. Inabsorption colorants, the incident energy is sufficiently high to initiate par-tial absorption or scattering. Physically, light absorption in colorant moleculesoccurs only for certain transitions between quantum energy levels – therefore,in special wavelength regions of visible light. The corresponding processes arecalled selective absorption or scattering. On the other hand, scattering of lightdepends on the electrical charge distribution and the geometry of the colorant


particles. In contrast to absorption pigments, dyes do not normally show anyscattering because the size of the isolated molecules in solution is too small forsuch an interaction. The light reflected in the direction of the eye initiates in theretina signals which are perceived usually as non-self-luminous colors.

The color separation of pearlescent, interference, and diffraction pigmentsis a consequence of the wave nature of light. In order to produce a suitedinterference effect, the pigment particles are built up of layers with differentrefractive indices of which the light waves interfere constructively or destruc-tively depending on optical path length. The layer thicknesses are smaller thanthe interfering wavelengths. In contrast, the particles of diffraction pigmentsshow an embossed regular grating structure at which suited wavelengths arediffracted. 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 illumi-nation with a suitable light source. Depending on the mechanism of lightgeneration, optical radiation sources have different spectral power distributions.On the basis of the emitted spectrum, illuminants can be divided into two cate-gories: temperature and luminescence radiators. The most important luminoussources of both classes are given in Table 2.1. In the following, we discussdetails of both categories because the illumination of color samples is our pri-mary context. In the near future, semiconductor diodes and lasers are expectedto replace, in part, the light sources used to date. Therefore, we also discusson these sources even though they are, thus far, rarely applied in color industrydespite a multitude of advantages.

Table 2.1 Kinds of optical light sources

Temperature radiator Luminescence radiator

Natural Artificial Artificial

Sunlight,Scattered light of theEarth 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 distributionsare often compared with the spectral energy distribution or temperature of aso-called blackbody radiator – also denoted as blackbody or cavity radiator. Atlower temperatures, metals emit heat energy in form of IR radiation; gradually,with increasing temperature, dark-red glow emanates. With a further increase


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 emittedlight increase. The wavelength with the most energy shifts to smaller wave-lengths, i.e., a blue shift. For an ideal blackbody, this radiation is generatedinside the cavity of a blackbody radiator and the outside of the cavity wallsabsorb all external electromagnetic waves. The ideal situation, therefore, is theemission of only the cavity radiation according to its temperature.

The radiation power S(λ,T)dλ of a blackbody radiator at wavelength intervaldλ is given by the Planck law of radiation [2]:

S(λ,T)dλ = c1

λ5 · {exp [c2/

(λT)] − 1}dλ. (2.1.1)

The radiation constants c1 and c2 have values of c1 = 2πhc2 = 3.74185 ×10−16 W m2 and c2 = hc/k = 1.43884 × 10−2 m K. In Equation (2.1.1), thewavelength λ should be in units of meters and the temperature T in units ofKelvin. The radiation constants contain the velocity of light in vacuum c andthe Boltzmann constant k. For derivation of Equation (2.1.1), Planck introducedh – now called the Planck constant.

Figure 2.2 shows the spectral power distribution in wavelength given byPlanck’s law. As can be seen, at a temperature of 500 K, the peak of spectralpower is in the IR range. For an increase to much higher temperatures, i.e., togreater 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 atthe respective edges of the visible range. The Planckian formula (2.1.1) contains

109

g

Visual range

f

e

d

a: 500 Kb: 1,000 Kc: 2,000 Kd: 4,000 Ke: 6,000 Kf: 10,000 Kg: 20,000 K

c

b

a

106

103

100

10–3

Ene

rgy

dens

ity /

W. m

–2. n

m–1

101 102 103 104

nmλ

Fig. 2.2 Spectral power distribution of blackbody radiator of different temperatures


two limiting cases: for short wavelengths Wien’s law of radiation and for longwavelengths Rayleigh–Jeans radiation formula. Before the quantum hypothesiswas 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 exchangesenergy with the surrounding radiation field only with an integer multiple of thequantum energy

E = hc

λ= hf . (2.1.2)

In this formula, f is the frequency of the corresponding wavelength. Both thecontinuous spectra of temperature radiators and the discontinuous line spectraof luminescence radiators are based on the emission of light quanta that areidentical with the already mentioned photons.

Because the color of the spectrum emitted by a blackbody radiator changeswith temperature, it is useful to introduce the term color temperature. With thisquantity, the emitted light of a source is compared with that of a blackbody radi-ator and thus characterized. The color temperature of an illuminant correspondsto the temperature of the blackbody radiator which emits the maximum of lightat the same color as the actual illuminant. Strictly speaking, only a temperatureradiator can be assigned a color temperature. Other optical radiators, such asluminescence radiators, are characterized by a so-called similar or correlatedcolor temperature.

The most well-known temperature radiator is the Sun. Inside the Sun, attemperatures higher than 107 K, deuterium is converted to helium by nuclearfusion (Bethe–Weizsäcker cycle) [3]. For generation of 1 mol helium, the gigan-tic energy of 1.55 × 102 GJ is released. The total solar fusion energy resultsin a Sun surface with a mean temperature of about 5,800 K and an exception-ally high radiation power of about 63.3 MW/m2. Merely a small fraction of thispower, namely the so-called solar constant with value 1.37 kW/m2, reaches theEarth’s atmosphere. This value reduces to about 1.12 kW/m2 if the Sun is atits zenith and the atmosphere is free of clouds. Already these considerationsindicate 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 theatmosphere; its intensity is reduced by absorption and scattering. The light scat-tering 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

N· π2(n − 1)

r2λ4· E2 · cos2 ϑ , (2.1.3)

short wavelength blue light is scattered more strongly than the long wavelengthred light because λ is contained in the denominator of this expression. The


further quantities in Equation (2.1.3) are defined as follows: J the intensity ofthe scattered light, N the number of scattering particles per unit volume V, n therefractive index of the scattering medium, r the particle radius, E the amount ofthe electric field strength, and cos2ϑ the phase function (see Section 5.1.5); ϑ

denotes the scattering angle with regard to the incident intensity. The Rayleighlaw 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 byscattering and absorption of light in the atmosphere, more precisely due to theair molecules as well as to aerosols (water drops, dust particles, etc.). On thelong and nearly tangential optical path of the light through the layer of air, bluewavelengths are more strongly scattered and absorbed. The remaining blue light,therefore, reaches the observer on the Earth with considerably less intensity ascompared with the much less scattered long wavelength red light. The Sun andthe sky, therefore, appear reddish.

In addition to dependence on daytime, received sunlight changes due toweather conditions, geographical latitude, season, and due to the approximately11-year sunspot cycle. Accordingly, the color temperature of daylight is subjectto substantial variations and takes values in the range of 5,500 K for direct sun-light to more than 14,000 K for blue zenith skylight. Simultaneously, the spectralpower distribution changes. This is shown in Fig. 2.3 with curves normalized atthe wavelength 555 nm. At this wavelength, the sensitivity of the human eye isat its highest (Section 2.4.6).

400 500

e

d

c

b

a

Rel

ativ

e sp

ectr

al e

nerg

y

600 700nmλ

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) mediumdaylight, and (e) direct sunlight [4]


The daylight variations mentioned above create extra complexities for theunambiguous visual and objective assessment of non-self-luminous colors andtheir typical properties. A single color sample can produce a completely dif-ferent color impression simply due to a changing illumination condition. Inthe practice of color physics, it is necessary to use reproducible artificial lightsources which have nearly constant spectral power distributions. These artifi-cial light sources are often referred to as technical sources. This corresponds toa constant color temperature if aging effects are neglected. From an economicpoint of view, the sources should also have a reliable working life of more than1,000 operating hours. These standards are fulfilled by most of the technicalilluminators of importance in the color industry; in the following section, weturn toward such kinds of sources.

2.1.3 Technical Light Sources

For solving coloristical problems of non-self-luminous colors, technical lightsources are used exclusively. The main reason for this is the high reproducibilityof the generated spectrum. In technical temperature radiators, a metal of highmelting point is heated up by an electric energy supply to such an extent that acontinuous spectrum is emitted in the visible range; this spectrum is similar tothat of a blackbody radiator of the same temperature. A temperature radiator inwidespread use is the tungsten filament lamp; its color temperature is essentiallydependent on the filament thickness, the applied voltage, and the kind of gasfilling of the bulb. The so-called tungsten–halogen bulb contains bromine oriodine which increases the light efficacy, the working life, as well as the colortemperature from about 2,800 to 3,000 K. The tungsten filament lamp of colortemperature 2,856 K is named standard illuminant A by the CIE.

The gradual loss of filament thickness in normal tungsten lamps is sloweddown by the included halogen: the vaporized tungsten combines with the halo-gen, cools down at the surrounded quartz bulb, and reaches – by convection – thehot filament surface; there it dissociates so that tungsten is removed. Tungstenfilament lamps typically emit light of yellowish color. The accompanying spec-tral energy distribution is shown in Fig. 2.4. Furthermore, in a tungsten arc lampwith an argon atmosphere, both tungsten electrodes are heated by an arc dis-charge in such a way that a radiation distribution is produced similar to thatof the tungsten filament lamp; the accompanying color temperature amounts toabout 3,100 K. A carbon-arc lamp shows a color temperature of 6,000 K and avery high luminance of about 1.6 Gcd/m2.1

1The unit candela (cd) is defined as the luminous flux radiated from 1/60 cm2 of a blackbodywith temperature 2.042 K.


300 4000

50

100

150

200

500

D65

A

Spe

ctra

l ene

rgy

dist

ribut

ion

S(λ

)

600nmλ

Fig. 2.4 Spectral energy distribution of a tungsten filament lamp (CIE standard illuminantA) and a UV-filtered xenon lamp (CIE standard illuminant D65)

The term luminescence radiators represents a group of radiators includingso-called discharge lamps, as well as photoluminescence radiators [5, 6]. In con-trast to temperature radiators, luminescence radiators emit either a line spectrumof discrete wavelengths or a band spectrum of broader wavelength intervals.Line spectra are exclusively generated by gas discharge lamps. The physicalmechanisms for generating line spectra are first to accelerate charge carriersby an electric field; during collision with the gas atoms, excitation energy istransferred to the outer electron orbits of these atoms. On the basis of the quan-tized energy of the electron shells, the electron transition into the ground levelresults in emission of light with discrete wavelengths λ according to Equation(2.1.2). The actual temperature of luminescence lamps is clearly far lower thanthe surface temperature of temperature radiators of the same light color.

Among the technical gas discharge lamps, only the filtered light of xenon ormercury vapor lamps is of major importance for visual assessment or spectralmeasurement of colors. The emission of light in gas discharge lamps is based onthe same physical mechanisms as in luminescence radiators. At first an electricvoltage pulse in a xenon atmosphere causes free charge carriers. In a high-pressure xenon lamp under pulsed or constant voltage, the charged particlesgenerate a nearly continuous spectrum in the visible range. This is accompaniedby a small amount of UV radiation. The spectral energy distribution shows a flatpeak at a wavelength of about 450 nm and the emitted spectrum shows only a


slight decrease in magnitude for longer wavelengths. Therefore, the perceivedlight appears slightly but insignificantly bluish; this can be seen in Fig. 2.4, curveD65. The radiation distribution is similar to that of diffuse daylight at middayon cloudless north sky, cf. Fig. 2.3, curve d. For these reasons, a UV-filteredxenon lamp of color temperature 6,500 K is used in the color industry to simu-late midday light. The spectral energy distribution of this xenon discharge lampis standardized; it is termed by the CIE as standard illuminant D65. The CIErecommends the use of xenon lamps with color temperatures of 5,000, 5,500, or7,500 K, if the standard illuminant D65 is not available.

The mercury vapor discharge lamp generates a line spectrum with emissionwavelengths of 405, 436, 546, 577, and 579 nm, as well as in the UV rangeof 254, 314, and 365 nm. Because of the energetically high UV amount, thisdischarge lamp is utilized in a so-called light booth for visual assessment of fluo-rescence colorants, artificial color fastness tests, and in fluorescence microscopy.A light booth consists of a small one-sided open compartment with one or twosmall platforms to lay down the color samples to compare, as well as differentnon-glare light sources which can be individually switched on. The above-mentioned emission wavelengths are also used for wavelength-scale calibrationsof color measuring instruments.

The UV fraction of the mercury spectrum is furthermore applied to stimulatethe phosphorus in fluorescent lamps in order to initiate photoluminescence inthe visible range. The spectral composition of the resulting band spectrum orthe resulting light color depends on the chemical structure and the mixing ratioof the involved phosphorus. For color assessment of special importance, there isthe cold white light of the fluorescent lamp CWF (identical with illuminant FL2) and the light emission of the so-called three-band lamp TL 84 (identical withFL 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. Fluorescentlamps are in widespread use only because of economic reasons: they have aluminous efficacy and a physical life which are about eight times higher thanthose of tungsten filament lamps, cf. Table 2.2.

Light sources of principle importance in the near future are expected to belight emitting diodes (LEDs) and lasers, which greatly ripened technically inthe 1960s. The central component part of an LED consists of a p–n semicon-ductor junction. A voltage between 1 and 15 V in conducting direction anda current of order 50 mA release photons in the p–n region. These photons aregenerated by an energy surplus from recombining electrons and defect electrons(holes). Available luminescence diodes doped with suited chemical compoundscan emit quite monochromatic light with half-widths of 6–25 nm, for example,at wavelengths of 400 nm (gallium-nitride diode), 600 nm (gallium-arsenic-nitride diode), and 660 nm (gallium-phosphide-zinc-oxide diode). The benefitsof LEDs are the short switching time of about 5 ns, the small spectral


400

Spe

ctra

l ene

rgy

dist

ribut

ion

S(λ

)

0

20

40

60

80

500 600

FL 11

FL 2

nmλ

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

CIE illuminantCIEabbreviation

Correlated colortemperature/K

Colorrenderingindex

Lightefficacy/lm/W CIE simulator

CIE standardilluminantA, eveninglight

A 2,856 100 12 Tungstenfilament lamp

CIE standardilluminantD65, middledaylight

D65 6,500 94 35 UV-filteredxenon lamp

Cold whitedaylight

FL 2 4,230 64 70 Fluorescentlamp CWF,cool whitefluorescent

Bluish whitedaylight

FL 7 6,500 90 80 Broadbandfluorescentlamp

White daylight FL 11 4,000 83 90 Three-bandlamp TL84


half-width of the emitted intensity, the high degree of optical efficiency, andthe long working time. Disadvantages up to now have been the low illumina-tion intensity in comparison to traditional light sources. Improvements in theserespects, at the time of this writing, are the subject of ongoing research anddevelopment.

The term laser is an abbreviation of “light amplification by stimulated emis-sion of radiation.” A laser is, therefore, an optical amplifier which is based onthe principle of stimulated emission of light. To initiate stimulated emission oflight2, 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 frequencyf has photon energy according to Equation (2.1.2). The primary requirementfor stimulated light emission is that this photon energy is at least the naturalenergy difference of the medium. In such cases, the medium that has some pop-ulation in an excited state has some return to the ground state. This emittedenergy is incorporated into the incident field. In order to obtain an amplificationof radiation by stimulated emission, the energetically higher levels or bands ofa medium should maintain a state with a greater degree of filling. This greaterelectron number or population in the upper energy state is usually maintainedusing an energy supply such as flash lamps, other laser pump sources, currentsin semiconductor laser, or atom/electron collisions.

Typical classification of lasers is along the lines of the physical state ofthe gain medium: solid state (crystals), semiconductor, liquid (usually organicdyes), or gas lasers, for example. The ruby laser with emission wavelength ofλe = 694.3 nm is a solid-state laser. Semiconductor lasers are, for example,indium-gallium-phosphide (In1-xGaxP) or aluminum-gallium-arsenide lasers(AlxGa1-xAs); the emitted monochromatic wavelength of each usually lies inthe range 500 and 1,000 nm depending on the content x of the indicated ele-ment. Dye lasers are the dominant class of liquid lasers; typical laser mediumsare 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 nmand 514.5 nm).

The advantages of lasers are clear, considering the outstanding features ofthe emitted light: constant frequency, highly monochromatic, spatial and tem-poral coherence, high beam directivity, and adjustable energy density. In thecolor industry, lasers have been successfully used for the determination of sur-face gloss, covering capacity and glittering of effect colorants, as well as sizedistribution of pigment particles in powders, among other things. In the follow-ing section, we concentrate on specific properties of light sources which are ofspecial interest for colorimetric applications.

2The opposite is absorption, or, more precisely, stimulated absorption.


2.1.4 Illuminants

In the previous section, the physical basics of light emission and the appli-cations in technical light sources have been introduced. Now, we direct ourattention toward the special handling of light sources in colorimetry or colormatching. Unquestionably, the vast variety of technical light sources compli-cates the unambiguous visual assessment of colors: colored objects are exposedto changing natural as well as artificial illuminations such as daylight, eveninglight, or fluorescence light. The change in illumination can alter the visual colorimpression (see below). The CIE has, therefore, recommended the most rep-resentative light sources to use for color assessment applications. For clearnessand better communication, four terms should be identified. These terms describethe different kinds of light sources:

1. CIE illuminant: this corresponds to a theoretical source of a tabulated relativespectral 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 specifiedseveral representative illuminants [7], among them are the following:

a. three temperature radiators designated D50, D55, D75 with color tempera-tures of 5,000, 5,500, and 7,500 K, respectively;

b. twelve fluorescent lamps designated from FL 1 to FL 12; the illuminants FL1–6 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. InFig. 2.5, only the spectral power distribution of illuminants FL 2 and FL 11are shown;

c. in the end, five high-pressure lamps designated as HP 1–5, of which two aresodium vapor lamps and three metal halide lamps; these are normally notsignificant 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 thePlanck 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-pressurexenon lamp shown in Fig. 2.4. Standard illuminant A is recommended for sim-ulation of room light in the evening, D65 of midday light of color temperature6,500 K.


The tabular values of a CIE illuminant are generally used for computa-tion of color values. The corresponding simulation illuminant serves for visualassessment of color patterns. In other words, the real light source which isused to illuminate a color sample is, for the purpose of calculation, substi-tuted by a theoretical simulation source, consisting of discrete wavelengthsand power emission. This can clearly be a reason for deviation between thevisual assessment and the colorimetric result. A further deviation can resultfrom the so-called CIE standard colorimetric observers. This is not discusseduntil 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 thestandard illuminant A is assigned a true color temperature, the illuminant D65and the fluorescent radiators have only correlated color temperatures. These arefor 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 perceivedcolor. This can be caused either by the colorants themselves or by the lightsource used. If the spectral power distribution is responsible for color changes,this is attributed to the color rendering of the illuminating source. The yellow-ish light of the sodium vapor lamp HP 1, for example, bathes each chromaticcolor in a pale yellow. This is because sodium emits only two closely spacedwavelengths of 589.0 and 589.6 nm in the visible range. The CIE proposed thedimensionless color rendering index Ra to characterize the grade of color ren-dering 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 thatcolors are quite distorted. In contrast, the CIE standard illuminant A takes thehighest 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 ratioof 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 higherlight efficacy than temperature radiators of equal or lower color temperature.

From a comparison of the spectral power distributions shown in Figs. 2.4and 2.5, it is possible to understand how the change of a source alters the colorimpression. Consider Fig. 2.4: using source A, the color sample appears moreyellow and red compared with illumination of a D65 simulator. This is becauseof the continuously increasing radiation energy characteristic of the source Afrom 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 FL2 source, or with FL 11 source, redder in comparison to D65 simulator. Colors

3By 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 pointin a sphere of radius 1 m – which cuts an area of 1 m2 out of the sphere surface, cf. Fig. 5.1.


illuminated with a D65 or FL 7 source are rendered and perceived in a similarlybalanced way as under midday light. This is because of the nearly constant andhigh 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 inter-ested in the color appearances that result. In a plane electromagnetic wave, theelectric and magnetic vectors E and H are perpendicular to one another, and,in addition, mutually perpendicular to the propagation direction. The so-calledwave vector k is oriented in the propagation direction. The electromagnetic wavecarries the energy flux density in the direction of k, given by vector S (named asPoynting vector) and relation

S = E × H. (2.1.4)

Figure 2.6 shows the connection between the three vectors E, H, and S. Inthe figure, the electric and magnetic vectors are shifted a quarter wavelengthin 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 asflux density, or short flux, is the origin of interactions with the molecules orparticles of colorants to produce colors. Color production of non-self-luminouscolors 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 smallerthan the size of the objects that it interacts with (i.e., macroscopic objects), thelight no longer behaves strongly as a wave, but rather propagates in straightlines according to geometrical optics. Reflection, refraction, absorption, or scat-tering can occur simultaneously if the light is incident on macroscopic boundarysurfaces consisting of mediums with different optical densities. The polarization


of light can intensify normal color appearance. This can appear especially forsome absorption pigments and liquid crystal pigments.

Materials can be illuminated by directional, diffuse, or mixed light. Quitesimple, but of great importance, is the directional reflection – also denoted asspecular reflection. Directed reflection arises from directional light at smooth,polished, or glossy surfaces, for example at organic binders, synthetic poly-mers, glasses, metals, as well as colorations with absorption and effect pigments.According to the reflection law, the angles of the incident ϑi and reflected lightϑ 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 inthe same plane, that of the paper in Fig. 2.7. It is important to note that for visualassessment of colorations of glossy surfaces one must strictly avoid observationsin the direction of the specular angle. For visual inspection of absorption col-orations with collimated light, the surface should be illuminated from the sideand 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 angleof incidence, and specular angle, each from normal to the surface

If the medium behind the glossy surface is transparent and of different refrac-tive index than the first medium, the beam is additionally refracted into thismedium. 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 refrac-tion ϑ2 depends on the angle of incidence ϑ1 and the ratio of refractive indicesn2/n1 of the adjoining mediums according to Snell’s law of refraction

sin ϑ1

sin ϑ2= n2

n1= n (2.1.5)

(original W. Snel van Royen, 1621). In general, the refractive indices are alsowavelength dependent, this normally results in violet light being refracted at asteeper angle than red light. This property is called dispersion [2] and results inprism effects.


n1

n2

a)

ϑ1

ϑ2

n1

n2

b)

ϑ1

ϑ2

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 surfacefollows from the Fresnel equation

r(μ,n) = 1

2

[(μn − w

μn + w

)2

+(

μ − nw

μ + nw

)2]

, (2.1.6)

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 electrody-namics [14]. The reversal of light direction does not change the reflected fractionnor the law of refraction. The reversibility of the light path without change ofeffect is a general principle of geometrical optics [15]; this principle is used incolor measuring methods among other things (Section 4.1.2).

In the case of light incident perpendicular to the surface, the special reflectedfraction is given by

r(1, n) =(

n − 1

n + 1

)2

. (2.1.8)

This follows from Equations (2.1.6) and (2.1.7) using μ = 1. For air with refrac-tive 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

4The cited refractive indices in this book represent values which – as usual – belong to thewavelength of the sodium line of 589.0 nm.


reflected from the surface of a colored sample; this amount is not available forfurther 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 n is introduced:

n = n(1 + iκ). (2.1.9)

The quantity n is divided into the real part n for the refraction and the imaginarypart nκ describing the light absorption at the interface. The quantity κ is namedattenuation coefficient. In Equation (2.1.9), i is the imaginary unit (i = √−1).For directional light incident perpendicular to the metal surface, the reflectedtotal 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 termedas absorption coefficient; some measured values of n, nκ , and r(n, κ) for metalsused for metallic pigments are listed in Table 2.7.

A further sort of reflection occurs if a light beam enters an optically thinnermedium coming from an optically denser medium. Note that the refracted raycannot exceed an angle ϑ2 = 90◦; see Fig. 2.9. For a refractive index n = 1.5,the corresponding incidence angle is ϑ1 = 41.8◦. In general, from the law ofrefraction (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 quantityγcr is called the critical angle of total reflection or in short critical angle. If

n1

n2

γcr γcr

ϑ2

ϑ1

Fig. 2.9 Critical angle γcr at a boundary surface of different refractive indices


the total reflected light cannot immediately leave a colored layer, it participatesfurther in the interactions with the color-producing particles until it is absorbedor leaves the layer. Total reflected rays of angles γ≥γcr are called partly directedin this text.

For unpolarized light, a further property follows from the law of refractionwith regard to the refracted ray. In the case that the reflected and the refractedrays make a right angle, the light of the reflected ray is linearly polarized, infact perpendicular to the plane of incidence; see Fig. 2.10. This special angle ofincidence is denoted as Brewster angle ϑB and is given from the law of refraction(2.1.5) with ϑ2 = 90◦ – ϑB:

tan ϑB = n. (2.1.11)

n1

n2

ϑB

ϑ2

Fig. 2.10 A reflected beamof Brewster angle ϑB islinearly polarizedperpendicular to the planeof incidence

The Brewster angle depends only on the ratio of the refractive indices at bothboundary 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 independence on n in Fig. 2.11. Polarized light produces always more intensivecolors than unpolarized light; polarized light is generated in some absorptioncolorants and especially in liquid crystal pigments.

In addition to that from Equation (2.1.6) and the above considerations, thereflection coefficient of directional light depends on the direction of polarizationparallel to the plane of incidence. These properties also follow from Fresnelequations [14]. This is shown in Figs. 2.12 and 2.13 for a refractive index valueof n = 1.5 in dependence on the angle of incidence ϑi. The outer reflectancecoefficient at the boundary of the optically thinner medium begins to differ fromone another for the two rectangular linear polarizations already for small angles


100

80

60

Ang

le /

degr

ee

40

20

0

Refractive index n1.0 1.2 1.4 1.6 1.8 2.0

ϑB

γcr

Fig. 2.11 Critical angle γcr and Brewster angle ϑB in dependence of refractive index n

1.0

0.8Polarisation:

parallel

normal

n = 1.5

0.6

0.4

Out

er r

efle

ctio

n co

effic

ient

0.2

00 20 40

Angle of incidence ϑ1

60 80

Fig. 2.12 Outer Fresnel reflection factor as function of angle of incidence for polarizationparallel and perpendicular to the plane of incidence

of incidence (Fig. 2.12). This difference increases strongly with the angle ofincidence. The inner reflection coefficient at the inner boundary of the opticallythicker medium shows the same behavior but is compressed into the angle range0 < ϑ2 < 41.8◦; see Fig. 2.13. The high increase of this reflection coefficient iscaused by the critical angle of total reflection.

Consider now diffuse illumination instead of directional light. This alters thereflection character. The majority of natural and artificial light propagates dif-fusely. Because of this, it is, perhaps, most reasonable to measure and visually


1.0

0.8 Polarisation

parallel

normal

n = 1.5

0.6

Inne

r re

flect

ion

coef

ficie

nt

0.4

0.2

0 20 40Angle of incidence ϑ2

60 800

Fig. 2.13 Inner Fresnel reflection factor as a function of angle of incidence for polarizationparallel and perpendicular to the plane of incidence

judge color samples under diffuse illumination. Ideal diffuse light is in the for-ward direction inside an angle range of ±90◦ and of equal energy over theentire range of these angles. Because of that the radiation power, the opticalinteractions, and specially the reflection conditions at the boundary surfaces arechanged. The reflection coefficients for diffuse radiation follow from energeticconsiderations leading to the relation

1 − r∗d

n22

= 1 − rd

n21

. (2.1.12)

The quantity r∗d denotes the reflection coefficient of diffuse light at the boundary

of the optically thinner medium with n1 and rd stands for the reflection coeffi-cient of the optically denser medium. In Fig. 2.14, the reflection coefficientsfor diffuse light are represented schematically by arrows for simplicity. For dif-fuse illumination from air of n1≈1.0 in a layer of refractive index n2 = 1.5, theappropriate reflection coefficients r∗

d = 0.09178 and rd = 0.59635 come from

Fig. 2.14 Reflectioncoefficients of diffuseradiation at a boundarysurface of differentrefractive indices(schematically)


1.0

0.8 rd

r

rd

0.6

0.4

0.2

1.0 1.2 1.4 1.6 1.8 2.00

Refractive index n

Ref

lect

ion

coef

ficie

nt

∗

Fig. 2.15 Three sorts of reflection coefficients in dependence on refractive index n: r fordirectional illumination perpendicular to the surface, r∗d for outer diffuse illumination, andrd for inner diffuse illumination of a material

the literature [13]. The reflection coefficients for diffuse light r∗d and rd as well

as for directional light at perpendicular illumination r are shown in Fig. 2.15 independence of the refractive index n.

The boundary surface reflection certainly complicates the visual and measur-ing assessment of colored samples: this surface reflection is superimposed onthe entire visual impression as well as the spectrometric measuring results. Butthe essential and interesting parts of color sensation are generated by the lightinteractions in the volume of a colored layer.

For the following, we define the reflection of an optical medium as theamount of incident radiation energy which is backscattered from thevolume and this is superimposed by the surface reflection energy.

Correspondingly, the transmission is the amount of the incident light energywhich overcomes the interactions in the volume and exits the secondboundary surface of the optical medium.

The accompanying energies are called reflection and transmission energy; theseare abbreviated by WR and WT.

The electromagnetic field of a light wave can drive vibrations of suitablecharge carriers in atoms or molecules of absorption colorants. This additionalabsorption of energy leads sometimes to emission of secondary radiation; thisprocess is denoted as scattering. The scattering is elastic if the wavelengths ofthe incoming and scattered light are equal. This is the case especially withinnon-self-luminous colors but also for Rayleigh and Mie scattering (Sections2.1.2 and 5.1.3, respectively). Inelastic scattering, however, produces a changeof scattered wavelengths such as in Raman and Brillouin scattering [16].


In addition to scattering, a part of the incoming light energy is normallyabsorbed by the charge carriers of the colorant molecules and not scattered.This causes an increased molecular vibration energy and, therefore, a tempera-ture increase of the coloration. The absorption of energy of amount WA is finallyabsent from the reflected, transmitted or scattered light. In the most colored lay-ers, scattering and absorption occur simultaneously in different amounts, andadditionally dependent on wavelength.

The three mentioned energy components WR, WT, WA come from the incidentenergy Wi. Therefore, the energy conservation law, in our case, amounts to

Wi = WR + WT + WA. (2.1.13)

Division by Wi results in

1 = R + T + A. (2.1.14)

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, andabsorption but also reflection factor, transmittance factor, and absorption factor,respectively.

The law of energy conservation is an axiom of physics and is of fundamentalimportance; in the above formulation, it plays a central role in the entire radia-tive transfer of optical systems. The energy conservation law is even valid foreach single wavelength, therefore, valid independent of the irradiated spectralpower distribution. Furthermore, this law is independent of any specificationsconcerning the interacting particles of the optical medium. From that follows abasic realization, which is of great importance for the further discussions in thistext:

The resulting values of reflection, transmission, or absorption are charac-teristic quantities of the optical medium; in our case, they are essentiallycaused only by the colorants of the chromatic color.

Reflectance and transmittance are determined with suitable color measuringinstruments (Sections 4.2.1 and 4.2.2); absorption and scattering are charac-terized by corresponding optical constants which follow from optical models(Sections 5.1.2 and 5.1.4). Absorption and scattering are generally the most


important quantities of absorption colorants. In effect pigments, however, thedominant processes are wavelength dependent such as interference or diffrac-tion. 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 essen-tially based on processes such as reflection, absorption, and scattering and areoccurring at the surface and in the volume of a colored sample. In contrast tothat, impressive color effects are generated by interference of light waves inpigment particles composed of an appropriate sequence of layers. Interferenceis an effect caused by superposition of suitable waves (of, e.g., liquids, gases,electromagnetic fields, elementary particles). Interference of light is, for exam-ple, responsible for the colors of soap lamellas, oil films on water, or coatedlenses [17]; the colors of opals, natural pearls, insect wings, or bird feathersare in addition based on interference. The colors of interference pigments resultfrom light waves, which are reflected at the inner and outer layer boundariesand which superimpose with the incoming waves. The produced colors are con-trolled by the thickness and refractive index of the different layers among otherthings. 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 thecolor change in dependence of the observation angle; this is in some way similarto diffraction colors.

A necessary requirement for interference is the existence of coherence. Mostof temperature and luminescence radiators emit incoherent waves, because thesingle atoms of the source oscillate independently from each other, only shortwave trains are produced; between the single waves exists no constant phaserelationship. Waves are coherent, if the time dependence of their amplitude isthe same irrespective of a phase shift. In the case of harmonic waves, this meansthat the frequencies of the waves have to be the same; however, they can havea constant phase difference. Coherent sine-shaped waves must, therefore, be ofequal frequency. Coherent waves can result, for example, from the reflection ofa radiative field at a mirror. From this perspective, laser light is of nearly per-fect coherence because it is amplified during multiple reflections. Interferencepigments normally consist of at least two layers of different refractive indices toproduce 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 interfer-ence of light at a plane parallel layer. The reflected waves of beams R1 and R2

interfere above the layer. The waves of R′1 initiated by R1 take a longer way to

the surface and, therefore, have an optical path length difference G with regardto the waves of R′

2. In view of the different path lengths, the ratio of refractive


R1

n1

d

n2

n3

R2 R '

ϑ1 ϑ1

ϑ2

1 R '2

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 causedby reflection of the waves at the upper layer surface, the difference G is given by

G = 2d ·√

n2 − sin2 ϑ1 + λ

2, (2.1.15)

where d stands for the layer thickness and ϑ1 for the angle of incidence. Atsome locations, the wave amplitude is increased by the so-called constructiveinterference of the incident and reflected waves. This occurs if G is an even-numbered 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; thisis used to a great extent for realization of different kinds of pearlescent and inter-ference pigments. For color sensation, the additional change of color impressionin dependence on the observation angle ϑz can be quite strange. The quantityϑz belongs to the different interference orders z instead of the constant angleϑ1. Generally, the intensity of the amplified waves decreases strongly with thenumber of z.


Some special interference features result in the case that light is incidentperpendicular to the surface of a layer. Colors of pearlescent and simple inter-ference pigments are visually characterized by observation perpendicular to thecolored surface; some important technical applications come out of this. FromEquation (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 bythe quantity d leads to a distance of Δd = λ/2n between two adjacent intensitymaxima. The same distance holds for neighboring minima.

These considerations are especially used to reduce the reflection of opticalsystems by destructive interference. With the so-called optical coating, the opti-cal surfaces are coated with an inorganic layer by physical vapor deposition; therefractive index nC of the coating has to satisfy the condition

nC = √n1n2, (2.1.19)

where n1 and n2 are the refractive indices of air and of the optical material,respectively. Unfortunately, the effectiveness of reflection reduction is limitedto a middle visible wavelength. To achieve a nearly regular reduced reflectionof wavelengths in the entire visible range, a multi-layered coating on both sidesof the optical element is necessary at the most 10 layers which are tuned witheach other. This is a type of dielectric coating called an anti-reflection coating.

The so-called dielectric mirror coating relies likewise on interference. Forthis, 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 opticalthickness dh = λ/4nh or dl = λ/4nl, then the reflected waves of first order inter-fere constructively with the incoming light caused by the additional phase jumpat the boundary of the optical denser medium. Therefore, a narrowband mirrorresults; the reflectivity depends on the difference of the refractive indices of thelayers [17]. With change of the layer parameters, the width of the wavelengthinterval can be controlled. These considerations are also used to achieve suitablelayer structures in pearlescent and interference pigments to produce a dominantcolor component.

Interference colors can be further improved by multiple reflection of lightbetween two semi-transparent mirrors at distance d, similar to the placement ina so-called Fabry–Pérot interferometer; see Fig. 2.18. One part of the reflectedlight is transmitted through the second layer. Multiple reflection leads to a greatnumber of partial beams, which interfere behind the second layer. The layer dis-tance d and the refractive index n of the medium between the layers are chosenin such a way that only a small wavelength band is transmitted; this construction


Substrate

nhdh

=

= λ

λdl 4nl

4nhnl

nhnl

Fig. 2.17 Layer sequencesof a dielectric mirror withhigh and low refractiveindices nh and n1

operates as an interference filter. For fixed distance d, this construction is alsocalled an etalon. The deciding parameters for the interference efficacy are n andd of the intermediate layer. Because adjacent beams have the same geometricaloptical 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 angleof beam incidence αz. For a layer thickness d = 300 nm and refractive indexn = 1.5, the wavelengths of violet and red light (400 and 700 nm) are separatedfor the first order by an angle difference of about 25◦. Founded on this principle,

dLQ

Q1

Qn

L

P

αz

Fig. 2.18 Fabry–Pérot interferometer: the partial waves of points Q, Q1 produce interfer-ences of “equal inclination”


in particular, is the angle-dependent color effect of multi-layered interferencepigments 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 ofthe wavelength of the light, the wave characteristics of light become very impor-tant. This is the situation, for example, at a diffraction grating. Upon passingthrough the grating, some portion of the light is deflected and/or is fanned outdepending on the grating geometry and the wavelength. This phenomenon isan example of Fraunhofer diffraction if the light beam is incident nearly per-pendicular to the grating [19]. In addition to macroscopic structured materials,diffraction pigments can be impressed with such grating structures. This leadsto color effects which are also depending on the angle of observation.

A simple macroscopic transmission grating is shown in Fig. 2.19, not toscale. The geometry is simply achieved by scratching or etching of equidistantgrooves in a thin plane parallel glass sheet. With recent techniques, diffractionpigments can be impressed with nanostructures. Each constant groove gap d,also called grating period, contains a narrow light-transmitting slit. The recip-rocal 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 arespaced with typically as much as 5,000 l/mm or more – the incident wave front

G1

αi

αi

αz

αz

G2

d

Fig. 2.19 Diffraction conditions of an optical transmission grating (schematically)


is diffracted according to the Huygens principle, which means that each point ofa wave front is assumed to be the origin of a new elementary wave [19]. Becausediffraction occurs at all illuminated grating slits, a pattern of constructively anddestructively interfered waves develops behind the grating. The path differenceG1 + 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 andαi for the angle of incidence. The diffraction maxima occur for a path differenceG1 + 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 bothsides of the zeroth order with symmetric intensity maxima and minima. Thewavelengths contained in the incident light fan out by the grating in such amanner that the condition in Equation (2.1.22) is fulfilled. The grating deflectslarge wavelengths stronger than shorter wavelengths; this is the converse of aprism. Moreover, the diffraction spectrum of the first order is of higher intensitycompared to that of a prism spectrum. In order to avoid an overlapping of thediffraction maxima of higher order, the incident angle αi and the grating periodd can suitably be tuned with each other (see below).

In addition to transmission gratings, reflection gratings are also commonlyused – these are especially realized in diffraction pigments. These can be formedby vapor coating both sides of a nontransparent grating structure with an addi-tional layer of a reflecting metal, cf. Fig. 2.20; this has the added bonus of apossible improvement in the mechanical stability of the thin plates. The wavesreflected from the periodically arranged mirrors interfere with the incomingwaves from the opposite direction. Consequently, the diffraction pattern alreadyknown from transmission gratings develops in front of the reflection grating.The cross section of the grooves can be produced as rectangular, triangular, orsine shaped. Reflection gratings are used in modern spectrophotometers andoptimized diffraction pigments, among other things. Examples of diffractionparticles are shown in Figs. 2.54 and 2.55.

Concerning the reflection grating in Fig. 2.20, the path difference G1 – G2 ofthe reflected waves from adjoining grooves follows from the expression

G1 − G2 = d( sin αi − sin αz) . (2.1.23)


αi

αi

αz

αz

G1

G2

d

Fig. 2.20 Diffractionconditions of an opticalreflection grating(schematically)

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 αi = α0 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 incomparison to prisms, but the incident intensity is distributed among all diffrac-tion orders. Among them, is the maximum for z = 0, which is of highestintensity, and also generally not of interest (see Fig. 2.21). This disadvantagecan be bypassed using a so-called echelette grating5; see Fig. 2.22. On thebasis of the special geometry of such a grating, nearly the entire intensity ofthe diffracted light can be concentrated into a particular diffraction order, asrequired.

To achieve this aim, the cross section of the grooves has to meet the followingrequirements:

1. The desired diffraction order zB is not zero; the reflecting grating elementsshould be tilted by an angle αB above the grating base; this angle is called theblaze angle, after the corresponding production method known as the blazetechnique.

5echelette: French, small ladder.


Δα Δβ

Fig. 2.21 Angle differences of diffraction maxima

2. The angle half-width α of the diffraction fringe, caused by this kind ofgrating element, has to be matched with the angle distance β between twosuccessive diffraction maxima; see Fig. 2.21.

In view of the first condition, it is useful to consider the angles from thegrating base normal. The blaze angle is, therefore, given by the simple relation

αB = (αi − αz)/

2, (2.1.25)

where αi 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

zBλB = d · (sin αi − sin αz) , zB = 0, ± 1, ± 2, ... . (2.1.26)

d

Grating normal Face normal

αB

αB

αi

αz

b

Fig. 2.22 Echelette grating with blaze angle αB


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 andthe diffraction angles. For this reason, echelette gratings can be realized withdifferent blaze angles. From the last two expressions, the condition

zBλB = 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 firstcase, we assume an illumination in the direction of the grating normal; seeFig. 2.22. In this case, the angle of incidence is αi = 0 and it follows fromEquation (2.1.27):

αB = 1

2arcsin

(zBλB

d

), zB = 0, ± 1, ± 2, ... . (2.1.28)

In the second case, the light is incident in the direction of the face normal, theso-called Littrow or autocollimation configuration. In this case, then the incidentangle is equal to the blaze angle αi =αB given by

αB = arcsin

(zBλB

2d

), zB = 0, ± 1, ± 2, ... . (2.1.29)

Note that because an echelette grating of sine-shaped cross section can beapproximated by a series of successive isosceles triangles, the outlined con-siderations are also applicable to that geometry.

From the second condition above, some further geometrical conclusionsresult. With the designations given in Figs. 2.20 and 2.22, the relation

b

d= cos αz

cos (αz − αB)(2.1.30)

can be derived. In other words, the triangle geometry depends on the blaze angleas 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 αz = 2αB. 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 αz = αB 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 gratingis right angled.

The utilizable wavelength range of such kinds of gratings is roughly limitedto the interval 0.7λB ≤ λ ≤ 2λB. Absorption and scattering dissipation reducethe efficiency of a blaze grating to about 70% [20]. Accordingly, the blaze tech-nique enables the focusing of about 70% of the influx into a desired z = 0diffraction order. Each diffraction pigment is normally optimized with regard tothe first diffraction order z = ±1. This diffraction spectrum can be observedsymmetrically with respect to the direction of illumination, and is followedby further orders of lower intensity, cf. Section 3.5.5. These principles applynot only to macroscopic gratings but also to diffractive pigment particles; seeFigs. 2.55 and 2.56.

2.2 Absorbing Colorants

After considering different light sources and basic light interactions in theprevious section, the second fundamental component for color producing ofnon-self-luminous colors is the color sample containing the colorants. Colorantscan be divided into two groups, depending on the dominant mechanism ofcolor production: classical absorption colorants and modern effect pigments(cf. Table 1.1). Industrially applied absorption colorants consist mainly of syn-thesized colors of inorganic and organic compounds, and in some rare cases ofmodified natural colors. In this section, we characterize dyes and absorptionpigments, describe the most important color attributes and the accompany-ing coloristic properties as well. Some of these properties are correlated withspecific 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. Eachof these color order systems is grouped according to preset characteristic crite-ria. On one such system is based a special CIE color space. It is also shownthat the color impression results from light interactions in the volume as well asat the surface of a color pattern. Properties of effect pigments are described inthe next section, which show a typical color development in dependence of theangle 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 phys-ical mechanisms [21]. In the case of non-self-luminous colors, these processesare entirely attributable to energetic interactions of electromagnetic waves withthe bounded electrons of atoms, molecules, particles, or crystallites of thecolor-producing material. With regard to absorption colorants, we first outline


some typical phenomenological properties of absorption pigments and after-ward those of dyes. The color origin of absorption pigments can be reduced toabsorption and scattering processes. Such kinds of light interactions are calledselective if they are effective in a narrow range of wavelengths in the visiblespectrum. Light is scattered by pigment particles if at least two conditions aremet: first, the particle dimensions and the wavelengths of the irradiated lightare on the same order of magnitude; second, the colorant molecules show spa-tially separated electric charge distributions – the so-called multipoles. Detailsof these are given in Sections 5.1.2 and 5.1.3.

Chromatic absorption pigments are also called colored pigments or some-times merely pigments. They consist of inorganic and organic compoundswhich, in either case, form crystallites of sometimes different types. The crys-tallite dimensions are typically of the same order of magnitude lesser as thewavelengths of light. Because of the charge separations in multipoles, the mor-phological non-uniform crystallites sometimes conglomerate to form differentlyshaped 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 ina binder or any polymer matrix. The pigments are usually uniformly dispersiblein such materials although some need a suited additive for that. These colorantsare 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 quitedifferent surfaces. In synthetic high polymers, the pigments tend to congregatein 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 (alsocalled hiding power), color strength, and tinting power. Requirements for opti-mized incorporation of pigments are sufficient wettability, dispersibility, as wellas compatibility of the binding materials used, polymers, or additives, amongother things.

Inorganic pigments consist of oxides, sulfides, sulfates, silicates, chromates,carbonates, and metal complexes, for example [22]. Compared to organic pig-ments, they are preferentially used on account of their distinct optical scatteringpower and the typical high hiding power. In comparison with organic pig-ments, due to their simple and stable molecular structure, inorganic pigmentstend to have better rheological behavior as well as increased weather resis-tance. Characteristically, inorganic pigments are mostly dull colors with lowercolor strength but with greater hiding power compared to organic colorants. Amultitude 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 azo-pigments, polycyclic pigments, and anthraquinone pigments. The outstandingfeature of organic pigments is their distinctive colorfulness or chroma in com-parison to inorganic pigments. This generally comes with a high color strength.


Compounds of polycyclic structures, compared to molecules with azo-groups,tend to disperse better in polymer binders, have a lower migration tendency, aswell as higher weather durability [23]. Table 2.3 shows the most commonly usedmodern inorganic and organic absorption pigments, differentiated with regard tothe 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 visi-ble range. They are preferentially used for pure white, increase in the lightnessof any coloration, or covering of a background. On the other hand, the character-istic feature of black pigments is the dominant absorption. These pigments areapplied mainly in tiny amounts for black colors and for darkening of absorptioncolors. With calibration series of white and black pigment mixtures, the calibra-tion of the lightness scale is, therefore, carried out between minimal scattering(pure black pigment) and maximal scattering (pure white pigment). An analogconsideration holds for the case of absorption (Section 6.1.1). It is further thecase that a really tiny amount of a black pigment improves the interference colorof transparent pearlescent or interference pigments; this is because the blackamount absorbs the complementary color produced of interference pigments.

Table 2.3 lists also fluorescence and phosphorescence pigments. These aresummarized by the term luminescence pigments. Both sorts absorb light nor-mally 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, apart of the absorbed quantum energy is reemitted but with longer wavelengths(lower energy) according to Equation (2.1.2). Fluorescence radiation is emit-ted spontaneously and phosphorous radiation, in particular, has a delay in thereemission. In contrast to phosphorescence (Section 4.2.6), fluorescence emis-sion stops immediately after illumination.

Unlike absorption pigments, dyes are completely soluble in a solvent or ina polymeric medium. The coloristic properties are essentially based on absorp-tion. On account of the absence of scattering, dyes are normally transparent –notable exceptions are dark dyes in high concentrations. Dyes consist nearlyexclusively of organic chemical structures. Typical groups of atoms with cova-lent bonds such as >C=C<, >C=O, or –N=N– (ethylene, carboxyl, or azogroup, respectively), called chromophores, are typically responsible for the col-oration of the organic compounds. The π-electrons6 of these covalent bondsabsorb a fraction of the incoming light waves. The incorporation of furthermolecular groups, the so-called auxochromes, causes a color shift either to

6In chemical compounds π -electrons form a pair of electrons which belong together to twodifferent atoms.


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higher wavelengths as with –NH2 and –OH groups (amino and hydroxyl groups,respectively) or to lower wavelengths with –NH–CO–CH3 (ethylene-acid-amidegroup), 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, crim-son, 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, andfluorescence dye [24, 25]. Owing to their molecular double bond structures,dyes show a poorer fastness to light and weather resistance in comparison topigments. The basic molecular interactions of fluorescence dyes and pigmentsare 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 colorantsmake up a so-called complementary color. This color is the perceived colorof 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 ofabsorption colorants

Rough spectral range ofabsorption/nm

Light color of the spectralrange

Perceived complementarycolor of the colorant

380–440 Violet Yellow-green440–480 Blue Yellow480–490 Green blue Orange490–500 Blue-green Red500–560 Green Crimson

560–580 Yellow-green Violet580–595 Yellow Blue595–605 Orange Green blue605–750 Red Blue-green750–780 Crimson Green


that the light and complementary colors reverse their roles at a wavelength ofabout 560 nm. Over and above that, in Table 2.19 are given some pairs andtriples of complementary colors; some of them are partly demonstrated in Colorplate 1.7 These relationships concerning complementary colors are valid foruniform spectral power distributions of the irradiated light similar to a xenondischarge lamp. Complementary colors are arranged opposite (according toHering color opponent theory) in a color plane of the CIELAB system; see Colorplate 4.

As mentioned in the previous section, the realization of a desired color isnormally achieved with mixtures of different sorts of colorants. Apart fromcoloristic aspects, concerns over the compatibility and color fastness of the com-ponents are in the forefront. Colorations of lacquers, plastic materials, or textilefibers consist usually of mixtures with three up to six or more different col-orants. Mixtures of different fluorescence dyes can be distorted by fluorescenceextinction if the quantum emission of one dye in the visible range causes afluorescence stimulation of a second dye in this range.

For the realization of a great number of different color shades, a selectionof at least 25 up to about 130 chromatic, white, and black absorbing pigmentshas to be made and as much as of 110 effect pigments. Among the coloredabsorption pigments, normally yellow and red should preponderate in compar-ison to violet, blue, or green shades; additionally, two to four brown colorantsare normally taken into consideration. Similar considerations should be takeninto account for dyes. The predicted color should match the reference color asexact as possible. In the majority of cases, there are additional properties, suchas high color constancy or low metamerism, which need to be fulfilled. It is,therefore, necessary to have a broad experience with the composition of thecolorant components and binding materials for mixing in order to achieve thecoloristic, processing, or basic performance conditions required with regard tothe reference color.

Color samples are termed as transparent, translucent, or opaque in depen-dence on their light transmittance properties. Requirements for transparentcolors are not only pure absorption and complete solubility of the used colorantsbut also the refractive indices of the applied colorant matrix (e.g., solvents, bind-ing agent, or plastic materials) have to agree with those of the used colorants.Transparent optical media are characterized by the wavelength-dependentabsorption coefficient. This coefficient follows from the spectrometric measure-ments of the transmittance and a suitable approximation of radiative transfer inoptical media (Section 5.1).

A transparent chromatic layer is perceived by way of not only transmit-ted light but also reflected light. The accompanying reflectance comes merely

7Color plates are inserted between Chapters 3 and 4.


Table 2.6 Light transmittance and spectral quantities of color samples

Light transmittanceMeasuringquantities

Determinationquantities Examples

Transparent Directed, diffusereflectance andtransmittance

Absorptioncoefficient K

Liquids, inorganic,organic glasses

Translucent,translucentnonopaque,translucentglimmering

Directed, diffusereflectance andtransmittance

Absorptioncoefficient K,scatteringcoefficient S,phase function p

Binders, foils ofpartiallycrystalline highpolymers, paper,opal glasses

Opaque Directed, diffusereflectance

Absorptioncoefficient K,scatteringcoefficient S,phase function p

Emulsion paints,lacquers,plastics, textiles,ceramics, leather

from reflection at the illuminated outer and inner boundary surfaces which iscaused by differing refractive indices. The magnitude of the reflected portionfollows from Equations (2.1.6), (2.1.7), (2.1.8), (2.1.9), (2.1.10) or (2.1.12). InTable 2.6, three different sorts of color samples with regard to the degree of lighttransmittance are listed along with some spectral measuring and determinationquantities.

Translucent color patterns such as turbid films, paper, or opal glass arecharacterized by selective absorption and simultaneous scattering. Translucentmedia are only light transmitting on a small scale; nonetheless, a coloredbackground is not completely covered. The light transmittance decreases withincreasing layer thickness, this is similar to transparent layers. Some organicpigments of light yellow, orange, or red shade are translucent as are somepearlescent and liquid crystal pigments. The scattering of light occurs at theirregular surfaces or edges of the pigment particles and caused by the electro-magnetic interactions with the multipoles of the pigment particles. In general,scattering of translucent colors depends on the pigment sorts used, the chem-ical structure of the surrounds, the refractive indices, and the structure of theboundary surfaces. Translucent colorations are particularly of interest for suchcoloristic applications, in which the same hue is to be realized simultaneouslyin a nearly transparent and almost opaque finish. In addition to reflectanceand transmittance, the characteristic quantities of translucent color samples areturbidity and covering capacity (Sections 3.4.3, 3.4.4, and 3.4.5).

The theoretical modeling of radiative transfer in translucent systems canactually be quite difficult. These complications are caused by the combinedprocesses of absorption and scattering, where the latter is anisotropic in some


cases. On the basis of the different optical effects, translucent materials can besubdivided 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 sur-rounded by a halo8; the primary ray is more attenuated than in the idealtranslucent case;

translucent gleaming: the energy of the primary ray is spread out in anintense halo; there is virtually no primary ray remaining at the secondboundary surface.

These different translucent states are best modeled with a multi-flux approxima-tion. For this, in addition to absorption and scattering coefficients of the opticalmedium, some additional optical quantities such as the phase function p, forexample, 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 coveredcompletely by this kind of colors. In all opaque systems light scattering isnormally the dominant process, and it is accompanied by more or less dis-tinct absorption. Scattering occurs isotropically without a preferred directionor, the other extreme, anisotropic with a specific preferred direction. Increasingscattering lowers the light transmittance and vice versa. The covering capac-ity of a coloration is, above all, caused by the scattering power of the pigmentparticles. The single spectrometric measuring quantity of opaque materials isthe reflectance. The reflectance, in general, depends on the measuring anglefor many kinds of effect pigments. Extreme optical states result in mixturesof absorption and effect pigments with different light transmittance. These aremost 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 thecolor of absorbing colorants is caused by light interactions such as scatteringand absorption. On the other hand, the produced visual color sensation is by nomeans completely characterized by those. The variety of different combinationsof wavelengths as well as the accompanying power distributions reaching theeye results in many colors, which can be described by different color attributes.For better understanding of the context, we use an analogy from acoustics.

8This 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.


A pure acoustic tone is unambiguous, physically described by its frequencyand amplitude. The same tone, produced from different music instruments, ishowever surrounded by a typical sound spectrum. In a similar way, each non-self-luminous color is produced not simply by a single light frequency but alsofrom various spectral values of the visible spectrum.9

The different wavelengths simultaneously entering the eye are perceived asa single color impression and not as separate single-colored wavelengths. Thisentire color impression can be verbally described by characteristic terms. Thedescription or comparison of colors is used in color industry not only from phys-ical or colorimetrical points of view but also according to coloristical attributes[27]. The following enumeration, which is not to be considered complete, givessome conventional terms for characterizing the color impression of non-self-luminous 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 suchas red, green, yellow, blue; hue and shade are terms equivalent to colortone, or tint, see below;

relative color strength, relative tinting strength: the color economy of anavailable colorant material relative to an arbitrarily chosen colorant ofequal or similar color;

color depth, color intensity: the color distinctiveness, which increases withenhancement of the same colorant amount;

dullness: a characteristic color feature which can be described by an existingamount of gray or black; it is the converse to brightness.

The quantitative determination of relative color strength is standardizedbased on colorimetric criteria (Section 3.4.2). These instructions underlie theformalism of the CIELAB or DIN99o color spaces. The following terms arealso used to denote a color point in color space:

lightness: a measure for the reflectance of a non-self-luminous colorant; thereflection ratio of absorption colorants is standardized by the so-calledgray scale in which black is assigned to the value of 0 and white to thevalue 1; fluorescent and effect colorants often have reflectance valuesgreater than 1, caused by the arbitrary fixing of the gray scale; self-luminous sources such as light sources or the sky are characterized bythe term brightness rather than lightness;

saturation: a quantity describing the colorfulness of colorants which doesnot change by further increase of the colorant concentration;

shade, color tone: this corresponds to hue; equivalent terms are tint or tinge;

9This metaphor is not to be confused with synesthesia, in which a physiological stimulusinduces a further stimulus, for example, colors are associated with music and vice versa.


chroma: an absorption colorant loses colorfulness with lower saturation;chroma depends on both saturation as well as lightness because a tinyamount of black reduces the colorfulness of a color.10

Common for characterization of color impressions are also adjectives andtheir comparative forms; their meaning is somewhat equivalent to the termsalready given above. Here are listed properties in opposing pairs:

colored, chromatic: any color, such as yellow, orange, red, or green; it isanalogous 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 colorantscan be directly manufactured with properties in the ranges of the last 12 listedextreme color states. Some of the cited characteristics correlate also with typ-ical special features of the corresponding spectral reflection or transmissioncurve traces. The measured spectrum can sometimes be interpreted as a kindof “finger print” of the accompanying color. Some of these properties can bevisualized 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 theangle-dependent spectral reflection of effect pigments.

The spectral reflectance of a chromatic absorption color is generally char-acterized by either a significant maximum (e.g., violet, blue, green) or a steeprise to higher wavelengths (e.g., yellow, orange, red) in the wavelength rangeof the complementary color or rather natural color; see Fig. 2.23. The high-est absorption exists in a wavelength range of a distinct reflection minimum;backscattering, however, dominates in the range of maximal reflection or theplateau 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 aconstant reflection of 1.0 and ideal black of 0.0; gray takes intermediate valuesdepending on the content of white or black. The decrease of spectral reflectionfor white or gray with shorter wavelengths is due to the tail of the UV absorptionof the underlying TiO2 pigment. The impression of white results exclusively

10These four color terms can be visualized by geometrical quantities in both mentioned colorspaces and further ones; see Sections 3.1.3 and 3.1.4.


0.8

a

b

c

d

e

R(λ)

0.6

0.4

0.2

400 500 600 700nm

0λ

Fig. 2.23 Spectral reflectance curves of chromatic pigments: (a) blue, (b) green, (c) yellow,(d) orange, and (e) red

0.8

R(λ)

0.6

0.4

0.2

400 500 600 700

a

b

c

0

nmλ

Fig. 2.24 Spectral reflectance curves of achromatic colors: (a) white, (b) gray, and (c) black


0.8

1bt

2bt

2dk

1dk

R(λ)

0.6

0.4

0.2

400 500 600 7000

nmλ

Fig. 2.25 Spectral reflectance of bright and dark pigments: 1bt bright blue, 1dk dark blue,2bt bright yellow, and 2dk dark yellow

0.8

R(λ)

0.6

a

b

c

0.4

0.2

400 500 600 7000

nmλ

Fig. 2.26 Spectral reflectance of different gray colors: (a) light gray, (b) middle gray, and(c) dark gray


0.8

R(λ)

0.6

2br

1br

1du

2du

0.4

0.2

400 500 600 7000

nmλ

Fig. 2.27 Spectral reflectance of brilliant and dull pigments: 1br brilliant blue, 1du dullblue, 2br brilliant yellow, and 2du dull yellow

from regular light scattering over the entire visible range. This is the case forexamples 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 maximumor a widened (narrowed) plateau region; a light (dark) gray shows a shift of thereflection level to white (black); see Figs. 2.24 and 2.26. Most of the color-ordersystems and the colored calibration samples for recipe prediction are based oncolored pigment mixtures with white and black colorants. It is remarkable thatthe human eye provided by nature is more sensitive to color differences betweendark colors (violet, blue, green) in comparison to light colors (yellow, orange,red). This is correlated with a low maximum respective high reflectance plateaurange.

The higher and steeper the rise of the curve to the plateau region or thesmaller the half-width of the reflection maximum, the more the color is per-ceived as brilliant, clear, or pure. Conversely, pale, dirty, or dull colors possessa spectral reflection characterized by a lower and broader maximum or overlap-ping maxima, compare in Fig. 2.27 curve 1br with 1du for a blue pigment. Thespectral reflectance of a dull yellow, for example, shows a more flat peak profileand a lower plateau range compared to a brilliant yellow, cf. curves 2br, 2du inFig. 2.27.

The terms outlined up to now are merely used to describe some typical col-oristical properties of classical absorption colors or colorants. This vocabulary


cannot be directly carried over to effect pigments. Rather than absorption andscattering, effect pigments produce new sorts of colors on account of differ-ent optical mechanisms; identical terms have, therefore, different meanings foreffect pigments than for absorption colorants. Metallic pigments, for example,produce a characteristic metallic lightness, brilliance, or hue extinction. Thisambiguity 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 distinguishingabout 10 millions of colors. It is further important to note that, in addition to theastonishing number of colors, a color can have different attributes; therefore, itseems essential to have systematic classifications for such a tremendous diver-sity of colors. Such classification systems serve not only as an overview but alsoas an improved communication about non-self-luminous colors, particularlyfor their use in difficult applications. From each of the established color-ordersystems, series of color samples exist for visualization. The antiquated colorclassifications are certainly not ordered after uniform criteria [28, 29]. Thechronologically first systems were arranged based on features, which includedthe actual knowledge about colors. Among the contemporarily used color-ordersystems are to differentiate roughly two groups: systems on coloristic and oncolorimetric basis. In the following, we sketch the common four representativeexamples of both groups.

The most important coloristic-order system is that of Munsell, established in1905. It is simultaneously comprised of various companion features such as,for example, precise nomenclature or systematic extension capability for addi-tional colors [30]. The corresponding color patterns are ordered according tothe three properties hue H, value V, and chroma C in three dimensions in acylindrical coordinate system. The true significance of this collection are thecolored patterns which display a nearly constant color difference between neigh-boring colorations. This was developed without any colorimetric background– an amazing for the beginning of the 20th century. In spite of the visuallynearly equal color steps, this color-order system was not accepted until 1976as a basis of the CIELAB system. Experience with the Munsell system hasbrought out critical disadvantages. Particularly unfavorable are the non-uniformperceived color differences of bright and dark colors. In remedy of these short-comings, the Munsell system was supplemented by an additional color patternin 1990.

The natural color system (NCS) was worked out in Sweden and is standard-ized there; it is based on the opponent color theory of Hering and is arrangedin pairs of the four chromatic colors red, green yellow, and blue as well as theachromatic colors white and black [31]. The patterns are organized in color


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 applicabil-ity. It incompletely covers the color space, and additionally, colors with glossysurface are inapplicably marked. Moreover, the arrangement pattern is visuallynon-uniform. Without a measuring device, this color system is, therefore, onlysuited for rough orientation in color space.

The so-called color index (C.I.) is suited for identification of colorants butrepresents no real color-order system as in the discussion above. It simply con-sists of a list with unsystematically assembled dyes and absorption pigments.These are partially denoted according to the origin (generic names) and accord-ing to the chemical constitution with natural numbers (constitution numbers)[32]. This listing offers a certain aid only in a few cases, if, for example, someof the colorants listed in the C.I. are to exchange with one another.

Strictly speaking, the widely distributed color registry RAL 840 HR inGermany is also not a color-order system in a broader sense. This registry wascreated to ensure that industrial colors are classified uniformly with definednames and numbers for better communication between public agencies and pro-ducers of consumer goods. The color patterns were originally vaguely arrangedin view of coloristic criteria; in the meantime, a modification was undertakenusing the so-called DIN color chart, see below.

It should be added that contemporary color systems also consist of patternswhich change uniformly by a suitable technical parameter such as the concentra-tion of the used colorants, for example. The corresponding inconstant changesof hue, lightness, or chroma certainly make color perception and color compari-son more difficult. A visual ascertainment of color differences is not ensured bysuch systems.

In contrast to the order arrangements above, the DIN color chart is acolorimetric-based color system [33]. It comes from the CIE chromaticity dia-gram; see Section 3.1.2 and Color plate 2. The color patterns are arranged withregard to three properties, similar to the Munsell system. These color proper-ties are denoted as darkness D, hue T, and saturation S. They correspond to thelightness L∗, hue H∗

ab, and chroma C∗ab of the CIELAB system (Section 3.1.3).

The OSA-UCS system (Optical Society of America Uniform Color Scales) isprincipally used in the USA. It consists of a total of 588 color patterns, fromwhich 12 colors at a time are positioned in the corners and one in the centerof a cubic octahedron [34]. With this system, a multitude of visual equidistantcolor scales can be established; visually equidistant means that adjacent colorpatterns always show the same visually perceived color difference independentof color point in color space. This system cannot be directly transformed intothe CIELAB system; the same holds for the Munsell system, NCS system, andthe DIN color chart. A reliable determination of color differences is impossibleon the basis of the OSA-UCS system.


Accordingly, it is advantageous to fall back on a universal applicable color-order system, which, for chromatic as well as achromatic colors, has the implicitmetric of a color space. The RAL design system is organized on such consider-ations. It is based on the structure of the CIELAB system. The RAL designsystem enables, with good approximation, the visual determination of color dif-ferences. The corresponding color collection is established as RAL design atlas[35]. There exists also a collection of 70 RAL effect colors, which cannot beclassified 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 anexpression of a subjective color perception. As already mentioned in Section2.1.5, the entire color impression is certainly composed of at least two com-ponents: the light interactions in the volume and at the boundary surface of acolored sample. In other words, the reflection or transmission from the volumeis superimposed on the boundary surface reflection. This reflection is causedby different refractive indices at the boundary surface. Such kinds of bound-ary surfaces are present in paints, coatings, plastic materials, emulsion paints,or ceramics. This distinction cannot be made for undefined surfaces such as oftextiles, uncoated papers, plasters, or suede leather.

The kind of surface reflection is also influenced by the structure of thesurface. A given color can exhibit a surface structure between two extremes:

matt: appears a rough (or structured) surface; this appearance is caused bycompletely (or partly) diffuse surface reflection;

high-glossy: appears a very smooth reflecting surface; such a surfaceinduces only directed reflection, which is called specular reflection, spec-ular gloss, or simply gloss. This behavior is described by the reflectionlaw.

Both the above surface properties should generally be interpreted as colorattributes.

For the illumination of a (color) pattern with directional light, the transitionbetween matt, half-matt, glossy, or high-glossy surfaces can be characterized bythe resultant diffuse or directed reflection with the aid of the reflection indi-catrix. This is a plane polar diagram which represents the angle-dependentintensity distribution of the light reflected from the surface. In reality, an indica-trix is in three dimensions. Four different indicatrices are shown schematicallyin Fig. 2.28, each caused by a different sort of surface reflection. The diffuseand directional reflection amounts are given by the shape of the envelope curveand enveloping surface of the intensity distribution.


Fig. 2.28 Reflection indicatrices of different surfaces: (a) matt: purely diffuse reflection,(b) half-matt: dominant diffuse, minor directed reflection, (c) glossy: predominant directedand minor diffuse reflection, and (d) high glossy: exclusive specular reflection

A diffuse reflecting surface of high roughness is achieved by various treat-ments, for example, with the help of suited polymer matrices or ceramics orpigment crystallites standing out non-uniformly from the boundary surface. Inaddition, the use of embossing dies is possible with regular geometrical sur-face forms such as micro-spheres and micro-prisms or irregular linen and otherfabric structures. Further methods are sanding, etching, or physical vapor depo-sition (PVD). Certainly, the realization of ideal matt surfaces is exceedinglydifficult.

A matt surface appears normally somewhat lighter than a high-glossy surfaceof the same material. This is caused by the higher reflection coefficient for dif-fuse 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 inde-pendent 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 min-imal color shift. This phenomenon comes from the superimposed scattering ofpigments near the surface. The entire diffuse reflection at the surface of a coloredlayer 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 componentoriginated from the volume because this shows the interesting light interactionswith 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 throughthe 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 reflectionis given by the refractive index of the binder. The pigments can, however, be


located in or near the surface, for example, by high pigment volume concen-tration (PVC), blooming, or flooding. In such cases, the arithmetic mean of therefractive indices of the involved materials is to be used. Such a surface bound-ary can have further color features, due to the fact that the refractive index ofmost colorants is dispersive. This effect is named bronzing; it can be presentin printing inks, lacquers, plastic materials, or textiles, and can be avoided byappropriate measures.

For unambiguous coloristic assessment of matt to high-glossy samples, it isabsolutely necessary to avoid the glare caused by specular reflection. Therefore,the sample containing absorption colorants is always illuminated laterally atan angle of 45◦ and viewed perpendicular to the surface; see Fig. 2.29a. Thereversed arrangement is also possible, but rarely used. In commercial lightbooths with lamps of different illuminants (normally D65, A, FL 2, FL 11 sim-ulators), the light sources are arranged laterally and glare-free as shown in thementioned figure. The color sample should be surrounded directly by a mid-dle gray and the assessment should be performed by keeping the so-called CIEreference conditions, cf. Section 3.2.2.

In contrast, the visual evaluation of the surface gloss is achieved with a fixedlight source and constant line of vision by tilting of the sample over a specular

Light source Observer Specularreflection

Color pattern

a)

b)> 60°

Fig. 2.29 Two different configurations of the three factors for color impression of absorptioncolors: (a) for coloristical assessment and (b) for evaluation of surface gloss


reflection angle range; see Fig. 2.29b. A light booth should, therefore, possiblyhave a tiltable support with angle scaling. The quantitative determination ofsurface reflection is carried out separately using a gloss meter; the reflectedintensity is registered at several variable angles between normal to the surfaceand 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 blend-ing, and change of gloss in dependence of the observation angle. To achievecomparable results, the radius of curvature of the substrate and the thickness ofthe coating have to be the same for all color samples of a collection. In contrast,coated curved substrate surfaces are absolutely unsuited for instrumental colormeasurements.

The evaluation of the surface reflection of colorations containing effect pig-ments is particularly critical. The optical properties of a metallic paint coating,for example, are essentially caused by specular reflection at the flake-shapedmetal particles. The flakes are primarily arranged parallel to the substrate sur-face. Therefore, specular reflection dominates, but it is superimposed by diffusereflection coming partly from the rough particle edges. For metallic pigments,the angular distribution of the reflection depends also on the illumination angleas well as the angle of observation.

As already explained in Sections 2.1.6 and 2.1.7, the color physical propertiesof effect pigments are also extremely angle dependent. Compared to absorp-tion colorations, the visual assessment of such colorations needs a much moresophisticated procedure, cf. Fig. 2.30.

The observation for effect pigments is also normally performed using a fixedlight source, but the classical method needs two identical colorations, one kepthorizontal and the other rotated by an angle < 45◦ from this position; seeFig. 2.30a. This procedure allows for the observation of the angle-dependentchange of lightness intensity. For flake-shaped metallic pigments, this angle-dependent change in reflected intensity is typical; it is the so-called lightnessflop.

The color changes of interference and diffraction pigments between the twoextreme observation angles is, however, termed as color flop. Figure 2.30bshows the modern arrangement for visual evaluation of effect colorations. Inthis configuration, the light source and the observer are fixed. Vertical move-ment of a color sample simultaneously changes both the angle of illuminationand angle of observation. Therefore, the observation of the color flop, forexample, needs only one color pattern and is carried out at the same surfacespot.

We have arrived thematically at the transition from absorption to effect pig-ments. These colorants have been used industrially since about 1970 and to anincreasing extent. In the following sections, we discuss the structure, morphol-ogy, and the spectral properties of the most important sorts of these moderncolorants.

2.3 Effect Pigments 63

Light source

Observer

Effect Color pattern

a)

b)

Fig. 2.30 Two different configurations for assessment of colorations containing effect pig-ments with fixed observer: (a) classical method (tilting): lightness flop and (b) modernmethod (vertical movement): color flop

2.3 Effect Pigments

Effect pigments have broken new ground in color physics, especially with regardto industrial-scale research, development, and application. The color productionof effect colorants is predominantly caused by anisotropic processes like singleor multiple reflection, interference, or diffraction. These processes are unreal-ized in absorption colorants. The generic term “effect pigment” is inadequatebecause colors generated by absorbing colorants are also based on an optical“effect”. However, flake-shaped pigment or shorter flake pigment is an accurateexpression for this sort of colorants. The generated color impression of effectpigments is extremely angle dependent. This is a function of both the illumina-tion and the observation direction. Effect pigments result in quite strange color


sensations for human color sense because our sense has evolved to perceive onlycolors from absorption colorations. In a practical sense, effect colorants needmore extravagant manufacture methods in comparison to absorption pigmentsand also a more extensive characterization, measuring techniques, application,and processing.

All types of effect pigments consist of flake-shaped particles with a largerange of typical lateral dimensions between 1 μm and 1 mm. This is morethan 10 – 1000 times larger than that of absorption pigments. The flake thick-ness has values between 10 nm and 1 μm. On account of the flake form, theresultant color effect is increasingly distinct with a more uniform morphologyand the more the particles are oriented in the binder parallel to the substrateor surface. Like absorption pigments, effect colorants can be of inorganic aswell as organic nature. With regard to the processes of color production, theyare divided into four groups (cf. Table 1.1). For historical reasons, they arenamed:

– metallic pigment;– pearlescent pigment;– interference pigment;– diffraction pigment.

In the literature, pearl luster pigments are often subsumed to the interferencepigment classification [36]. The laws used to describe the optical properties ofmetallic pigments are essentially geometrical optics; all other sorts of effectpigments are generally described by wave optics.

Metallic pigments consist normally of a metal or an alloy of metals. Thetypical metallic gloss is increasingly brilliant the more uniformly the flakes areoriented parallel to the boundary surfaces of a coating. The so-called metalliceffect is mainly a consequence of the directional and diffuse reflection at thesurface and the edges of the flakes.

In contrast, pearlescent pigments consist of two or more layers with a highindex 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 oftenapplied. The specific pearl luster depends on the permutation of the layers. Thisluster originates from single or multiple reflections at the layer boundaries fol-lowed by interference of the light waves. Differing optical layers are behindthe general function of interference pigments; this does not require the use ofa mica substrate. An interference pigment subgroup is the so-called opticallyvariable interference pigments. The high ratio of refractive indices, in con-junction with different layer thicknesses, fans out the first or more interferenceorders in such a way that a variety of interference colors are to observe angledependence.


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 mate-rials known from nanotechnology. The ferromagnetic particles can be orientedwith an external magnetic field before the crosslinking of a binder. The pro-duced unusual but often impressive colors require that effect pigments undergoa more subtle and closer examination and handling compared with absorptioncolorants.

2.3.1 Types of Metallic Pigments

Metallic pigments, generally consisting of metal flakes, are employed mainlyon account of the metallic reflection from the flake-shaped particles. This kindof reflection consists of superimposed specular and diffuse components whichproduce unusual color effects compared with absorbing pigments. Conventionalmetal flakes have mean lateral dimensions ranging from about 5 μm to nearly50 μm, whereas the thickness varies between roughly 100 nm and 1 μm. Insome extreme cases, the particles have dimensions which are up to 10 timeshigher. The ratio of thickness to diameter of the particle is called the form factorand 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 forsinter metals, building materials, explosives, or pyrotechnics, for instance, asfunctional or chemically reactive particles.

In this text, we are mainly interested in the metallic reflection. This propertyis caused, in simplified physical terms, by the fact that individual metal atomscan easily release the bonding electrons. In lattice arrangements, the metal atomscompletely loose the valency electrons. These electrons form the electron gaswhich is distributed among the remaining ions so that each ion is fixed on acorresponding lattice position. On account of its interaction with the electrons,an external light wave from a normal source cannot penetrate the very denseelectron gas. The majority of the light is rather reflected and the remainingpart is absorbed within a very small penetration depth. Reflection and absorp-tion produce the typical metallic brilliance and characteristic natural color ofmetals [14].

The change in electron gas density at the metal surface results in lightdispersion in the visible range, among other things. This causes a light-, gray-,or low-colored metallic effect. The theoretical reflectivity of metals is givenby 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 formetals that are most commonly used for metal pigments. In this listing, themetals are arranged according to decreasing reflectivity. The given optical


Table 2.7 Reflectivity, refractive index, absorption index for perpendicular incident light atwavelength of λ = 589.3 nm and T = 293 K as well as melting point of metals used formetallic pigments [37]

MetalReflectivityr (n, κ)

Refractiveindex (n)

Absorptionindex (nκ)

Meltingpoint Tm/K

Ag 0.99 0.052 3.91 1,235Al 0.912 1.181 6.99 933Au 0.888 0.280 2.91 1,336Cu 0.804 0.493 2.80 1,356Zn 0.768 2.74 5.77 693Ni 0.664 1.71 3.61 1,726Fe 0.586 2.91 3.58 1,809Mo 0.575 3.40 3.56 2,890Ti 0.565 2.09 3.11 1,933W 0.524 2.83 3.02 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 meltingtemperatures of the given metals are higher than those of the highest flowtemperature of normal polymer melts. The refractive index is also subject todispersion; 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 oflight c in vacuum; this is not in contradiction to the special theory of relativitybecause only the group velocity – with which energy or signals propagate –cannot exceed the velocity of light c. Clearly, the actual reflectivity is lower thanthe theoretical one. The real reflectivity depends on the details of morphologyof 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 thathistorical laxness in naming remains an issue. Terms such as aluminum bronzeor silver bronze instead of aluminum pigments, gold bronze or even the moregeneral metal bronzes, are still in widespread use today by pigment manufactur-ers, colorists, and even in modern literature [38–40]. Actually, aluminum bronzeconsists of copper alloyed at most 12% aluminum; silver bronze is an alloy ofsilver and tin; gold bronze is a solid blend of suitable amounts of copper andzinc; genuine bronze, however, consists of copper alloyed with tin.


Apart from dispersion and particle size, the character of the metallic colorimpression is influenced by further details. Among them are the chosen metalor alloy, the manufacturing and processing method of the flakes, and the wet-tability in binders. In the following, we give a survey of the influence of theseparameters with regard to the visual perceived metallic effect.

First of all, the chosen metal is responsible for the brilliance of the naturalmetallic 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 metalgloss and, therefore, have a different meaning from that which was outlined forabsorption pigments in Section 2.2.2. Additional natural metallic colors can berealized using mixtures of metallic pigments: Ni flakes lighten and Fe particlesgray the metallic effect. Also alloys such as brass (alloy of Cu and Zn) aresuited for gold-yellowish to reddish color, for example. Metallic pigments aremanufactured with mixtures or alloys only if the required metallic effect is notachievable using only conventional metal flakes.

The most commonly used metallic pigments from modern point of view aregiven in Table 2.8. Uncoated metal flakes based on natural metals have the mostdiversity. Particles with especially even surfaces can be manufactured usingthe PVD method. For this, a polymer foil is vapor coated in vacuum with ametal and afterward crushed at temperatures far below the glass transition tem-perature of the polymeric material. These flakes are termed as crushed PVDfilms.

Due to modern developments, even colored metallic flakes can be man-ufactured. In these cases, a colored component is superimposed on the

Table 2.8 Classification of metallic pigments

Metallic pigment Typical examples

Uncoated metalflakes

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 withabsorptionpigments

Inorganic or organic pigments in silicon dioxide or acrylatecoating fixed on aluminum or “gold bronze” flakes as substrate(CVD procedure)

Partially oxidizedand oxide-coatedmetal flakes

Partially oxidized from the surface aluminum flakes, copperflakes, zinc/copper flakes (“fire colors”);

coated aluminum flakes: iron-III-oxide, tin oxide, zirconiumoxide, iron titanate, cobalt titanate


metallic effect. There are two different methods for manufacturing. In the first,absorption pigments are suitably fixed at the surface of the flakes by chemicalvapor deposition (CVD) [38, 39]. The second method is based on metal flakeswhich are partly oxidized from the surface, or coated with metal oxides. Suchmetal flakes produce an intense color effect, sometimes called “fire colors.”These intense colors are caused by multiple reflections at the transparent outerlayers with varying refractive indices; the multiple reflected waves then inter-fere. Technically, such colorants are not metallic pigments in the strict sense,rather just a multi-layered interference pigment on top of a metal substrate. Inmost cases, the original metallic brilliance of the metal substrate is lost.

It must be noted that the chosen manufacturing method is of great influenceto the resultant coloristical properties of metallic pigments. For shaping of nat-ural particles, the melt is pressed through a narrow nozzle of suitable geometrywith high pressure. Due to high flow velocities in the nozzle channel, often upto 400 m/s, the velocity gradient leads to an atomizing of the melt into roundand contracting tiny droplets outside of the nozzle tip. After cooling, they aretransformed 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 toprevent clumping or welding of the particles, long-chained fatty acids are oftenadded, 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 entiresurface of the resulting flakes; this certainly changes their wettability especiallyagainst binding materials. Because the end groups of the fatty acids are depen-dent of surface tension and behave either hydrophilic or hydrophobic, the metalflakes 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 nearthe surface and (b) non-leafing or nearly uniform distribution


illustration of two flake arrangements in a binder, the first is called leafingand the second non-leafing. The tendency to form the leafing arrangement isstronger with the lowering of the wetting with the surrounding polymer. Leafingflakes result from coating with stearic or palmitinic acid; non-leafing particlesare usually obtained with oleic acid, for example. It is worth mentioning thatthe sort of wetting is generally correctable afterward with suitable additives. Ifthe flakes are dispersed in the melt state of plastic materials, the leafing is gen-erally avoided due to the high structural viscosity of the melt.11 A measurementmethod for determining the leafing behavior is detailed in the literature [41].

Leafing pigments incorporated in transparent binding agents show high bril-liance due to a uniform and constant reflection. The abrasion resistance of thesurface film is often reduced and, therefore, an additional top coat is usuallyapplied. In contrast, the parallel and compact flake arrangement often behaveslike an optical or mechanical barrier: in addition to visible wavelengths, itreflects 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 radiationas well as corrosion prevention pigments. Further non-colored applications ofmetallic 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 themorphology of the flakes. The wet milling procedure of Hall predominantlyproduces particles of irregular and uneven surfaces along with high edge errors– they are, therefore, quite accurately called cornflakes. Typical aluminum corn-flakes are shown in Fig. 2.32. The picture was taken with a scanning electronmicroscope (SEM). The irregular particle edges result from fracture from otherflakes during the milling process within the ball mill. The uneven surfaces arecaused by abrasion of the coarse edges of colliding and pressed particles. Atthe particle surfaces shown in Fig. 2.32, it is possible to discern some remainsof broken edge zones and indentation traces of striking balls. Both the unevensurface structure and the rugged particle edges are responsible for the typicallyincreased diffuse light scattering of cornflakes. The light reflected from suchflakes is composed of a directional and a superimposed scattering component.The accompanying indicatrix corresponds to that of Fig. 2.28c. The amount ofdiffuse reflected light is increased, therefore, with more uneven particle surfacesand rugged flake edges. With increasing particle scattering, there is a reductionof brilliance, that is, “it turns gray.”

11Structural viscosity means that the viscosity has a nonlinear dependence on shear velocity;this is in contrast to constant Newtonian viscosity.


Fig. 2.32 SEM picture of typical cornflake particles of aluminum (source: Eckart WerkeGmbH, Velden, Germany)

Sophisticated grinding techniques with metal brushings or polishing pasteshave been used since about 1980 to reduce this brilliance loss. These techniquesallow for the manufacture of thicker metal flakes with relatively plane surfacesas well as even or rounded edges. Particles of this kind are often called silverdollars, of which an example is shown in Fig. 2.33. These sorts of flakes reflectlight with a dominant directional component accompanied by a considerablylower scattering. A paint film with silver dollars and clear top coat is, there-fore, lighter and more brilliant than the one with cornflakes of the same metaland identical particle size distribution. Silver dollar pigments are preferentiallyemployed in high-quality systems such as automotive coatings, the so-calledmetallics. They are also used in high polymer materials and printing inks.

Shear stable flakes of upward 10 times the particle thickness of cornflakescan be realized in order to withstand processing techniques of high pressure orhigh shearing stress (e.g., ring main pumps, injection molding, blow molding, orextrusion). Particles with nearly plane surfaces and high brilliance can also bemanufactured by PVD coating of thin polymer foils. They do, however, exhibitan undefined breaking edge. A representative example is shown in Fig. 2.34.

In addition, it is possible to produce metallic pigments of constant thick-ness and of geometric regular shapes. These sorts of particles are called glitterflakes. To describe the glitter effect, the terms sparkle and glittering are alsoused. Both expressions are often utilized simultaneously, although they havesomewhat different meanings.


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: EckartWerke GmbH, Velden, Germany)


Sparkle is the property that single flake particles are directly recognized visu-ally due to their expanded planar reflection surfaces. This is typically the casefor mean particle sizes of about 30 μm and larger. The metal flakes are per-ceived separately on account of the surface reflection contrasting to the darkersurroundings. They behave as isolated microscopic mirrors. In contrast to glit-tering, see below, neither the morphology nor the lateral dimensions of sparkleparticles are necessarily uniform. The phenomenon of sparkle (also referred toas sparkling, optical roughness, micro-brightness, glint, or diamonds) is presentin quite an assortment of effect pigments and is particularly observable withdirectional light; see also Section 3.5.1.

In contrast, glittering is exclusively due to particles of uniform and regulargeometry. These particles are manufactured in the form of squares, rectangles,rhombs, or circles by cutting or punching-out from metal foils or metallizedpolymer foils. In Fig. 2.35 an example of nearly quadratic aluminum glitterflakes cut from ribbons with a band knife is shown. Glitter flakes are of nearlyuniform lateral dimension compared with conventional manufactured metallicpigments in ball mills. They are produced with sizes of 50 μm up to as much as2 mm. They are generally at least 10 times thicker than usual cornflake or silverdollar particles.

With regard to quadratic and rectangular glitter flakes, often specificationssuch 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)


multiplication of each of these numbers with one thousandth inch (2.54 ×10–3 cm) gives the middle lateral extension of the corresponding particles. Thismeans, 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 extremeprocess control in the Hall technique, it is also possible to produce spherical pig-ment 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 usualmetal pigments. These consist either of metal flakes covered by absorption pig-ments or metal flakes partially oxidized from the surface or oxide-coated metalparticles. In the first case, the metal particles are coated with silicon dioxide or apolyacrylate containing inorganic or organic absorption pigments. In Fig. 2.36,there is an SEM photograph of aluminum flakes with a silicon dioxide coatingof embedded inorganic pigment particles. This picture shows not only the coarsesurface structure of the flakes but also the size proportion of the absorptionpigments having only a few nanometers to the around two orders of magni-tude larger sized metal flakes. From this difference in size, the typically higherscattering power of absorption pigments compared to effect pigments is alsounderstandable.

Colored metal effect pigments consist also of partially oxidized or oxide-coated flakes, which are manufactured using the CVD procedure. Partially

Fig. 2.36 Aluminum flakes coated with silicon dioxide and embedded inorganic pigmentparticles (source: Eckart Werke GmbH, Velden, Germany)


oxidized flakes of aluminum, copper, or zinc/copper are generally preferred.Iron-III-oxide-coated aluminum flakes are also common. All of these pigmentsproduce particularly impressive reddish colors – and are, therefore, also calledfire colors. These unusually striking colors are due to the combination of threeeffects: first, absorption and scattering of copper, zinc, or iron-III-oxide; sec-ond, interference caused by the layer construction; third, metallic reflection ofthe particles.

Already the concept of the glitter flakes suggests that the character of themetallic effect is particularly dependent on the particle size. All particles,however, are not of the same size; therefore, the metallic effect is in generalinfluenced by the particle size distribution. On the other hand, the size distri-bution can be controlled partly by the milling and sieving process; from thesemanufacturing steps, an asymmetrical particle size distribution with respect tothe 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 quantityd50 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 thedistribution.

In addition to the use of scanning electron microscopy, the laser granulometrymethod has proven quite useful for the determination of the mean particle sizeof effect pigments and the accompanying size distribution. The laser method isfounded on scattering and diffraction of the particles suspended in a suitableliquid. This so-called laser granulometrical operation is suited only as a relativemethod, this is, not as an absolute method.

20

10

Rel

ativ

e fr

eque

ncy

%

Cum

ulat

ive

freq

uenc

y cu

rve

10–1 100 101

d50

102

100

50

0d /μm

0

Fig. 2.37 Curves of particle size distribution and of cumulated frequency of an aluminumcornflake pigment with same value of d50 ≈ 20 μm as in Fig. 2.38


The size distribution of effect pigments is characterized by the so-calledwidth W, which is given by the quotient W = (d90 − d10)/d50 > 1. The quanti-ties d10 and d90 mean that 10 and 90% volume, respectively, of the particles havelateral dimensions of Φ ≤ d10 and Φ ≤ d90. A narrow distribution with low Wproduces a more brilliant metallic effect in comparison to a broader distributionof equal d50 value; see Figs. 2.37 and 2.38. The concentration of small parti-cles is lower in a narrow distribution than in a broad distribution. However, thegreater the number of small-sized particles present, the more gray and paler themetallic effect appears. Of course, with smaller flakes edge scattering prepon-derates, and in addition, the parallel configuration of the flakes is more distortedthan with larger sized particles.

The metallic reflection of typically narrowly distributed silver dollar pig-ments is consequently more distinct than that of traditional cornflakes.Cornflakes show a significantly broader particle size distribution. Among mod-ern metallic pigments, silver dollar flakes of aluminum are the most light andmost brilliant particles. According to Figs. 2.37 and 2.38, there is always anelevated number of particles smaller than 5 μm.12 This increased content offine particles is unavoidably caused by the grinding process and is quite typicalfor the manufactured metal powders. The fine particles give rise to a scatteringcomponent which reduces the metallic brilliance.

Finally, the production of the metallic effect is also influenced by the ori-entation of the particles in the polymeric surrounding medium. The particle

20

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uenc

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rve

10–1 100 101

d50

102

100

50

0d /μm

0

Fig. 2.38 Curves of particle size distribution and of cumulated frequency of an aluminumsilver dollar pigment with same value of d50 as in Figs. 2.37

12Particles smaller than 5 μm contribute to particulate (dusty) matter.


alignment is primarily determined by the processing techniques used. The max-imum possible metallic reflection is achieved by complete flake parallelism tothe bounding faces of a plane parallel layer; this is equivalent to a mirror. Localperturbations of particle alignment parallel to the paint coating can be caused byturbulent motion of the solvent during evaporation; such kinds of heterogeneitylead to mottling or flocculation. Both kinds of visible non-uniformities are alsoknown from coatings with absorption pigments. Lacquers with low solid-statecontent display a more distinctive metallic effect than systems with higher solid-state content (so-called high solids). This is because the lower viscosity makesthe 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 forparallel alignment of the particles. In high polymer materials, the flake pigmentsorient themselves according to the prevailing flow conditions. The alignment ofthe particles direct after surface formation is nearly maintained during coolingtime and concurrent volume contraction. The collision of two melt fronts causesa 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 inthe mold [38].

2.3.3 Coloristic Properties of Metallic Pigments

The geometry, morphology, and reflection of metallic pigments produce a vari-ety of unusual color effects which need to be described in detail. The mostimportant coloristic characteristics of metallic pigments are given in Table 2.9.From this apparent arbitrary division it is possible to discern two groups: inthe first group, the indicated effect properties increase with expanding lateraldimension of the particles and for the second group, they decrease. This inversebehavior and the complex color attributes of metallic pigments demand acloser examination in comparison to the more simple properties of absorptionpigments.

First, the five special features of the first group will be discussed. The metalliccharacter or metallic gloss depends on the ratio of the directional to the diffusereflection. Both components are directly proportional to the quotient of the sur-face to the edge length of the metallic flakes. The higher this ratio, the moredistinctly developed the metallic character. Small particles normally give rise toa higher edge scattering and, therefore, produce a poor and gray metallic effect.Conversely, flakes with a lateral dimension greater than 30 μm show a strik-ing metallic character. In general, the narrower the particle size distribution, themore distinct the metallic luster.


Table 2.9 Correlation between particle size and coloristical properties of metallic pigments(other used terms in brackets)

Assessment of characteristicparticle diameter d50, non-leafing pigments

Characteristic of metallicpigment

≤10 μm: fine pigmentsCornflakes

≥30 μm: coarse pigmentsSilver dollars, glitter flakes

Metallic character (metallicgloss)

Insignificant, matt, gray Quite distinct, brightened

Brightness (brilliance) Low HighReflection brightness

(whiteness)Minor Enhanced

Sparkle, glittering (opticalroughness)

Invisible Visually noticeable

Graininess (coarseness,texture)

Low Visible

Lightness flop (flop, flip,travel, two-tone)

Light Dark

Hue extinction Enhanced LowCovering capacity (hiding

power, opacity)Enhanced Low

Distinctiveness of image(DOI)

High Minor

The brilliance of metallic pigments is, in essence, caused by the directionalreflection component. Metallic flakes, therefore, appear all the more brilliant thehigher the directional reflected light amount and the lower the diffuse reflectioncomponent. The brilliance, and consequently the directional reflected com-ponent, is reduced with smaller and more uneven surfaces of the pigments,with broader particle size distributions and with greater irregularities in particleorientation in the surrounding polymer material.

The reflection brightness or whiteness characterizes the lightness of themetallic effect. This property is a measure of the total reflected light and iscomposed of the directional and diffuse components. Consequently, reflec-tion brightness differs from lightness of absorption pigments, which is due toscattering and absorption. In connection with effect pigments, the term reflec-tion brightness has, therefore, a quite different meaning from the lightness ofabsorption colorants (although both quantities are determined with the samemeasuring and evaluation system). In fact, the spectral reflection of metallicpigments behaves similar to that of white/black mixtures of absorption pig-ments. Metallic pigments certainly show a key difference: the spectral reflectiondepends on the angle of illumination and direction of observation.

This angle dependence is shown clearly, for example, by the reflectance ofan aluminum cornflake pigment in Fig. 2.39. In this illustration, the reflectance


4000

50

100

150

R (%)

500 600

110

λ /nm μas /degree

75

45

2515

Fig. 2.39 Spectral reflectance of a cornflake aluminum pigment in dependence of the wave-length λ measured at aspecular angles of μas = 15º, 25◦, 45◦, 75◦, 110◦; illumination angleβ = 45◦

R is plotted in dependence of wavelength λ for five standardized aspecularmeasuring angles μas and an illumination angle of β = 45◦.13 With increas-ing measuring angle, the reflectance behaves similar to that of light white andmiddle 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 aspecu-lar angle of μas = 0◦. This drastic change in brightness in dependence on theobservation angle is characteristic for metallic flakes; it is termed as lightnessflop or short flop (see below).

The reflectance increase near the specular angle can be further raised, withinlimits, with a narrower particle size distribution or altogether larger sized flakes.Measured reflectance values higher than 100% are absolutely usual and produceno inconsistency with conservation of energy. Because of the lack of suitedand corrosion-resistant metallic standards, the reflectance scale is based on thereflectance of a white (scattering) standard which is interpreted as a reflectanceof 100% (Sections 2.2.3 and 4.1.2). Real effect pigments can have reflectancevalues up to about R = 800%.

13For nomenclature and counting of angles, see Section 4.1.2, Figs. 4.5 and 4.6.


Metallic pigments of irregular lateral dimension greater than about 30 μmproduce a phenomenon termed as sparkle in the last section. This effect is alsocalled sparkling or optical roughness. For particle dimensions of this size orlarger, the naked eye can distinguish single flakes of nearly equal orientationat the surface of a coating or plastic material. This is caused by the increasedintensity of directionally reflected light at the larger particle surfaces (similarto parallelized crystals of an illuminated snow surface). As a consequence ofthe distorted orientation of the flakes, sparkling changes in dependence on boththe illumination and observation angle. Leafing flakes develop no sparkling independence of the particle size because nearly all flakes have an alignment par-allel to the surface of the coating or the plastic material. Sparkle is not restrictedto 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 dis-appears completely and turns into a kind of graininess of the particles. Underthis lighting condition, only a kind of fixed snowing picture is observable nearthe surface of the coating. This phenomenon is also called coarseness, texture, orvivid “salt and pepper” and is independent of observation angle. The impressionof 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 above-mentioned lightness flop (also light to dark flop, flop, flip, travel, two-tone) canbe regarded as the most important and visually most striking property of metal-lic pigments. This term characterizes the decrease in lightness that a metalliccoloration shows under diffuse illumination between two extreme angles ofobservation, especially at angles for perpendicular observation and an anglegreater 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 flake-shaped 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 eyeafter interactions with the flakes. The observer registers the reference lightness.Now, for angles nearly parallel to the surface, the light path through the layer islonger. For this reason more interactions can take place with the particles of thelayer, that is, at the surface or edges of the flakes. Due to this, light is increas-ingly scattered or reflected out of the line of observation and, therefore, only asmall amount of the interacting light reaches the eye. This results in a registeringof a reduction of lightness in comparison to the perpendicular observation.

14Perpendicular observation means, in practice, that observation angles of βν = ±20◦,referred to the vertical, are permitted.


This flop is termed as light if only a small lightness difference is observedbetween both extreme observation angles. It is, however, called dark if a largelightness difference is registered. For finer and irregularly shaped flakes (e.g.,cornflakes), for broader accompanying particle size distribution, and for greaterparticle disorder in the layer, the flop is lighter. Conversely, the flop is the moredark, for greater evenness of the particle surfaces, for more rounded flake edges(silver dollar flakes), for narrower size distributions, and for more consistentparallel orientation of the particles to the surface boundary of the layer. Thelightness flop can be altered afterward to some degree by adding inorganic ororganic absorption pigments (see Table 2.10).

Table 2.10 Lightness and color flop of effect colorations

Flop kind Flop characterEffect pigment/absorption pigment Typical examples

Lightnessflop

Light Metallic pigment Fine non-leafing cornflakes,eventually with orientationdistortion medium

Metallic pigment andabsorption pigment

Scattering, inorganic, andorganic; for example, titaniumdioxide, chromium titanate

Dark Metallic pigment Coarse non-leafing silver dollarflakes, normal silver dollarflakes, PVD flakes

Metallic pigment andabsorption pigment

Transparent, inorganic, andorganic

Colorflop

Colored Absorption pigment Blue with green flop:phthalocyanine pigments ofneutral color flop; blue withred flop: α/ε-phthalocyaninepigments

Absorption andpearlescentpigment

Combination of hidingabsorption and transparentpearlescent pigments,nano-titanium dioxide

Interference pigment Interference pigments withextreme color flop: LCP, flakescoated with silicon dioxide,aluminum oxide,iron-III-oxide, magnesiumfluoride

Diffraction pigment Aluminum or nickel substratePVD coated withchromium/magnesium fluorideor magnesium fluoride/silicondioxide


The phenomenon of lightness flop can be examined quantitatively by a glossmeter. The usual measuring angles μν = 20◦, 60◦, 85◦ with regard to the nor-mal of the surface are certainly not sufficient. This is already clear from theangle-dependent reflectance measurements in Fig. 2.39. A reliable characteris-tic value describing the lightness flop of a single-layered metallic formulationis the so-called flop index; however, for clear-over-base paints, the so-calledmetallic value is used (Section 3.5.1).

As mentioned, some metallic systems are mixed with absorption pigmentsfor coloring or covering of the background. These systems have a more or lesscolored flop; see Table 2.10. Mixtures with absorption pigments always result ina lighter flop compared to the natural metallic pigment. This effect is generallycalled color flop.

Mixtures of pearlescent and metallic pigments normally produce a lighterflop than the corresponding single natural pigments. However, the brilliance isusually raised at perpendicular observation. This behavior can be reversed withsuitable pigment combinations. The color flop of interference and diffractionpigments is generally accompanied by a distinct color change. This change ismainly due to the interference or diffraction maximum of first order (Sections3.5.3 and 3.5.5).

A particular kind of color flop is given by a mixture of a metallic flakeswith titanium dioxide, provided that nanoparticles of the rutil modification areused. The observable minor color shift caused by the nanoparticles is gener-ated by the selective scattering of waves in the region of blue wavelengths; thisspecial phenomenon is called frost effect [44]. Such a layer has a yellowishcolor at top view but for a flat angle of observation, a bluish color impres-sion results. Accordingly, the shorter blue wavelengths are more scattered thanthe other longer wavelengths, in agreement with Rayleigh’s law (2.1.3). Thiscomparatively low effect is also observed with other absorption or pearlescentpigments of lateral dimensions in the nanometer range. Altogether, the colorflop of a formulation can be controlled within limits by adding small amountsof nanoparticles. Certainly, the frost effect lowers the entire brightness of therelevant coloration.

The next property of interest in Table 2.9 is the hue extinction. This fea-ture characterizes the capability of a metallic pigment to change or to covercompletely the natural color of an absorption pigment incorporated into a for-mulation. In the literature [39], this ability is called “hue saturation,” which isagain misleading, because this term implies a saturation of the relevant absorp-tion colorant. The extent of the hue extinction is related to the covering capacityof the metallic particles. In this case, for metallic particles this term has thesame meaning as it does for absorption pigments (Section 3.4.3). Both the hueextinction and the hiding power are improved with smaller cross sections of theparticles, broader particle size distributions, larger flake thicknesses, and denserpacking of the flakes.


Finally, there is the so-called distinctiveness of image (DOI). In addition tolightness flop and hue extinction, this property lists among the central character-istics of single as well as clear-over-base paints of metallic coatings. The DOIvalue represents the uniformity of the observable metallic reflection. It dependsmainly on the particle size and orientation of the flakes in a layer. The dis-tinctiveness of image is again improved by smaller particles and more highlyparallelized grade of the flakes. The DOI value of large-sized flakes nearlycorrelates with the glittering effect. The determination of the DOI value bymeasurements 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 essentiallybased on constructive interference. Pearlescent pigments imitate the nacre lusterof natural pearls. The brilliant colors and unique luster are due to superimposedlight interactions such as absorption and multiple reflection at different bound-ary surfaces of the particles. Interference pigments generate substantially morebrilliant colors than pearl luster pigments. The terms pearlescent and interfer-ence pigments are often wrongly used as synonyms for both pigment sorts,although only pearlescent pigments have the typical luster of natural pearlscoming from the depths to the surface.

The particles of pearl luster and interference pigments consist of layers withdifferent refractive indices. The layer thicknesses are on the order of magnitudeof visible wavelengths. The entire flake thickness varies from about 30 nm to1 μm and the mean lateral dimension of the transparent to opaque pigmentsextends – similar to metallic flakes – from about 5 to 300 μm. Pearlescent,interference, and diffraction pigments can also exhibit sparkling. This size-dependent phenomenon is, in this case, generally darker than the sparkle ofmetallic pigments because the reflection is caused only by the difference ofrefractive indices instead of metallic reflection.

The color-producing properties of pearlescent, interference, or diffractionpigments are dependent on the particle geometry, especially on the interferinglight interactions, and the color physical conditions in the particle surround-ing. 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 refractiveindex n at the interface, the thickness d of each single layer, and the observa-tion or interference angle αz. These parameters can be tuned in such a way thatonly the first interference order (z = 1) occurs in the range of normal observa-tion angles. In this case, the higher orders can be neglected or are simply not toobserve.

The incoming light waves are partly reflected at each boundary sur-face of a particle, cf. Fig. 2.16. The constructive interference of the waves


produces the matt to high brilliant color appearance. The interference color isobserved at the specular angle on the illumination surface and the complemen-tary color is transmitted by transparent flakes. Each single pigment, therefore,behaves as an interference filter, which the incoming light waves split up into areflected interference component and a complementary transmitted or absorbedcomponent.

As a result of the different refractive indices at the interfaces as well as themorphology of the particles, the following light interactions together contributeto the color appearance of pearl luster and interference pigments:

– constructive interference produces the sometimes intense colors which changein dependence of the angle of observation; the different colors and the angledependence are given by the refractive indices, the thicknesses, and thenumber 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 andinterference pigments are composed. The materials are ordered accordingto increasing values of refractive index nD. In comparison, air at a pres-sure of 1.0 bar at room temperature T = 298 K has a refractive index ofonly 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 Organic materials 1.35–1.70MgF2 Magnesium fluoride 1.384Proteins Proteins 1.40SiO2 Inorganic glasses 1.458Alumina silicate Mica, muscovite 1.50CaCO3 Aragonite 1.68Al2O3 Aluminum oxide 1.768Guanine, hypoxanthine Natural pearl essence 1.85Pb(OH)2·2PbCO3 Basic lead carbonate 2.00BiOCl Bismuth-oxide chloride 2.15Fe3O4 Magnetite 2.42TiO2 Anastas/rutil 2.5/2.7α-Fe2O3 Hematite 2.88


materials. Because the relevant substances are anisotropic crystalline, the indi-cated n values represent a mean. The refractive indices of the substances givenin Table 2.11 are subject to dispersion.

Table 2.12 is arranged by pigment classes: pearl luster, interference, anddiffraction pigments. In other literature, these are often gathered arbitrar-ily under the collective name: special effect pigments [18, 40]. Our furtherdiscussion relates to the pigment classification and terms given in Table 2.12.This fixes a unified nomenclature for all sorts of pearlescent, interference, anddiffraction pigments.

Pearlescent pigments of the simplest structure are substrate free and formflake-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 effectpigment

Unsystematicnames Typical examples

Pearlescentpigment

Platelet-like singlecrystals

Natural pearl essence, basic lead carbonate,bismuth-oxide chloride, α-iron-III-oxide,titanium dioxide, mixed-phase pigments ofaluminum oxide, manganese-iron-III-oxide

Mica-basedpearlescentpigments

Substrates: natural or synthetic muscovite layers:titanium dioxide (rutil or anastas),iron-III-oxide, chromium-III-oxide, silicondioxide (multi-layer principle)

Interferencepigment

Special interferencepigments

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

Liquid crystalpigments (LCP)

Polysiloxanes in cholesteric phase, cross-linkedin layers

Optical variableinterferencepigments (OVIP)

Substrates: aluminum, aluminum oxide,iron-III-oxide, silicon dioxide, glass flakes;

Layers: aluminum, chromium, iron-III-oxide,magnesium fluoride, silicon dioxide, titaniumdioxide

Extendedinterference films

Multi-layer film consisting of polyacrylates,polypropylene with polyethylene terephthalate,polystyrene, or polycarbonate

Diffractionpigment

Grating pigments Al substrate with symmetrical PVD layers ofMgF2 or Cr/MgF2

Ferromagnetic: Ni substrate with symmetricalPVD layers of MgF2/Al or Cr/MgF2/Al


guanine, 5–25% hypoxanthine), basic lead carbonate, bismuth-oxide chloride,or α-iron-III-oxide, as well as mixed phases of aluminum oxide or manganese-iron-III-oxide. On account of the lack of a mechanically stabilizing substrate,these pearl pigments will not easily survive shear and pressure flow of technicalprocessing. They are similar to ground shells and are, therefore, limited to asmall range of applications [40].

However, for the most part, the flake-shaped pearl and interference pigmentsconsist of a symmetrically coated substrate of at least one additional layer.The most used substrates are natural or synthetic mica, aluminum, aluminumoxide, chromium, iron-III-oxide, or synthetic silicon dioxide. The lamellate cen-ter should have a great difference in refractive index compared to that of thecoated layers.

Pearlescent pigments are mostly based on mica substrate. This is a nativedepositing layer silicate, named muscovite, with total molecular formulaKAl2[(OH, F)2 AlSi3O10]. Instead of natural muscovite, also synthetic micais increasingly being used. The synthesized material shows a more uniform-layered structure and produces, therefore, more brilliant interference colors.Apart from metal oxides, further coating substances are fluorides or sili-con dioxide, also cobalt and iron titanate, chromium phosphate, silver, gold,molybdenum, or chromium [18, 46–48]. The symmetric permutation of layersof the flakes is achieved by normal chemical procedures or vacuum evaporationcoating by the PVD or CVD method [49, 50]. Examples of pearl luster pigmentsbased 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 modifiedto produce a variety of further impressive colors. Intensified interference colorsand simultaneously selective absorption, analogous to colored pigments, can beachieved by coating mica with two or more metal oxides of different refractiveindices. Such kinds of flakes are also called combination pigments. Comparedto single-coated mica pigments, they show more brilliant and brighter interfer-ence colors, as well as a more distinct color flop. The color flop is called distinctif a variety of interference colors are to observe. Conversely, the color flop isless 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 pearles-cent and absorption pigments. Because of the underlying two different colorproduction mechanisms, combination pigments are also termed as two-colorpigments or color-flop pigments.15 In dependence on the observation angle,

15Not only combination pigments produce a color flop but rather interference pigments withother layer combinations as well as diffraction pigments, cf. Table 2.10., Section 2.3.3.


Fig. 2.40 Cross section of a symmetrical multi-layer pigment; permutation of layers fromthe centered mica substrate: titanium dioxide, silicon dioxide, titanium dioxide; overall layerthickness about 500 nm (source: Merck KGaA, Darmstadt, Germany)

either the gloss is composed of the absorption and interference color or thenon-self-luminous color of the absorption pigment is dominant.

The most important combination pigments are TiO2-coated mica flakesvapor-coated with further oxides such as α-Fe2O3 (hematite modification),Fe3O4, or Cr2O3. As shown in Fig. 2.40, the muscovite substrate can be coveredwith two different oxide layers of TiO2 and SiO2. On account of the six bound-ary layers with different refractive indices, 15 interference combinations arepossible. These produce extreme interference colors which are superimposedby the absorption colors of both oxides.

Mica pigments vapor-coated with TiO2 and top-coated with other metaloxides such as TiO2–x, TiOxNy, FeTiO3, or nanocarbon particles embeddedin TiO2 generate silver gray or black pigments of improved compatibil-ity with colored pigments. Transparent mica pigments can be produced inform of nano-sized particles by a suitable precipitation method of oxides oroxide hydrates; these colorants are called transparent colors. Moreover, mod-ified process engineering allows for the manufacture of pigments of minorgloss [41].

The top-coat of an interference pigment can also consist of a pure metal. Asubstrate of a metal (Al or Cr) or metal oxide (Al2O3, Fe2O3, SiO2) is coatedwith a glassy layer of another refractive index (TiO2, MgF2), as well as anevaporated semitransparent metal top-coat (Cr, Ni, or Al). The inner and outerreflecting layers form together a Fabry–Pérot etalon, cf. Fig. 2.18. This struc-ture causes increased interference intensities and a sharp color flop by multiplereflection. An interference pigment showing a distinct color flop is generallynamed as optical variable interference pigment (OVIP).

An example of such an OVIP of layer composition MgF2/Al/MgF2 is shownin Fig. 2.41. In this SEM picture, it is particularly interesting to see the quite


Fig. 2.41 SEM photograph of an optical variable interference pigment with symmetricallayer composition of MgF2/Al/MgF2; cf. Color plate 9 (source: Flex Products Inc, SantaRosa, CA, USA)

even surfaces and the sharp edges of the pigment particles. The even surfacesindicate also internally even surface boundaries and, therefore, brilliant inter-ference colors followed by a distinct color flop. The sharp edges indicate thatthe flakes are broken at low temperatures and sifted out. The particles shown inFig. 2.41 have a mean lateral dimension of d50 ∼= 20 μm and a thickness of about100 nm. An impression of the color flop produced by this pigment is given bycomparing the two pictures of Color plate 9. Both photos show the same imagefield of a light microscope in bright- and dark-field illumination; bright fieldmeans illumination from the top of the surface and dark field means interfer-ence from the side of the color sample. In this case, the colored flop changesfrom green to violet (see also Section 3.5.3).

Interference pigments of special shish-kebab layer structures and consist-ing of organic polymers are termed as liquid crystal pigments (LCP). A liquidcrystal state is arranged without exception of rod- or elliptical-shaped poly-mer molecules consisting of suitable dipole moments or polarizing groups. Thecorresponding textures are optically anisotropic and are, for example, used inseven segment displays for more than four decades. The accompanying textureis called liquid crystalline or mesomeric phase because the molecular confor-mation corresponds neither to a random liquid nor to an ordered crystallinestate.


There exist altogether three different liquid crystalline textures. The cor-responding molecular configurations are termed as nematic, smectic, andcholesteric:

– nematic: the molecules are aligned parallel to their longitudinal axes, are arbi-trary slidable in the axial direction, and are rotatable around the longitudinalaxes independent of one another;

– smectic: the molecules are oriented with their long axis perpendicular to eachmonomolecular sheet; the movement of the molecules is restricted to rotationsaround the longitudinal axes;

– cholesteric: the molecules are arranged parallel to one another and groupedin layers; the layers are systematically turned toward each other by a specificangle; the mobility of the molecules is the same as in the nematic phase.

These molecular configurations are schematically sketched in two dimensionsin 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 structuresnormally starts with polymer molecules in the nematic phase. This state is con-verted into layers of cholesteric texture – for example, with silicones – at highertemperatures in the presence of a chiral additive. The single parallel layers arethen cross-linked and fixed using UV radiation; see Fig. 2.43. Each layer istwisted by a constant angle relative to the adjacent layer. The nearly identicalmolecular conformation with regard to the initial layer is attained after passingthe so-called pitch height p of about 100 nm. On account of the systemati-cally twisted molecular conformation inside the pitch, the transmitted light iscircularly polarized by this structure. The pigment particles have thicknesses


Fig. 2.43 Parallel andcross-linked layers ofpolysiloxane molecules incholesteric texture forminga half pitch of a liquidcrystal 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 partialreflection at the pitch surfaces and the rotated molecular arrangement causesseveral optical effects which greatly affect the interference behavior of thesepigments:

– a kind of gloss coming from the depths, which is attenuated in pearl lusterpigments because the light must pass through various pitches and layers;

– on account of reflections between adjacent pitch surfaces, the interferencewavelength λ changes according to Equation (2.1.20) for z = 1 and p = 2d;the wavelength decreases with increasing angle of observation from the verti-cal; an example of transparent liquid crystal pigments is shown in Color plate10;

– caused by a low pitch value, only one single interference order is observablewithin ±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; seeTable 2.13. An example of an uncoated glass substrate and coated with TiO2 isshown in Fig. 2.44. The differences in refractive indices at the interfaces causenot only unusual brilliant and pure interference colors but also sparkle effectswhich are even colored. Pigments of other compositions, thicknesses, and per-mutation of layers cause impressive color flops. These occur nearly throughoutthe 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 trans-parent polymer foils with different refractive indices (1.48 ≤ n ≤ 1.60). Thefilms are partly colored with absorption pigments. The original low interfacereflectivity is improved by semitransparent silvering of some internal foils. Thefull foil sequence has a thickness of up to 400 μm and contains a maximum


Table 2.13 Some optical variable interference pigments

Substrate Coating Peculiarities

Al2O3 Depending on coatingthickness dTiO2Fe2O3

Lateral dimension5 μm ≤ φ ≤ 30 μm

Colors:“Silver,” yellow over blue-green until blue;“Bronze,”, “Copper,” red interference colors;sparkle pigments for φ ≥ 30 μm

Ca–Alborosili-cate

TiO2, Fe2O3, SiO2:SiO2/TiO2 inmulti-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 rutilcompared to anastas

Fe2O3 Layer configuration:Fe2O3/SiO2/Fe2O3/SiO2/Fe2O3

Colored flop: violet to orange-“gold”; top coatingof Fe2O3, corrosion resistant

Metals andmetalalloys

Mono-layers:Al, Zn, Cu–Zn alloys;SiO2/Al/SiO2,α-Fe2O3/Al/α-Fe2O3

Multi-layers:From the surfacepartially oxidized andoxides of metal flakes

Fabry–Pérot etalons; cf. Table 2.8

Fig. 2.44 (a) Uncoated borosilicate substrate, (b) coated with titanium dioxide layers; totalflake thickness of about 300 nm (source: Merck KGaA, Darmstadt, Germany)

of 70 films. The multi-layer films are crushed at temperatures below the low-est glass transition temperature of the polymers used and are sieved in differentfractions.


2.3.6 Spectral Behavior of Pearlescent and InterferenceColorants

Pearl luster and interference pigments are either nearly transparent or opaque.The most important representatives of both groups are shown in Table 2.14. Inthis section, we limit ourselves to describing only transparent particles becausethese colorants have more interesting color shades. First, we discuss the depen-dence of the color impression on the background color; thereafter, we exploremethods for covering coatings. As already mentioned, the interference colorappears in the direction of the specular angle; this corresponds to the inter-ference angle of first order. The complementary color is transmitted by thetransparent particles and absorbed by opaque flakes.

Table 2.14 Examples of nearly transparent and opaque pearlescent and interferencepigments

Light transmittance Examples

Nearly transparent TiO2 pigment, Fe2O3 combination pigments on mica substrate;Fe2O3 coating of Al2O3 substrate; coated SiO2 flakes; liquidcrystalline polysiloxanes

Opaque Reduced TiO2 on white mica; multi-layer pigments: Al flakescoated with SiO2, Fe2O3; Al or Cr platelets vapor coated withMgF2, Cr, or Ni

The total color impression of transparent interference pigments is stronglyinfluenced by the chosen background; this is clearly shown in connection withFig. 2.45. Because a black background absorbs the complementary color, onlythe interference color is observed above the coating. The interference color cor-responds to the mass tone of the pigment. On account of the additional lightscattering, which is generated to a greater or lesser degree by the corners oredges 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 transmit-ted complementary color and is only slightly absorbed. The interference color isthen superimposed upon by the scattered amount of the complementary color indirection of the specular angle. In all other directions, only the scattered comple-mentary color is observed. Consequently, over a black background, the naturalcolors of an interference pigment are observed and over a white background,the covering capacity. These uncolored background surfaces allow also for thedetermination of the reflectance and transmittance of a transparent or translucentlayer from reflection measurements (Sections 3.4.3 and 4.2.4).

In the case of a colored background, the interference color is clearly super-imposed upon by that color. Because the interference and absorption colors can


Interferencecolor

Complementarycolor

Black White Colored

Fig. 2.45 The color impression of colorations with transparent interference pigments isaffected by the chosen absorbing or scattering background

be either identical or different, a variety of color flops are possible. At curvedsurfaces (which are always to be avoided for color measurements), the inter-ference and the absorption color can be observed simultaneously. Transparentinterference pigments mixed with colorants of complementary mass tone resultin a white color according to the laws of additive color mixing. Mixtures oftransparent interference pigments with other pigments of similar color producemore dull colors like the single colorants.

As an alternative to a white background, a scattering silver-colored metallicor pearlescent pigment of d50 value less than 10 μm can be used. Such param-eters for the pearlescent pigment normally ensure a high DOI value. Preferredbright silvery pigments for this purpose are mica flakes coated with TiO2 oraluminum 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 thechroma of pearlescent and interference pigments. This is in analogy to white inmixtures of colored absorption pigments.

In the following, we consider in more detail the color systematic and thecorresponding spectral reflection which result from thickness changes and com-position of the layers. For this, we restrict ourselves to the pigments with layercompositions which were already discussed in the previous section, among otherthings. They are as follows:

– titanium dioxide evaporated mica particles;– mica flakes coated with iron-III-oxide;


– two mica-based combination pigments of titanium dioxide in rutil modifica-tion: 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 interferencepigments. This goes especially for the accompanying colorimetric behavior ofthese 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 isshown in the upper half of Color plate 7. This picture was taken under brightfield illumination. From the top view, the particles produce a yellow colorimpression over a black background. The non-uniform colors of the particlesare caused by different layer thicknesses and by flakes tilted with regard to theimage plane. This is further elucidated with the example of the red pearl lusterpigment in Color plate 8. In this case, the particles in the same field are recordedin using bright and dark field illumination.

The comparatively high-valued refractive index of titanium dioxide (n = 2.5or 2.7) together with the low value of muscovite (n = 1.5) offers suitable con-ditions for developing neatly ordered interference colors. However, if the micasubstrate is already flake shaped, TiO2 crystallizes in a thin film which is onlysuited for interference. Among the three possible crystal modifications of tita-nium oxide – rutil, anastas, and brookit – the rutil structure is preferred in thiscase.

The dependency of the interference color on the titanium-dioxide-layer thick-ness is given in Table 2.15 (cf. Table 2.5). Each color impression over blackbackground changes with increasing layer thickness from metallic “silver” overcopper-red to green. These are no spectral colors because the accompanyingcolors are, in each case, composed of several adjoining interference wave-lengths. The different wavelengths are selected by varied layer thicknesses ofthe metal oxide and by particles tilted differently toward the image plane (seeColor plates 7 and 8).

Under diffuse illumination, these pearl luster pigments produce the spectralreflectance over black background shown in Fig. 2.46. With increasing layerthickness, the peak shifts to longer wavelengths and simultaneously broadens.In the figure, this begins in the violet region. The reflectance minimum alsomoves to longer wavelengths, in the figure starting from the yellow range. Thespectral reflectance of the “silver” pigment corresponds to that of a light grayhue or to that of aluminum cornflake pigments. This suggests the substitution ofthe metallic aluminum pigment by the cheaper pearlescent pigment in suitablecases.


Table 2.15 Interference colors depending on layer thickness of titanium dioxide on micasubstrate (cf. Table 2.5)

Layer thicknesstitanium dioxide/nm

Plateletthickness/nm

Interference color –inherent color overblack background

Transmittedcomplementary color

40–60 120–140 “Silver” “Silver”60–80 140–160 Yellow Blue80–100 230–250 Red Green90–110 250–270 Copper-red Blue-green

120–130 280–300 Violet Yellow-green100–140 310–320 Blue Yellow120–160 370–390 Green Red

Now, assume that the peaks in Fig. 2.46 can be interpreted as interferencewavelengths of first order. Clearly, this is not exact, but sufficient for the fol-lowing estimations. If we use the values of the relevant refractive indices ofTable 2.11 and assume perpendicular observation, then Equation (2.1.18) deliv-ers an approximate value for the thickness of the titanium oxide layer. For the

80

R (%)

60

40

20

0400 500 600

ab

d

c

e

f

a: 40 – 60

Layer-thickness in nm

b: 60 – 80c: 80 – 100d: 120 – 130e: 100 – 140f : 120 – 160

nmλ

Fig. 2.46 Spectral diffuse reflectance of mica pigments of different TiO2 coating thick-nesses; measurements over black background, de:8 geometry16

16The corresponding de:8 measuring geometry (see Section 4.1.2) simulates diffuse illumi-nation conditions in closed rooms.


last five flakes indicated in Table 2.15, this approximate calculation results invalues which are in the given thicknesses intervals. The systematic changesin spectral reflectance are characteristic features of the basis pigment series:the spectral reflectance curves measured under diffuse illumination are “finger-prints” of the relevant pearl pigments. This is an analog to absorption colorants.These fingerprints are sometimes utilized for analyzing mixtures with furtherpigments.

Using directional illumination and angle-dependent reflectance measure-ments, particularly important information about the properties of the relevantinterference pigments can be obtained. For the moment, we restrict the dis-cussion to only one illumination angle although the colors of pearlescent,interference, and diffraction pigments depend on the illumination as well asthe observation angle. The five spectral reflectance curves in Fig. 2.47 weremeasured with the green pearlescent pigment, which has a peak at 507 nm inFig. 2.46, curve (f). The film of pearl luster pigments over a black backgroundis illuminated at an angle β = 45◦ and the spectral reflectance is measuredat aspecular angles μas = 15◦, 25◦, 45◦, 75◦, and 110◦. As can be seen, thepeak reflectance reduces dramatically with increasing measurement angle and itshifts to slightly shorter wavelengths. For observations near the specular angle,the reflectance exceeds values higher than 1.0 or 100%. The chosen five mea-suring angles are by no means sufficient to gather the entire color dynamics ofpearlescent and interference pigments [52, 53].

2.3.6.2 Iron-III-Oxide on Mica Substrate

Crystalline α-Fe2O3 has the highest refractive index of n = 2.88 among the sub-stances listed in Table 2.11. As mentioned in the previous section, the total colorimpression of the layer composition with mica results from superposition ofthe layer-dependent interference color and the absorption color of the hematite.Iron-III-oxide produces a red to reddish-brown absorption color which is fur-ther modified by the thickness of the outer layer, see lower picture of Colorplate 7. The color impression changes with increasing layer thickness frombronze colored to copper to purple or even reddish-green at the highest layerthickness. 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 iseven amplified by the corresponding, nearly equal interference color like yel-low, copper, and red. We return to the hue dependence of the layer thickness inSection 3.5.3.

The superposition of interference and absorption leads to brilliant colors inthe vicinity of the specular angle. Near this angle, the purple and reddish-greenpearlescent pigments have a violet or green interference color caused by therelative high layer thickness of the hematite. With regard to comparable outer


150

R (%)

100

50

0400 500 600

75° 110°

45°

25°

15°μas =

λnm

Fig. 2.47 Spectral reflectance of the green interference pigment from Fig. 2.46 at fiveaspecular measuring angles μas; measurement over black background, illumination angleβ = 45◦

layer thickness, the TiO2-mica pigments produce a broader variety of inter-ference colors, whereas the iron-III-oxide produces diverse types of red hues.The distinct brilliance of the α-Fe2O3 pigments comes from the slightly higherrefractive index of the hematite in comparison to that of titanium dioxide. Theincreased covering capacity is again a consequence of the typically increasedscattering of the inorganic oxide.


80

a: BronceFe2O3-Layerthickness

b: Red-golden

abc

d

e

c: Copperd: Purplee: Red-green

R (%)

60

40

20

0400 500 600

nmλ

Fig. 2.48 Diffuse spectral reflectance of mica pigments coated with Fe2O3 of different layerthicknesses; measurement over black background, measuring geometry de:8

2.3.6.3 Combination Pigments

Interference with more brilliant colors and higher absorption is generated bycoating the substrate with two or more different metal oxides. A multitudeof combination pigments are based on titanium dioxide-mica flakes, wherethe flakes are additionally vapor coated with Fe2O3 or Cr2O3. These sorts ofcombination pigments show, in comparison to the original single-coated micapigments, higher brilliance and a more distinct color flop.

In the following, we consider the reflection behavior of mica combinationpigments composed of layers of titanium dioxide in rutil modification coatedwith iron-III-oxide. The optical interactions between both metal oxides lead tomany brilliant golden colors reaching from pale yellow-gold to rich red-goldto green-gold. With the addition of an oxide layer, a clear color extension withregard to the simple Fe2O3-mica particles is achieved. Furthermore, the changeof the layer thicknesses of the two metal oxides generates a wealth of super-imposed interference and absorption colors. The thicknesses of all three layerscan be tuned with each other in such a way that the interaction of the interfer-ence and absorption components leads to a demanded coloristical effect, withinlimits.

Similar features result from the substitution of the outer Fe2O3 layer byCr2O3. The combination of Cr2O3 with TiO2 in anastas modification results in


80

Fe2O3

TiO2 Rutil

Fe2O3

TiO2 Rutil

Cr2O3

TiO2 AnastasCr2O3

TiO2 Anastas

R (%)

60

40

20

0400 500 600

nmλ

Fig. 2.49 Diffuse spectral reflectance of two combination pigments Fe2O3/TiO2 (rutil),Cr2O3/TiO2 (anastas) on mica substrate of different layer thicknesses; measurement overblack background, measuring geometry de:8; the curves of Fe2O3/TiO2 are shifted 20 unitstoward higher reflectance values for better overview

high-luster blue-greenish to moss-green colors. Figure 2.49 shows the spectralreflectance curves measured under diffuse illumination of Fe2O3/TiO2 pigmentand Cr2O3/TiO2-mica pigment. Each has two different outer layer thicknesses,but the total coating thickness is constant in each case. The greater thickness ofthe outer oxide layer reduces the reflection. This is clearly caused by increasedabsorption due to greater layer thickness. In the case of a higher layer thicknessof Cr2O3, this pigment additionally develops a clear peak in comparison to thequite broad peak belonging to the thinner outer layer. The increased influenceof the Cr2O3 layer on the interference development can be ascertained from thereflectance curve (f) in Fig. 2.46 for the green pearlescent pigment together withthe two lower curves in Fig. 2.49. Altogether, titanium dioxide is responsiblefor the brilliance of the colors and the outer layer thickness for the interferencecolor. The included absorption colors of iron oxide or chromium oxide existotherwise under all observation angles.

Nearly equal-colored oxide layers create a pearl luster effect of intensivecolors which, at nearly all observation angles, show a noticeable color shift.However, if the color of an absorption colorant corresponds to that of the com-plementary color of the interference pigment, then a distinct two-colored effectis achieved, especially in the oxide combination of Cr2O3/TiO2. Further inor-ganic absorption pigments such as Prussian blue, cobalt blue, Fe3O4, or carbon


black generate, in combination with titanium oxide on mica substrate, unusualcolor effects as well.

2.3.6.4 Liquid Crystal Pigments

The color flop of liquid crystal pigments consisting of polysiloxane dependson 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 withblue/green-flop are shown in Color plate 10 at bright and dark field illuminationover black background. The noticeable sparkle particle there is already greenfrom the top view because of the higher pitch height compared to the otherflakes. To the present day, mixtures of the transparent particles with absorptionor other effect pigments produce unequaled and extremely brilliant colors.

As mentioned at the beginning of the section, further shades can be obtainedwith a suitable background color. With regard to liquid crystal pigments, thisconcept is underlined by the example in Fig. 2.50. The reflectance curves corre-spond to background colors of white, red, and black as well as each top coatedwith a transparent film of the same liquid crystal pigment. The reflectancepeak over black at 512 nm corresponds to the green color impression fromthe top view. The red background leads to a minimal blue-tinged red and the

80

R (%)

60

40

20

0400 500 600

Black

Background alone

Layer over background Red

White

λnm

Fig. 2.50 Spectral reflectance of a transparent liquid crystal pigment with d50 = 30 μm overwhite, red, and black background, as well as backgrounds alone; wavelengths of maximumreflectance over background: 512 nm (red), 531 nm (black); measuring geometry de:8


white background creates a very light pink. The flat maximum of the whitebackground at a wavelength of 490 nm is caused by fluorescence emission ofthe contained optical brightening agent (Section 4.2.6).

Figure 2.51 shows the directional reflectance over a black background forillumination angle β = 45◦ and aspecular observation angles μas = 15◦, 25◦,45◦, 75◦, 110◦. With increasing measuring angle, the wavelength of the peakshifts from 483 to 520 nm. Simultaneously, the peak height decreases from R =108% to about R = 2%. The angle dependence of the interference wavelengthcorresponds to the cosine function in Equation (2.1.20).

100

μas = 15°

d50 = 30 μm

R (%)

50

0400 500

110°

600λ

nm

β = 45°

25°

45°75°

Fig. 2.51 Spectral reflectance of a liquid crystal pigment with d50 = 30 μm for five aspecularmeasuring angles; measurements over black background, illumination angle β = 45◦

The brilliance of liquid crystalline pigments depends also on the averagelateral dimension of the flake particles. This can be seen from the reflectancemaxima in Fig. 2.52. The reflectance curves are measured for three differentparticle size distributions over the same black background and at constant illu-mination and aspecular angle of β = 45◦ and μas = 15◦, respectively. The flakeshave 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 ratios30:23:18 of accompanying d50 values. In addition, this result is confirmed bymeasurements over red and blue background. The height of the reflectance max-imum of liquid crystal pigments is, therefore, directly proportional to the meanflake size. Clearly, large-sized LCPs orient better to the background surface, inanalogy to metallic flakes. These larger particles then show increased brilliance


100

μas = 15°d50 = 30 μm

R (%)

23 μm

18 μm50

0400 500 600

β = 45°

λnm

Fig. 2.52 Directional reflectance at constant aspecular measuring angle μas = 15◦ of a liquidcrystal 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 impor-tant pearl luster and interference pigments are outlined in Sections 3.5.3 and3.5.4.

2.3.7 Opaque Films Containing Absorbing and Effect Pigments

From discussions up until now, it is clear that the creation of new colorations bymixtures or films consisting of modern effect and classical absorption pigmentsrepresents quite a challenge. Especially needed to meet this challenge are hid-ing layers which consist of transparent effect pigments and covering absorptionpigments. A coating is called covering or hiding, if any colored background canno longer be observed from above the film (Section 3.4.3).

Covering layers with coarse metallic, transparent pearlescent, interference, oreven diffraction pigments are produced by mixtures of colorants which generatesuited scattering or absorption. It is also important to consider the change ofthe originally desired color effect with the addition of further colorants and alsothe compatibility with the pure effect pigment. Experience shows that coveringcoatings with effect pigments can, in the most cases, be manufactured with threedifferent colorants: carbon black, suitable absorption pigments, and fine metallicpigments [54].


A small amount of carbon black turns out to be quite effective for this. Theresulting dark and sometimes even intense colors are caused by absorption ofthe complementary color with carbon black already inside the layer. Only asmall volume amount < 1.0% of carbon black is normally sufficient. For largerconcentrations, 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 alsoresult in covering layers of additionally impressive colors. Small amounts causemostly brilliant interference colors. Larger amounts, however, can obliterate thepearl luster and interference effect: on the one hand, the interference intensityis increasingly masked and on the other hand, the complementary and part ofthe interference color are absorbed depending on the chroma of the absorptionpigment.

Finally, in the third method, the transparent pearl or interference pigment ismixed with a small amount of a special fine and, therefore, strongly scatteringmetallic pigment. In this case, the covering formulation is, however, accompa-nied by reduced brilliance, color saturation, and gloss. In all three mentionedcases, it is important to pay attention to the compatibility of the added compo-nents. Furthermore, the added amounts should be as small as possible in orderto result in a coloristic effect changed only slightly.

Altogether, the level of pigmentation of effect pigments in recipes dependson the desired color effect, the spreading rate of the pigment, and the molecularsurroundings. For a few applications the pigment volume content is shown inTable 2.16. Apart from the application, the processability, the light, temperature,or weathering resistance, etc., additionally determine the total pigment amountof 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 0.5–2 0.5–20Thermoplastics, thermosets 0.5–3 0.5–2Printing inks 1–45 1–30Cosmetics 1–15 1–50Toiletries 0.05–1 0.05–1

From color physical point of view, mixtures of effect pigments together orwith absorption colorants obey the laws of additive or subtractive color mix-ing (Section 2.4.3). Mixtures or layers of effect pigments show additive colormixing if the colors of the single pigments are based on the superposition ofwavelengths; see Table 2.17. But, as soon as the light interacts only with one


Table 2.17 Additive and subtractive color mixing of effect and absorption pigments

Pigment combination Color mixing Cause

Interference pigment mixedwith interferencepigment

Additive Superposition of reflectedinterference and transmittedcomplementary color

Interference pigment mixedwith diffraction pigment

Additive Superposition of interference,diffraction, and transmittedcomplementary color

Interference pigment onabsorption pigment

Additive and subtractive Superposition interference color,absorption of complementarycolor and selective absorptionof the colored pigment

Interference pigment mixedwith absorption pigment

Subtractive Colored pigment absorbs parts ofthe complementary and naturalcolor of the interferencepigment

Absorption pigment mixedwith absorption pigment

Subtractive Each colored pigment absorbsparts of the influx light

absorption pigment together with any further pigment sort, the resulting colorimpression is based on subtractive color mixing; see also the literature [54, 55].Additive color mixing is fundamental in the human color sense and the basedon colorimetry of versatile industrial applications.

Finally, we return to optical properties of interference pigments whichdepend on the particle size and morphology. Smaller particles show a reducedpearl luster effect in comparison with those of larger sized. This is because thehigher edge scattering reduces the luster. In the case of dominant scattering,the pearl luster and gloss of interference pigments can even disappear com-pletely. An increasing lateral size dimension up to 200 μm improves not onlythe brilliance but also the sparkle of the pearlescent and interference pigments;furthermore the color travel passes more wavelengths. However, with increasingflake geometry, the hiding power and DOI are reduced. The pigment propertiesshown in Table 2.18 correlate with related properties of metallic pigments listedin Table 2.9. In other words, comparable color properties of metallic, pearles-cent, and interference pigments change in the same direction depending on theflake 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 oftransparent effect pigments. An advantage of these pigments is the fact that thecolor effect is not distorted by additional colorants, but the absorption and self-scattering of the particles softens the original color. Further similarities betweendifferent effect pigment sorts are uncovered in Section 3.5.3.


Table 2.18 Assessment of some properties of pearlescent and interference pigments independence of the particle size

Particle size Φ/μm

Property Φ < 5 5 ≤ Φ ≤ 25 10 ≤ Φ ≤ 60 30 ≤ Φ ≤ 200

Brilliance Low Silky Very well SparklingColor flop Reduced Low Striking DistinctCovering capacity Excellent Very good Good LowDOI Very good Good Low Very low

2.3.8 Colors of Diffraction Pigments

Although the diffraction of light waves has been known since the beginningof the 19th century, this phenomenon has only been used in color physics fora few years [56]. Waves are diffracted, analogous to interference, when theyinteract with structures of dimensions on the same order of magnitude as thewavelengths. Polychromatic light is split up by diffraction into the spectralcomponents. Reflective diffraction pigments are the sorts that is of interest inindustrial color physics. These consist of a metal substrate with a grating ofembossed periodic grooves. In addition, the substrate is coated with inorganicsubstances; see Table 2.12. Each particle works as a reflection grating.

The nano-engineering method of interference lithography can be used toproduce periodic grating structures on surfaces. This method is based on theinterference of two laser beams; see Fig. 2.53. With the two coherent wavesfrom the same source, each of wavelength λL, an interference fringe pattern ofparallel fringes of distance d results (Michelson configuration). This distance isgiven by the relation

d = λL · sin ϑ , (2.3.1)

λL

λL

d

2ϑ

Fig. 2.53 Generation of parallel structures with two coherent light rays using the Michelsonconfiguration (schematically)


where ϑ denotes the half of the divergence angle. The periodic laser fringepattern is directed onto a metallized thermoplastic film or photoresist film sothat this pattern is transferred into the film as an exposure. After removingthe organic backing layer by thermal or chemical procedures, the remainingmetal foil of projected groove geometry is evaporated in vacuum with furthersubstances which are also used in nanotechniques. The substrate is coated sym-metrically so that the diffraction always develops at the illuminated surface ofthe reflection grating.

The films of up to 1 μm in thickness can be broken up into particles with lat-eral dimensions between 10 and 300 μm using ultrasound. The resulting flakescan be sifted by pigment size. Flakes with mean diameters of d50 = 20±2 μmare preferably used for print media and coatings [56]. The regular grating pat-terns consist not only of parallel but also rectangular, diagonal, or hexagonallines. Presently, diffraction pigments are manufactured with 100 up to 5,000equidistant parallel lines per millimeter (l/mm). The cross section of the groovescan be chosen in such a way that the first diffraction order corresponds to thegeometrical direction of reflection (blaze techniques, Section 2.1.7).

The diffraction particles shown in Fig. 2.54 have a grating constant of1,000 l/mm. The substrate consists of highly reflective aluminum of about 80 nmthickness and periodic folding. Using PVD techniques, the metal film is coatedon both sides with MgF2 of about 450 nm thickness; see cross section at fracturein Fig. 2.55. Diffraction pigments have been produced industrially since 2002,although symmetric grating cross sections have been used in technical opticssince about 1980.

The spectral reflectance of diffraction pigments with three different grat-ing constants measured by diffuse illumination and de:8 geometry is shownin 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; gratingconstant 1,000 l/mm (source: Flex Products Inc, Santa Rosa, CA, USA)


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)

80

70

R (%)

60

50

40

30400 500 600

3,000 l/mm

2,000 l/mm

1,400 l/mm

nmλ

Fig. 2.56 Spectral reflectance of diffraction pigments of magnesium fluoride/aluminum ofthree different grating constants; the middle and upper curves are shifted 5, respectively 10units toward higher scale values

is between R = 0.4 and R = 0.7. This quantity depends on the reflectivity ofthe metal layer, the number and thickness of the non-metallic vapor-depositedfilms, the accompanying refractive indices, as well as the mean particle size. Thepigment with 1,400 l/mm produces a silver metallic color impression at obser-vation perpendicular to the coating surface. The nearly flat spectral reflectance


shown in Fig. 2.56 is known from silver-colored metallic or pearlescent pig-ments. Under diffuse illumination, particles of grating constant 2,000 l/mmappear bluish and those of 3,000 l/mm produce a yellow-orange colorimpression.

The almost equal form of the reflectance curves in Fig. 2.57 indicates thatthe thickness of the aluminum substrate between 80 and 240 nm is, as toexpect, of no influence with regard to the color impression. For a fixed grat-ing constant of 1,400 l/mm, the height of the reflectance – and, therefore, thebrightness – is only slightly increased with aluminum thickness. With substratethicknesses greater than 240 nm, the surface roughness increases and, therefore,also the interface scattering. This scattering reduces, however, the intensity ofdiffraction.

70

R (%)

60

50006005004

240 nm

160 nm

80 nm

nmλ

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 10units toward higher scale values

Reflective diffraction pigments consisting of a ferromagnetic substrate allowfor the orientation of the particles according to an external magnetic field.Preferred ferromagnetic materials are nickel, iron, cobalt, but also elements ofthe lanthanide series. For better understanding of the orientation of ferromag-netic particles in an external magnetic field, it is useful to make a short excursioninto magnetostatics.

The ferromagnetic state in solids is caused by non-compensated electronspins of the unsaturated 3d- and 4f-electron shells of metal ions. The unbalanced


angular momentums of the electrons behave, therefore, like magnetic elemen-tary 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 externalbounding face and the second, the exchange force forces the dipoles to par-allelize to each other in the volume. In a magnetic material, anisotropic andexchange forces produce zones of equal magnetization direction. These zoneshave linear extensions between 1 μm and 1 mm which are called domainsor Weiss areas, after their discoverer P.E. Weiss. An external magnetic fieldcan drive two geometrical processes in the domains: a change of the three-dimensional extension as well as a rotation from the original position at constantvolume.

Both effects are represented schematically in Figs. 2.58a–c. Figure 2.58arepresents the original position of four domains in a ferromagnetic substance.A weak external magnetic field causes a shift of the domain walls; seeFig. 2.58b. An even higher external magnetic field strength turns the molec-ular magnets more into the direction of the external field, accompanied by afurther extension of the domain volume, Fig. 2.58c. In general, domain wallshifts occur at moderate magnetic field strengths and domain rotations only athigher strengths.

The basic driving mechanism for the orientation of ferromagnetic domainsor particles parallel to an external field is the tendency of such systems to seeka state of minimal total energy. This is achieved by an internal demagnetizationfield which counteracts the external field. A sufficiently high external magneticfield strength causes a total rotation of the domains. If the lateral dimensions offree particles are on the order of magnitude of the domains, then the rotationinto magnetic field direction is performed by the entire particle. This effect is

a) b) c)

H H

Fig. 2.58 Schematic representation of Weiss domains in a ferromagnetic material: (a) with-out external magnetic field, (b) with weak magnetic field, and (c) with strong externalmagnetic field H

2.4 Observer 109

known from iron filings, which align along the lines of an external magneticfield. Also ferromagnetic diffraction pigments are subject to such rotations. Withthe help of an external magnetic field, a nearly uniform orientation of diffractionpigments of ferromagnetic substrate can, therefore, be fixed before and duringcrosslinking of a binder.

The both diffraction pigments given in the last line of Table 2.12 are fer-romagnetic. With an additional Ni layer for the substrate, their compositioncorresponds to the two- and three-layered diffraction pigments one line higherin the table. The ferromagnetic particles consisting of the three different lay-ers 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 fur-ther PVD coating with chromium causes a gold-yellow color. The spectralreflectance curves of ferromagnetic diffraction pigments are of the same shapeas the curves of non-ferromagnetic particles with grating constants of 1,400 and2,000 l/mm; see Fig. 2.56. Certainly, on account of the particle orientation in amagnetic field, an angle-dependent colorimetrical behavior results, one whichhad not been observed before (Section 3.5.5).

After a detailed description of the optical operation modes of industriallyused colorants, we can conclude: between the rock and cave paintings of naturalcolors and the modern produced and applied colors there was, without doubt,an impressive historical development. This is accompanied by broad researchas well as process and application technology in color industry. In spite of this,all presently known and also newly developed or modified colorants are merelyorientated 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, themost important and final crucial factor for the emergence of color perceptionis the observer. His/her subjective color sensation comes from the remaininglight waves that reach the retina of the eye after source light interacts withthe colorants. Nearly all efforts in processing and applying natural, modified,and synthesized colorants are oriented toward the capability of human colorsensation. Long ago, Newton emphasized the fact that color production is ulti-mately based on neural processes. This means that outside the visual cortex,colors do not exist, but only electromagnetic waves. In the following, we givea brief overview of the modern physiological and neurological understandingof color sensation [57, 58]. These connections lead directly to the fundamentalGrassmann laws of additive mixing of colors. The standardized CIE color valuesof the years 1931 and 1976 as well as the broad color physical and colorimetricalapplications are based on these laws.


2.4.1 Color Perception and Color Theories

As already mentioned in the introduction of this text, color perception is pro-duced by psychophysical and neural processes. Color sensation is, therefore,not directly measurable with normal physical methods. The first important ele-ment contributing to overall color perception is the eye. The essential opticalcomponents of the human eye for image formation are shown in Fig. 2.59. Thecornea is only 0.5 mm thick and of fixed focal length of 25 mm, the iris has alightness-dependent aperture ratio of 28:1, and the crystalline lens is of variablefocal length. This focal length amounts about 50 mm for the resting eye whenrelaxed for distant vision. For an eye of normal vision, these optical elementsprovide a clear and focused image on the retina in the area of the fovea. In theretina are located two types of photosensitive receptors: first, the rods respon-sible 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 than10 cd/m2 (photopic vision).17 If the eye is fully adapted to darkness, just ninephotons are required before a light stimulus is detected. In cases of middle illu-mination for luminance in the range of 0.01 and 10 cd/m2, rods and cones aresimultaneously active (mesopic vision).

The retina of the human eye contains altogether about 125 million visualcells, but only 5% consist of cones. In the small area of the fovea for visualangles of about ±0.5◦, there are only cones present. Here they are of maximumdensity and enable focused vision only at this spot of the retina. The majority of

Crystalline lenslris

Cornea Fovea

Macula

Optic nerves

Optic axis

Retina

BlindSpot {

Fig. 2.59 Horizontal section of the human eye

17For 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 anglegreater than ±5◦ (for visual angle, see Fig. 2.65). At the place of the blind spotof missing visual cells, the cord of the optic nerves continues to the brain.18 Thedifferent density distributions of rods and cones in the human retina are shownin Fig. 2.60.

Four different photosensitive pigments are contained within the outer zonesof 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 towhich a derivative of vitamin A1 molecule is bound. This chromophoric groupis common to the four pigments. The absorption spectrum of a photosensitivepigment depends on the kind of protein as shown in the normalized representa-tion in Fig. 2.61. The pigment in the rods, called rhodopsin, shows an absorptionmaximum at the wavelength of 498 nm, the tails of the maximum project intothe spectral absorption ranges of the cones. The absorption maxima of the threecone pigments occur at wavelengths 437, 533, and 564 nm. These wavelengthsare perceived as blue, green, and red and the corresponding cones are, therefore,called blue, green, and red receptors. In the English-speaking medical literaturethey are denoted as S-, M-, and L-cones, indicating the selective sensitivity atshort, middle, and long wavelengths of the visible spectrum. The three conetypes are not equally distributed throughout the retina. The relative distribu-tion for blue:green:red is about 1:20:40. From the similar shapes of absorption

150

100

Num

ber

of r

etin

al r

ecep

tors

× 1

03 /mm

2

50

0–80° –40°

Angle from fovea center40°

Rods

Cones

Blind spot

80°0°

Fig. 2.60 Density distribution of rod and cone receptors across the human retina

18In modern neurology, the retina is interpreted as a part of the brain.


1.0

0.5

ConesRods

0400

437 498 533 564

500 600

Rel

ativ

e ab

sorp

tion

nmλ

nmλmax

Fig. 2.61 Normalized spectral absorption of the four different photo receptor types in thehuman retina [57]

curves in Fig. 2.61, it is possible to conclude that the spectral absorption mech-anisms of the three cone types are basically identical, although the curves seemto be shifted along the wavelength axis.

Up until now, we have assumed normal color perception, called trichromacyon account of the three different cone receptors. Some sort of color vision defi-ciency with at least one defective color receptor occurs in about 0.5% femalesand about 7% males [58–60]. Although some animal species show an evolution-ary caused tetrachromacy [61], this property has almost disappeared completelyof human beings. In only extremely rare cases of women a fourth color receptorwas proven; such a receptor shows a maximum sensitivity in the range of yellowwavelengths [62].

The unusually varying description of defective color vision in the literatureis a consequence of the fact that previous generations of researchers used theconstrained color perception for indications of the neural color sensation. Thefollowing 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 ofone 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; dichromasiesare the most frequent anomalies in humans and can be passed on genderspecifically. Dichromates have only two color receptors, leaving red-, green-,and blue-yellow blindness;

– achromatopsy: this term is a synonym for complete color blindness. Affectedpeople do not possess any of the three well-operating color receptors; suchpeople can only differentiate lightness levels.

Although the after retinal occurring neural processes are only vaguely under-stood for normal color vision – and surely will remain for a long time at thislevel understanding – we follow at least roughly the path of the neural signals inthe brain. This discussion is also carried out here to indicate to the reader howdifficult the search of an adequate color vision theory is. About 50 ms after pho-ton absorption in the photo pigments, retinal signals reach the optic nerve behindthe eye. Each left and right half of the retina of both eyes form a nerve fiber; seeFig. 2.62. At the position of the optic nerves crossing over, the so-called chiasmaor optic chiasma, each nerve fiber coming from the left and right half of bothretinas is shared to the related brain lope. In the optic chiasma, however, thereis no mixing of the incoming neural signals from both eyes. The subsequentoptic tract ends at the region of the so-called lateral geniculate nucleus, where

Lateral geniculate nucleus

Optic tract

Optic radiations

Visual cortex

Chiasma

Optic nerve

Fig. 2.62 Top view of the head to the human brain with indicated path of neural signalsbetween the two retinas and the visual cortex; the visual cortex is in no way a sharp restrictedregion of both brain lopes, but individually different expanded


the separate incoming neural impulses from both eyes are united into groups.Along several optic radiators, the transformed signals directly reach the regionat the back of the brain lopes. This is the location of the center of our visualperception, called the visual cortex. In one special zone of the visual cortex, theactual color perception is produced, just about 100 until 150 ms after photonabsorption in the retina.

On the basis of this incomplete knowledge, it is necessary to have at least anadequate theory of human color perception. Although the trichromatic colortheory of Young–Helmholtz and the opponent color theory of Hering havebeen shown to be true on physiological basis, neither theory can concretelyexplain the mechanism in the visual cortex for producing color perception(cf. Chapter 1). Likewise the modern retinex theory of Land, based on stud-ies of color constancy, delivers no usable ideas about the emergence of colorimpression 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 receptorsof the trichromatic theory. In the second zone, the generated nerve impulsesare transformed according to Hering’s theory into an achromatic signal andtwo 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 acceptedbasics of both theories mentioned above. On the basis of current knowledge,it is possible to distinguish 30 different zones of the brain responsible forvision. Merely five of them are assigned to the color sense, of these only onedominates for color perception. The neural processes between photon absorp-tion in the retina and induced color impression in the visual cortex remainunclear.

It is not surprising, therefore, that only the physiological confirmed theoriesof Young–Helmholtz and Hering lead to scientific color applications such ascolorimetry. The lacking of a theory which accurately describes the human colorsense turns out to be disadvantageous, in particular for quantification of visuallyperceived color differences. As shown in Sections 3.1 and 3.2, only empiricalformulas are given to express a color difference numerically. This unsatisfactorysituation 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 com-plex processes of color sensation. Among these are the so-called simultaneouscontrast, negative, or positive after-images or phosphene perception. Theseeffects are important in different color applications and need to be taken into

2.4 Observer 115

consideration during color assessment. These are, therefore, considered brieflyhere.

The term simultaneous contrast describes the phenomenon that the lightnessand the color of the surroundings influence the color impression. We shoulddifferentiate between simultaneous lightness contrast and simultaneous colorcontrast. A middle gray, for example, appears darker in a white neighborhoodthan in a black one; this is lightness contrast. In a similar manner, differencesbetween dark chromatic colors are resolved worse with bright-surround fieldthan with dark-surround field; this is color contrast. For visual assessment ofcolor differences, it is, therefore, necessary to always use the same achromaticsurrounding color (Section 3.2.2). Phenomenon of simultaneous color contrastis more varied than simultaneous lightness contrast. In both cases, the contrastis amplified just at the edges of color areas. The so-called lateral inhibitionis responsible for the altered color perception. This term means that the neuralsignals in adjacent receptors within the retina interact with one another. Changesthat 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 thatmany object colors are unchanged in spite of illuminant change. For example,a blue color is still perceived as the same blue, although the spectral energydistribution of the illuminant is varied.

Another property of the visual sense is combined with the so-called after-image. This after-effect occurs, if a single-colored area of high color saturationis seen with fixed eyes during about 1 min, and without movement of the eyesor head. If the eyes are afterward adapted to a white area, the color impressionremains for some time. This negative after-image is produced in the complemen-tary color. The reason for this is that the most of the corresponding receptors aredesensitized during the fixing of the chromatic surface; the remaining sensitizedreceptors continue to have a reinforced effect during the white impression.

The contrary phenomenon becomes apparent if the eyes are closed for someminutes, and then for a short time directed toward a contrasting object and thenclosed again. The resulting positive after-image shows that the color sensationactually lasts longer than the original action of the light. A longer continuinginvoluntary persistence occurs on chromatic adaption.

After-images are in particular of importance for colorists if color shadesare to be judged after a bright lighting phase with monochromatic sources.Therefore, before assessment of critical hues, for example, is important to lookat a large, plane, and achromatic area for several minutes in order to avoidinfluences of after-images.

A further time-dependent characteristic of color perception is associated witha short viewing of a color stimulus. For a viewing time of less than 0.1 s, mosthues appear progressively desaturated. In the case of very short stimuli of about3 ms duration, monochromatic light in the range from 490 to 520 nm appears


achromatic white or gray. These effects are attributed to the property that theresponse time of the receptors is clearly shorter for achromatic colors than forchromatic colors.

Colors can be perceived, quite astonishingly, also without an outside stim-ulus; this phenomenon is called phosphene. After the eyes are accommodatedto 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-dependentchanging light areas or colored schlieren. Phosphene occurs in addition withoutdark adaption by sudden pressure or electric current. In these cases, the influ-ence from outside the closed eyes evokes disturbances in circulation and neuraltransmission.

There are further phenomena of color perception which depend on spatialconditions or movement of the colored object. These are not of interest to colorphysics 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 andlightness, although we are surrounded by an even greater variety of electro-magnetic waves of different frequencies and changing intensities. But theseelectromagnetic waves are responsible for further color effects such as additivecolor mixing, which is effective especially in the human eye, or subtractive colormixing which, for example, is present in absorption colorants. Both phenomenaare 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 conse-quence of subjective color judgment and, up to now, the inability to detectdirectly the chromatic signals at each position from the retina to the visual cor-tex by objective measurements. Therefore, Grassmann tried an indirect way tocome closer to the human color sense [65]. In order to describe color impres-sions quantitatively, he avoided some of the briefly mentioned problems byusing three monochromatic light sources of different wavelengths; see Fig. 2.63.Consequently, color stimuli are generated under defined conditions and coloreffects can be observed and registered. Non-self-luminescent colors are unsuitedfor such investigations, because the colors of these light sources are required tobe produced quite simply, reproducible, and additionally, they need to be mixedtrouble-free with one another. For better understanding of the results achievedby Grassmann, it is useful to go into details of subtractive and additive colormixing, both of which are basic properties of color physics.

Subtractive color mixing is present, for example, after polychromatic lighthas passed through an optical selective filter: one part of the incident light isabsorbed by the filter, and, therefore, denoted as subtracted. In Table 2.19, some

2.4 Observer 117

Red

Green

Blue

Observer

Incandescent lamp

Whitescreen

Blackpartition

Fig. 2.63 Configuration for producing light colors for additive color mixing

examples of subtractive color mixing are listed, cf. also Color plate 1, overlap-ping upper colors. In the case of several simultaneously used filters, the resultingtransmitted color is independent of the order of the filter. Subtractive color mix-ing dominates in all sorts of absorption colorants and their mixtures; the colorresult of a colorant mixture is, therefore, independent of addition sequence.Subtraction of light waves occurs also in special cases of mixtures with effectpigments, 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. Additivecolor mixing is subject to photons of visible light, provided they enter theretina at the same time. Superimposed, the waves or photons are denoted asadded. If the retinal photo pigments are stimulated simultaneously by poly-chromatic light, merely one single color stimulus is induced. In this contextthe synonymous term “additive color mixing of light” is correct.

Further examples of additive color mixture are computer or televisionscreens. 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. Colorpixels of such small lateral dimension cannot be perceived separately by theeye at sufficient distance; therefore, only a single color stimulus is produced. Amacroscopic example is shown in Color plate 1, lower overlapping colors, cf.Table 2.19.


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 Red Green, blue CyanYellow, cyan Green Blue, red MagentaCyan, magenta Blue Red, green YellowMagenta, yellow, cyan Black Green, blue, red White

From the position and shape of the curves in Fig. 2.61, it is clear that the lightabsorption of the red, green, and blue color receptors occurs in different and par-tially overlapping spectral regions, although only one color stimulus is evokedin the retina. The color stimulus Φ clearly depends on wavelength λ. If the pho-tons of the source directly reach the retina, the color stimulus Φ(λ) equals thespectral 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 transmissionT(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 stim-ulus is summed up to form an aggregate stimulus, exactly the same procedureas in the retina or in screens. All further color physical themes dealt within thisbook, such as color vision, colorimetry, color measurement, or color recipe pre-diction, are based on the fundamental empirical laws of additive color mixingformulated by Grassmann in 1853.

As briefly mentioned at the beginning of this section, for his investiga-tions, Grassmann used three monochromatic light sources emitting constant red,green, and blue wavelengths, respectively. With a similar configuration to thatshown in Fig. 2.63, but without the incandescent lamp, a new light color is mixedon a white field by superposition of these three wavelengths. The experimentalresults show that any additive color mixing is characterized by three arbitrarilychosen primaries R, G, B, in this case lights, which are given by the correspond-ing color values R, G, B. They correspond to the relative luminance of the lightsources used. Of importance is that each of the three color values R, G, B is notnecessarily restricted to a fixed wavelength in the red, green, or blue range; theyare 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 athree-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 ofadditive color mixture:

1. For identification of a color stimulus specification, three independent pri-maries, 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 colorstimulus 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 hisfirst law, each color stimulus specification C is represented by an equation of theform

C = RR + GG + BB. (2.4.5)

It is called the color equation. Equation (2.4.5) is of central significance toall of color physics. It is valid for arbitrarily selected primaries R, G, B. Thethree color values R, G, B provide the contributions of the three primaries tothe color stimulus specification C. In other words, the color values describethe entire color impression. This is synonymous with the statement that everycolor 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 colorimpression.

The second law of additive color mixing turns out, for example, to be appli-cable to all cases of color matching; it is the basis of color recipe prediction. Forany color impression, it is irrelevant of which individual colorant componentsthe corresponding coloration is composed. The same holds for the mixture oflights of different spectral distributions. If, for example, two arbitrarily givencolor stimulus specifications C1 and C2 are matched by three primaries R, G, B,then from the first Grassmann law, it follows

19The exponent T symbolizes a transposed vector.


C1 = R1R + G1G + B1B , (2.4.6)

C2 = R2R + G2G + B2B. (2.4.7)

According to the second law, the additive mixture of both color stimulus spec-ifications 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, fromwhich is not possible to discern whether or not it consists of several individualcolor components (i.e., color values).

The third law of additive color mixing implies that if one or more com-ponents of the mixture are gradually changed, then the resulting color valuesalso change gradually, that is, as opposed to changing in a discontinuous fash-ion. Therefore, if we assign the color stimulus specification to a point inthree-dimensional space, all additively mixed color stimuli generate an owncontinuous and coherent color solid, the color space.

Grassmann has formulated originally four laws, which in modern literatureare summarized to the three given above. In the next section, we pursue theindustrially important question, how we can use color values to treat colorimpressions objectively?

2.4.4 Tristimulus Color-Matching Experiments

According to the laws of additive color mixing, a given color is characterizedby three color values R, G, B. For handling of these laws, it is useful to establishthe optional primaries R, G, B in such a way that at least the requirements thatfollow 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, thelisted first three criteria [7]. The final listed requirement is as yet not satisfacto-rily solved (see, e.g., Section 3.2). The CIE 1931 system rests on the results oftristimulus color-matching investigations of Wright [66] and Guild [67], whichused ten and seven people, respectively. For these experiments, the completeconfiguration 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 illumi-nating a bipartite white screen which was shielded against the other half. On thissecond field, the additive mixture of three primaries was projected. These werethe matching stimuli of the three monochromatic lights. By using adjustablelight controllers, the observer subjectively adjusted the light flux of the threeprimaries to obtain a color match between the two separated fields. Wright andGuild used three monochromatic light sources of wavelengths 700.0, 564.1, and435.8 nm. In the case of a match, the test stimulus was characterized by the threeluminance values of the primaries.

Before the actual matching experiments were performed, the intensities of thethree 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, normalizedwith regard to the radiant energy density of the primaries for white balance: theaccompanying 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 istermed as Ci. The matching color values of the three primaries are called color-matching values and are assigned by ri, gi, bi; they are valid especially for thechosen primaries R, G, B [68, 69]. Due to the subjectively different color sen-sation of the observers, the ri, gi, bi values fluctuate. Their mean values aredenoted by ri, gi, bi.

In the case of match, the color equation

Ci = riR + giG + biB (2.4.9)

is fulfilled according to the first Grassmann law. However, the matching proce-dures certainly show that not every given spectral color can be matched withthe preset primaries. For example, a blue-green color of wavelength 490 nmdoes not match by mixing the blue or green primaries alone. In this case, thecolor match of equally saturated color fields is only achieved if an amount rio ofthe primary R is directly added to the given test stimulus specification Ci. Thisprocedure is called outer mixture and is represented by the color equation

Ci + rioR = giG + biB. (2.4.10)

By adding the quantity −rioR to each side of color equation (2.4.10), an equationanalogous to Equation (2.4.9), but with negative amount −rio on the right-handside, results. This is a less than satisfactory situation to which we return in thenext section.

For continuous wavelengths λ, the mean color-matching values ri, gi, bi

turn into the color-matching functions (CMFs), which are assigned to r(λ),


0.4

0.3

0.2

0.1

0

–0.1

Col

or m

atch

ing

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435.8

b (λ)

400 500

546.1 700.0

600nmλ

–

g (λ)–

r (λ)–

Fig. 2.64 Color-matching functions r(λ), g(λ), b(λ) of the equienergy spectrum usingwavelengths of 700.0, 546.1, and 435.8 nm for primaries R, G, B

50 1.8

9.1

10°2°

Fig. 2.65 Visual angles of 2◦ and 10◦

g(λ), b(λ), and shown in Fig. 2.64. The color match on both color fields is car-ried out with a visual angle of 2◦ by the observer; see Fig. 2.65. Under thisobservation angle and at normal viewing distance of 50 cm, a circle area of1.8 cm in diameter is perceived. In the same angular range, the fovea of theretina contains only cones (Fig. 2.60). An observer, which fulfills these condi-tions, is called 2◦ standard observer, abbreviated 2◦ observer, and is representedby the three CMFs r(λ), g(λ), b(λ).

As shown in Fig. 2.64, the CMFs have unequal peak heights. This repre-sents the different sensitivities of the corresponding three retinal color receptors.Among the CMFs, only the function r(λ) has a negative amount with the dipminimum at about 522 nm. The negative proportion is a consequence of theouter 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 cor-responding CMFs are zero. This can be taken from Fig. 2.64 for wavelengths of435.8, 546.1, and 700.0 nm.

Finally, it needs to be pointed out that the trichromatic matching experimentswere achieved only with few people, under photopic vision with an observa-tion 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 usediscrete wavelengths λi in the following. A trichromatic stimulus is induced,according to the explanations in Section 2.4.3, by additive mixture of allmonochromatic color stimuli Φ i = Φ(λi). In the case of non-self-luminous col-ors, 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)

or

Φi = S(λi) · T(λi), (2.4.12)

because a non-self-luminous color is to illuminate with a source of spectralpower distribution S(λi). Each retinal color stimulus Φ i is represented by a cor-responding color stimulus specification Ci. If there are simultaneously i = 1,2, . . . , N stimuli Ci, the total color stimulus specification is given by additivemixture:

C =N∑

i=1

Ci. (2.4.13)

Applying Equation (2.4.8) with N ≥ 2,

C =N∑

i=1

Ci =(

N∑

i=1

Ri

)

R +(

N∑

i=1

Gi

)

G +(

N∑

i=1

Bi

)

B (2.4.14)

follows. The color values Ri, Gi, Bi correspond, on the other hand, to the productof the color stimulus Φ i, one of the respective CMFs ri, gi, bi, and the techni-cally given wavelength interval width Δλ of the used illuminant. From this, it ispossible to write the equations for the color values:

Ri = ΦiriΔλ, (2.4.15)


Gi = ΦigiΔλ, (2.4.16)

Bi = ΦibiΔλ . (2.4.17)

If we insert these relations into Equation (2.4.14) and compare the new equationwith Equation (2.4.5), finally the color values R, G, B of a non-self-luminouscolor follow from expressions:

R =N∑

i=1

ΦiriΔλ, (2.4.18)

G =N∑

i=1

ΦigiΔλ, (2.4.19)

B =N∑

i=1

ΦibiΔλ. (2.4.20)

If the emitted wavelengths are quite closely spaced together so that infinitesi-mally small wavelength intervals dλ can be assumed, the discrete color stimuliΦ i can be written as the color stimulus function Φ(λ). Then, the color-matchingvalues ri, gi, bi also become the CMFs r(λ), g(λ), b(λ). Accordingly, the sumsin Equations (2.4.13), (2.4.14) and (2.4.18), (2.4.19), (2.4.20) should be substi-tuted by integrals and the integration limits correspond to the lower and uppercutoff wavelengths of the visible range.

In this text, the sum notation is generally preferred. Two straightforward rea-sons for this preference are as follows: first, the spectral power distributionS(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 measurein one of these wavelength interval widths. Therefore, the color values R, G, Bof 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 frommeasurement.

To summarize, we emphasize that owing to additive color mixture, a givencolor can be described by three corresponding numerical color values R, G,B. These are merely representatives of the corresponding color and are by nomeans absolute values. On the basis of the experimental connections, they canbe interpreted as the red, green, and blue components of a color shade. In thefollowing section these results are finally modified for practical applications incolorimetry.

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 aregion of negative values of the CMF r(λ) shown in Fig. 2.64: this is extremelyunreasonable. 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, cannotbe clearly interpreted in a coloristic sense. More confusing is, for example, a redcoloration with a color value of R = 0. The occurrence of negative color valuesis due to the choice of the three real primaries R, G, B. Negative color valuescannot be altogether avoided with the spectral energy distribution of technicallight 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] andGuild [67] – the so-called virtual primaries X, Y, Z. These follow from a suit-able numerical transformation of the previous real primaries R, G, B [7]. Thevirtual primaries X, Y, Z are chosen in such a way that the following criteria arefulfilled:

– X, Y, Z are by definition independent of each another, and are, therefore, notproducible by mixing (the same requirement as for the real primaries R, G,B);

– the new CMFs x(λ), y(λ), z(λ) always take values ≥ 0 and follow from theprevious CMFs by an appropriate transformation (see below);

– the virtual primaries X, Y, Z are adjusted in such a way that the correspond-ing tristimulus values X, Y, Z are equally valued for the chromaticity of theequienergy spectrum: X = Y = Z;

– the two virtual primaries X and Z are chosen in such a way that only the colorvalue Y is proportional to the lightness of a color.

The new color quantities X, Y, Z are called standard color values. The newCMFs x(λ), y(λ), z(λ) are named standard color-matching functions (SCMFs)and are given with the previous CMFs r(λ), g(λ), b(λ) by the empirical matrixequation

⎛

⎝x(λ)y(λ)z(λ)

⎞

⎠ =⎛

⎝2.768892 1.751748 1.130160

1 4.590700 0.0601000 0.056508 5.594292

⎞

⎠ ·⎛

⎝r(λ)g(λ)b(λ)

⎞

⎠ . (2.4.21)

These SCMFs belong to the 2◦ observer, called CIE 1931 observer; the corre-sponding graphs are shown in Fig. 2.66 [7]. Discrete values of these functionsare used to calculate the standard color values X, Y, Z, see below.


In practice, all color samples for visual assessment have a larger sized coloredarea 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 angleof 2◦ covers only the area of the fovea. Although there is the highest cone den-sity, the induced color stimulus from this spot is insufficient for an adequatecolor assessment. Because of that, the CIE introduced in 1964 the so-called 10◦observer, also termed as CIE 1964 observer, based on investigations of Stilesand 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 theliterature [70–72].

Whereas the primaries of the 2◦ observer are related to the wavelengths700.0, 546.1, and 435.8 nm and the primaries of the 10◦ observer have thecorresponding wavelengths 645.2, 526.3, and 444.4 nm. For the normal visiondistance of 50 cm, the visual angle of 10◦ covers a circle area of 8.8 cm in diam-eter, 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 CIErecommended the 2◦ observer for visual angles between 1◦ and 4◦, and the 10◦observer for visual angles > 4 ◦. The 4◦ limit was arbitrarily established althoughthere exists no discontinuity of color perception at this angle.

The SCMFs of the 10◦ observer x10(λ), y10(λ), z10(λ) are distinguishedfrom those of the 2◦ observer by the subscript 10. The values follow froma transformation similar to Equation (2.4.21) using the corresponding CMFsr10(λ), g10(λ), b10(λ) according to the equation

⎛

⎝x10(λ)y10(λ)z10(λ)

⎞

⎠ =⎛

⎝0.341080 0.189145 0.3875290.139058 0.837460 0.073160

0 0.039553 1.026200

⎞

⎠ ·⎛

⎝r10(λ)g10(λ)b10(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 dif-ferent observer fields. The SCMFs of both observers are together representedin Fig. 2.66. The maxima of the functions y(λ) and y10(λ) are normalized atλ = 555 nm to 1.0. Due to the different visual field of the observers, the corre-sponding curves do not match perfectly. For one and the same color, the standardcolor values corresponding to each observer are also not identical. From thenonlinear wavelength dependence of both CMFs follows that the correspond-ing standard color values cannot be converted into one another. Although the10◦ observer is used to an increasing extent in color industry, in order to avoidambiguity, the observer must be clearly indicated with the results.

For the last adjustment criterion of the four listed above, it should bestated that the graph of the function y10(λ) agrees with the measured luminousefficiency V(λ) of the human eye

2.4 Observer 127

4000

0.5

1.0

1.5

2.0

500

Sta

ndar

d co

lor

mat

chin

g fu

nctio

n

600 700 nmλ

y (λ)

2°10°

z (λ)

x (λ)

x (λ)

Fig. 2.66 Color-matching functions of the 2◦ and 10◦ standard observers (CIE 1931 and CIE1964 observers, respectively)

y10(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) inFig. 2.67 correspond to the sensitivity of the eye for scotopic and photopicadaption, respectively. The curves are shifted with respect one another by about40 nm. This is described by the so-called Purkinje effect. From the half-widthsof 150 nm, it follows that the middle wavelengths of the visible spectrum areperceived with particular sensitivity under both adaption conditions.

Now, the CIE standard color values X, Y, Z are simply given from theprevious quantities R, G, B by substituting the discrete color-matching valuesri, gi, bi of the 2◦ observer in Equations (2.4.18), (2.4.19), and (2.4.20) by thecorresponding quantities xi, yi, zi:

20Since 2005, the CIE’s altered recommendation [71]; since 1931 it was accepted y(λ) =V(λ).


4000

0.5

1.0

500

Rel

ativ

e lu

min

ous

effic

ienc

y

600

V '(λ) V (λ)

700nmλ

Fig. 2.67 Relative luminous efficiency of the human eye in scotopic adaption V ′(λ) andphotopic adaption V(λ)

X =N∑

i=1

ΦixiΔλ, (2.4.24)

Y =N∑

i=1

ΦiyiΔλ, (2.4.25)

Z =N∑

i=1

ΦiziΔλ. (2.4.26)

The standard color values for the 10◦ observer follow from the same considera-tions using x10, i, y10, i, z10, i instead of xi, yi, zi and are denoted by X10, Y10, Z10.

According to the last three relations, the standard color values of a col-oration can be explicitly calculated if the retinal color stimuli Φ i are knownfrom Equation (2.4.11) or (2.4.12). The spectral power distribution S(λi) of thelight source used is known from CIE tables. This means that the spectral powerdistribution of the real source is substituted by a corresponding artificial sourcefor the determination of color values. The same is the case with regard to theobserver: the individual observer is substituted by one of the standard observers.In addition, the measured reflection or transmission of a given color sample candiffer in different color measuring devices. The retinal color stimulus valuesabove are, therefore, idealized quantities and it is, therefore, not astonishingthat color values can differ from the individual visual assessment.

Nevertheless, a given coloration is unambiguously characterized by three cor-responding numerical standard color values. Colors of equal standard values are

References 129

perceived as equal, even if they consist of different sorts of colorants (e.g., dyesor absorption pigments). Because of this, it is not possible to infer the con-stituent colorants from the numerics of the standard color values. At best, withexperience, one can estimate the lightness, chroma, or hue of the color. On theother hand, a single color value alone is not of main interest in color physicalapplications. Of much greater importance is the color difference between twoor more similar color shades. Such questions and answers to them for nearly allsorts of colors are discussed in the sections of the following chapter.

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