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Transcript
Chapter 2
Light Sources, Types of Colorants, Observer
In this chapter, the fundamental conditions for color production are discussed.
In simplified terms, the visual color impression of non-self-luminous colors is
ultimately due to three independent components: the light source, the colorants
of the color pattern, and the observer. The color perception depends, therefore,
on the specific properties of these factors. Factors of particular importance are
as follows:
– the spectral power distribution emitted of the light sources used;
– the light interactions with the colorants of the color sample, especially the
resultant absorption, scattering, reflection, transmission, as well as interference or diffraction;
– the color perception capability of the observer.
We will go into these three factors in more detail in the following sections.
To begin with, we deal with the most important light sources used for color
assessment and the most simple light interactions of colorants. The composition and the typical spectral properties of industrially applied colorant sorts are
described in detail. The explanation of color sensation of the observer seems
initially to be out of scope; however, this theme is necessary to consider for at
least two reasons: first, some phenomena of the human color sense really stand
out. These have to be taken into account during color assessment. Second, color
perception is affected by the law of additive color mixing, upon which the entire
colorimetry and the corresponding applications of industrial color physics are
founded.
2.1 Optical Radiation Sources and Interactions of Light
Without light there exists no color. The concept of color is bound to visible
wavelengths. Therefore, we turn at first toward the typical properties of natural
G.A. Klein, Industrial Color Physics, Springer Series in Optical Sciences 154,
C Springer Science+Business Media, LLC 2010
DOI 10.1007/978-1-4419-1197-1_2, 11
12
2 Light Sources, Types of Colorants, Observer
and man-made light sources because the spectral power distribution of an
illuminant affects the color impression. Due to ever-present changes in natural daylight, such a source is unsuited for producing a consistent color sensation
with an unchanging non-self-luminous color. On account of this uncertainty,
we are forced to rely on man-made sources of constant and reproducible light
emission – normally in the visible range. For a reliable assessment of colors
in industry, the spectral power distributions of two commonly used man-made
light sources have been standardized. The actual physical processes producing
color appearances can be described by elements of simple geometrical optics as
well as some effects of wave and quantum optics. In this section, these interactions are described in so far as they are significant for better understanding of
the color physical properties of modern industrial colorants.
2.1.1 Visible Spectrum and Colors
The electromagnetic spectrum covers an enormous range of wavelengths λ
from, for example, values such as λ ≈ 1 fm (1 fm corresponds to 10–15 m) for
cosmic radiation to λ ≈ 10 km for radio waves, therefore a range of around 19
orders of magnitude; see Fig. 2.1. On the other hand, the visible range of humans
is only a small part of the spectrum of electromagnetic waves. Merely wavelengths in the very small interval from 380 to 780 nm are normally perceived
by humans as visible light. Wavelengths at the left end of the range between
10–15
10–12
10–9
10–6
10–3
1
λ
m
103
1
2
3
4
5
6
7
8
9
10
Violet
Green Orange
Blue Yellow
Red
380 nm
f
Hz
1021
1018
780 nm
1015
1012
109
106
Fig. 2.1 Spectrum of electromagnetic waves: 1 cosmic radiation, 2 gamma radiation, 3 Xray radiation, 4 ultraviolet radiation, 5 near-ultraviolet radiation; 6 infrared radiation, 7 radar
waves, 8 VHF waves, 9 television waves, 10 radio waves
2.1
Optical Radiation Sources and Interactions of Light
13
380 and 440 nm are perceived as violet. With increasing wavelength, the color
impression changes to blue, green, yellow, orange, and finally red. Red is perceived at wavelengths above 600 nm. The associated wavelengths are subject to
individual variations in color perception.
The so-called spectral colors are the purest producible colors. They are characterized by a wavelength width of less than 1 nm (i.e., with a laser). On
the other hand, if the radiation contains nearly all wavelengths of the visible
spectrum and of equal intensity, the resulting color impression is white light
(e.g., white clouds). For the entire range of visible light between about 380 and
780 nm to be perceived, there must be sufficiently high intensity. Under normal
illumination conditions, the wavelength interval that can be seen by humans is
restricted to between about 400 and 700 nm. Many modern color measuring
instruments work in this limited range [1].
Apart from its wave character, light also exhibits simultaneously particlelike properties. To this day, perhaps, this dualism is not understood in terms
of everyday human experience. The corresponding particles of electromagnetic
radiation, and therefore of visible light, are the so-called photons. Photons in the
visible range carry a sufficient amount of energy for selective stimulation of the
photosensitive pigments in the retina of the eye to initiate color impression.
The eyes should, however, be protected from dangerous ultraviolet (UV) or
infrared (IR) radiation. However, radiation of wavelengths near the visible range
which cannot be directly perceived by humans can, in conjunction with suitable
colorants, cause different physical effects. Luminescence colorants, for example, absorb energy at UV wavelengths and then emit most of this energy at
longer wavelengths – usually within the visible or IR range. The needed transitions from energetic steady states occur either spontaneously by fluorescence
or delayed by phosphorescence. The energy surplus is converted into molecular vibration energy and leads macroscopically to a temperature increase. The
energy absorption of normal absorption colorants in the visible or IR range
is also transformed into molecular vibration energy. If this energy conversion is accompanied by a color change, such kinds of colorants are denoted
as thermochromic. Moreover, colorants are termed as phototropic, if the color
change is only caused by energy absorption at visible wavelengths. On the other
hand, excessively high UV or IR radiation energy is sometimes able to initiate
irreversible molecular changes, which result in bleaching or total loss of color.
In contrast to the above-mentioned colorants, overall the greatest percentage of industrially used colorants contain absorption and effect colorants. In
absorption colorants, the incident energy is sufficiently high to initiate partial absorption or scattering. Physically, light absorption in colorant molecules
occurs only for certain transitions between quantum energy levels – therefore,
in special wavelength regions of visible light. The corresponding processes are
called selective absorption or scattering. On the other hand, scattering of light
depends on the electrical charge distribution and the geometry of the colorant
14
2 Light Sources, Types of Colorants, Observer
particles. In contrast to absorption pigments, dyes do not normally show any
scattering because the size of the isolated molecules in solution is too small for
such an interaction. The light reflected in the direction of the eye initiates in the
retina signals which are perceived usually as non-self-luminous colors.
The color separation of pearlescent, interference, and diffraction pigments
is a consequence of the wave nature of light. In order to produce a suited
interference effect, the pigment particles are built up of layers with different
refractive indices of which the light waves interfere constructively or destructively depending on optical path length. The layer thicknesses are smaller than
the interfering wavelengths. In contrast, the particles of diffraction pigments
show an embossed regular grating structure at which suited wavelengths are
diffracted. The distance between two light-transferring slits is about 1 μm.
2.1.2 Types of Light Sources
The perception and assessment of non-self-luminous colors requires illumination with a suitable light source. Depending on the mechanism of light
generation, optical radiation sources have different spectral power distributions.
On the basis of the emitted spectrum, illuminants can be divided into two categories: temperature and luminescence radiators. The most important luminous
sources of both classes are given in Table 2.1. In the following, we discuss
details of both categories because the illumination of color samples is our primary context. In the near future, semiconductor diodes and lasers are expected
to replace, in part, the light sources used to date. Therefore, we also discuss
on these sources even though they are, thus far, rarely applied in color industry
despite a multitude of advantages.
Table 2.1 Kinds of optical light sources
Temperature radiator
Luminescence radiator
Natural
Artificial
Artificial
Sunlight,
Scattered light of the
Earth atmosphere,
stars,
galaxies
Blackbody radiator,
incandescent lamp,
arc lamp
Gas discharge tube,
fluorescent lamp,
light emitting diode (LED),
source of coherent light (laser)
For a common characterization, optical radiation source output distributions
are often compared with the spectral energy distribution or temperature of a
so-called blackbody radiator – also denoted as blackbody or cavity radiator. At
lower temperatures, metals emit heat energy in form of IR radiation; gradually,
with increasing temperature, dark-red glow emanates. With a further increase
2.1
Optical Radiation Sources and Interactions of Light
15
of temperature, the color changes to orange and yellow, finally to bluish white.
During this process, both the radiation energy and the brightness of the emitted
light increase. The wavelength with the most energy shifts to smaller wavelengths, i.e., a blue shift. For an ideal blackbody, this radiation is generated
inside the cavity of a blackbody radiator and the outside of the cavity walls
absorb all external electromagnetic waves. The ideal situation, therefore, is the
emission of only the cavity radiation according to its temperature.
The radiation power S(λ,T)dλ of a blackbody radiator at wavelength interval
dλ is given by the Planck law of radiation [2]:
S(λ,T)dλ =
λ5
c1
dλ.
· {exp [c2 (λT)] − 1}
(2.1.1)
The radiation constants c1 and c2 have values of c1 = 2πhc2 = 3.74185 ×
m2 and c2 = hc/k = 1.43884 × 10−2 m K. In Equation (2.1.1), the
wavelength λ should be in units of meters and the temperature T in units of
Kelvin. The radiation constants contain the velocity of light in vacuum c and
the Boltzmann constant k. For derivation of Equation (2.1.1), Planck introduced
h – now called the Planck constant.
Figure 2.2 shows the spectral power distribution in wavelength given by
Planck’s law. As can be seen, at a temperature of 500 K, the peak of spectral
power is in the IR range. For an increase to much higher temperatures, i.e., to
greater than 104 K, this peak shifts over the visible range into the UV range.
For temperatures of about 7,600 and 3,700 K, the peak of the spectrum lies at
the respective edges of the visible range. The Planckian formula (2.1.1) contains
10−16 W
109
Energy density / W.m–2.nm–1
Visual range
g
a:
500 K
b: 1,000 K
c: 2,000 K
d: 4,000 K
e: 6,000 K
f: 10,000 K
g: 20,000 K
106
f
e
d
103
c
b
100
a
10–3
101
102
103
104
Fig. 2.2 Spectral power distribution of blackbody radiator of different temperatures
λ
nm
16
2 Light Sources, Types of Colorants, Observer
two limiting cases: for short wavelengths Wien’s law of radiation and for long
wavelengths Rayleigh–Jeans radiation formula. Before the quantum hypothesis
was established, both laws lead to inconsistent infinite energies in the UV range
(“UV catastrophe”).
The primary assumption made by Planck is that a radiating system exchanges
energy with the surrounding radiation field only with an integer multiple of the
quantum energy
E=
hc
= hf .
λ
(2.1.2)
In this formula, f is the frequency of the corresponding wavelength. Both the
continuous spectra of temperature radiators and the discontinuous line spectra
of luminescence radiators are based on the emission of light quanta that are
identical with the already mentioned photons.
Because the color of the spectrum emitted by a blackbody radiator changes
with temperature, it is useful to introduce the term color temperature. With this
quantity, the emitted light of a source is compared with that of a blackbody radiator and thus characterized. The color temperature of an illuminant corresponds
to the temperature of the blackbody radiator which emits the maximum of light
at the same color as the actual illuminant. Strictly speaking, only a temperature
radiator can be assigned a color temperature. Other optical radiators, such as
luminescence radiators, are characterized by a so-called similar or correlated
color temperature.
The most well-known temperature radiator is the Sun. Inside the Sun, at
temperatures higher than 107 K, deuterium is converted to helium by nuclear
fusion (Bethe–Weizsäcker cycle) [3]. For generation of 1 mol helium, the gigantic energy of 1.55 × 102 GJ is released. The total solar fusion energy results
in a Sun surface with a mean temperature of about 5,800 K and an exceptionally high radiation power of about 63.3 MW/m2 . Merely a small fraction of this
power, namely the so-called solar constant with value 1.37 kW/m2 , reaches the
Earth’s atmosphere. This value reduces to about 1.12 kW/m2 if the Sun is at
its zenith and the atmosphere is free of clouds. Already these considerations
indicate the necessity of carrying out outdoor exposure tests of industrial colors
(Section 3.4.5).
Along the way to the Earth’s surface, the light interacts with particles of the
atmosphere; its intensity is reduced by absorption and scattering. The light scattering is caused by the molecules in the air and this is responsible, for example,
for the blue sky. According to the Rayleigh law
J=
V π 2 (n − 1) 2
·
· E · cos2 ϑ,
N
r 2 λ4
(2.1.3)
short wavelength blue light is scattered more strongly than the long wavelength
red light because λ is contained in the denominator of this expression. The
2.1
Optical Radiation Sources and Interactions of Light
17
further quantities in Equation (2.1.3) are defined as follows: J the intensity of
the scattered light, N the number of scattering particles per unit volume V, n the
refractive index of the scattering medium, r the particle radius, E the amount of
the electric field strength, and cos2 ϑ the phase function (see Section 5.1.5); ϑ
denotes the scattering angle with regard to the incident intensity. The Rayleigh
law is only valid for wavelengths λ which are longer than the particle radius r.
In contrast to the blue color of the sky, sunrise and sunset are caused by
scattering and absorption of light in the atmosphere, more precisely due to the
air molecules as well as to aerosols (water drops, dust particles, etc.). On the
long and nearly tangential optical path of the light through the layer of air, blue
wavelengths are more strongly scattered and absorbed. The remaining blue light,
therefore, reaches the observer on the Earth with considerably less intensity as
compared with the much less scattered long wavelength red light. The Sun and
the sky, therefore, appear reddish.
In addition to dependence on daytime, received sunlight changes due to
weather conditions, geographical latitude, season, and due to the approximately
11-year sunspot cycle. Accordingly, the color temperature of daylight is subject
to substantial variations and takes values in the range of 5,500 K for direct sunlight to more than 14,000 K for blue zenith skylight. Simultaneously, the spectral
power distribution changes. This is shown in Fig. 2.3 with curves normalized at
the wavelength 555 nm. At this wavelength, the sensitivity of the human eye is
at its highest (Section 2.4.6).
a
Relative spectral energy
b
400
c
d
e
500
600
λ
700
nm
Fig. 2.3 Relative spectral energy distribution curves of daylight, normalized at 555 nm: (a)
cloud-free zenith skylight, (b) cloud-free north skylight, (c) overcast skylight, (d) medium
daylight, and (e) direct sunlight [4]
18
2 Light Sources, Types of Colorants, Observer
The daylight variations mentioned above create extra complexities for the
unambiguous visual and objective assessment of non-self-luminous colors and
their typical properties. A single color sample can produce a completely different color impression simply due to a changing illumination condition. In
the practice of color physics, it is necessary to use reproducible artificial light
sources which have nearly constant spectral power distributions. These artificial light sources are often referred to as technical sources. This corresponds to
a constant color temperature if aging effects are neglected. From an economic
point of view, the sources should also have a reliable working life of more than
1,000 operating hours. These standards are fulfilled by most of the technical
illuminators of importance in the color industry; in the following section, we
turn toward such kinds of sources.
2.1.3 Technical Light Sources
For solving coloristical problems of non-self-luminous colors, technical light
sources are used exclusively. The main reason for this is the high reproducibility
of the generated spectrum. In technical temperature radiators, a metal of high
melting point is heated up by an electric energy supply to such an extent that a
continuous spectrum is emitted in the visible range; this spectrum is similar to
that of a blackbody radiator of the same temperature. A temperature radiator in
widespread use is the tungsten filament lamp; its color temperature is essentially
dependent on the filament thickness, the applied voltage, and the kind of gas
filling of the bulb. The so-called tungsten–halogen bulb contains bromine or
iodine which increases the light efficacy, the working life, as well as the color
temperature from about 2,800 to 3,000 K. The tungsten filament lamp of color
temperature 2,856 K is named standard illuminant A by the CIE.
The gradual loss of filament thickness in normal tungsten lamps is slowed
down by the included halogen: the vaporized tungsten combines with the halogen, cools down at the surrounded quartz bulb, and reaches – by convection – the
hot filament surface; there it dissociates so that tungsten is removed. Tungsten
filament lamps typically emit light of yellowish color. The accompanying spectral energy distribution is shown in Fig. 2.4. Furthermore, in a tungsten arc lamp
with an argon atmosphere, both tungsten electrodes are heated by an arc discharge in such a way that a radiation distribution is produced similar to that
of the tungsten filament lamp; the accompanying color temperature amounts to
about 3,100 K. A carbon-arc lamp shows a color temperature of 6,000 K and a
very high luminance of about 1.6 Gcd/m2 .1
1 The unit candela (cd) is defined as the luminous flux radiated from 1/60 cm2 of a blackbody
with temperature 2.042 K.
2.1
Optical Radiation Sources and Interactions of Light
19
200
Spectral energy distribution S (λ)
A
150
D65
100
50
0
300
400
500
600
λ
nm
Fig. 2.4 Spectral energy distribution of a tungsten filament lamp (CIE standard illuminant
A) and a UV-filtered xenon lamp (CIE standard illuminant D65)
The term luminescence radiators represents a group of radiators including
so-called discharge lamps, as well as photoluminescence radiators [5, 6]. In contrast to temperature radiators, luminescence radiators emit either a line spectrum
of discrete wavelengths or a band spectrum of broader wavelength intervals.
Line spectra are exclusively generated by gas discharge lamps. The physical
mechanisms for generating line spectra are first to accelerate charge carriers
by an electric field; during collision with the gas atoms, excitation energy is
transferred to the outer electron orbits of these atoms. On the basis of the quantized energy of the electron shells, the electron transition into the ground level
results in emission of light with discrete wavelengths λ according to Equation
(2.1.2). The actual temperature of luminescence lamps is clearly far lower than
the surface temperature of temperature radiators of the same light color.
Among the technical gas discharge lamps, only the filtered light of xenon or
mercury vapor lamps is of major importance for visual assessment or spectral
measurement of colors. The emission of light in gas discharge lamps is based on
the same physical mechanisms as in luminescence radiators. At first an electric
voltage pulse in a xenon atmosphere causes free charge carriers. In a highpressure xenon lamp under pulsed or constant voltage, the charged particles
generate a nearly continuous spectrum in the visible range. This is accompanied
by a small amount of UV radiation. The spectral energy distribution shows a flat
peak at a wavelength of about 450 nm and the emitted spectrum shows only a
20
2 Light Sources, Types of Colorants, Observer
slight decrease in magnitude for longer wavelengths. Therefore, the perceived
light appears slightly but insignificantly bluish; this can be seen in Fig. 2.4, curve
D65. The radiation distribution is similar to that of diffuse daylight at midday
on cloudless north sky, cf. Fig. 2.3, curve d. For these reasons, a UV-filtered
xenon lamp of color temperature 6,500 K is used in the color industry to simulate midday light. The spectral energy distribution of this xenon discharge lamp
is standardized; it is termed by the CIE as standard illuminant D65. The CIE
recommends the use of xenon lamps with color temperatures of 5,000, 5,500, or
7,500 K, if the standard illuminant D65 is not available.
The mercury vapor discharge lamp generates a line spectrum with emission
wavelengths of 405, 436, 546, 577, and 579 nm, as well as in the UV range
of 254, 314, and 365 nm. Because of the energetically high UV amount, this
discharge lamp is utilized in a so-called light booth for visual assessment of fluorescence colorants, artificial color fastness tests, and in fluorescence microscopy.
A light booth consists of a small one-sided open compartment with one or two
small platforms to lay down the color samples to compare, as well as different
non-glare light sources which can be individually switched on. The abovementioned emission wavelengths are also used for wavelength-scale calibrations
of color measuring instruments.
The UV fraction of the mercury spectrum is furthermore applied to stimulate
the phosphorus in fluorescent lamps in order to initiate photoluminescence in
the visible range. The spectral composition of the resulting band spectrum or
the resulting light color depends on the chemical structure and the mixing ratio
of the involved phosphorus. For color assessment of special importance, there is
the cold white light of the fluorescent lamp CWF (identical with illuminant FL
2) and the light emission of the so-called three-band lamp TL 84 (identical with
FL 11); the three-band lamp has radiation maxima at wavelengths of about 440,
550, and 610 nm; see Fig. 2.5. These wavelengths have spectral colors of blue,
green, and red and cause trichromatic a neutral white light color. Fluorescent
lamps are in widespread use only because of economic reasons: they have a
luminous efficacy and a physical life which are about eight times higher than
those of tungsten filament lamps, cf. Table 2.2.
Light sources of principle importance in the near future are expected to be
light emitting diodes (LEDs) and lasers, which greatly ripened technically in
the 1960s. The central component part of an LED consists of a p–n semiconductor junction. A voltage between 1 and 15 V in conducting direction and
a current of order 50 mA release photons in the p–n region. These photons are
generated by an energy surplus from recombining electrons and defect electrons
(holes). Available luminescence diodes doped with suited chemical compounds
can emit quite monochromatic light with half-widths of 6–25 nm, for example,
at wavelengths of 400 nm (gallium-nitride diode), 600 nm (gallium-arsenicnitride diode), and 660 nm (gallium-phosphide-zinc-oxide diode). The benefits
of LEDs are the short switching time of about 5 ns, the small spectral
2.1
Optical Radiation Sources and Interactions of Light
21
Spectral energy distribution S(λ)
80
60
FL 11
40
FL 2
20
0
400
500
λ
600
nm
Fig. 2.5 Spectral energy distribution of fluorescent lamps: cool white fluorescent CWF
(illuminant FL 2) and three-band lamp TL84 (illuminant FL 11)
Table 2.2 Properties of five selected illuminants
Color
Correlated color rendering
temperature/K index
Light
efficacy/
lm/W
2,856
100
12
Tungsten
filament lamp
CIE standard
D65
illuminant
D65, middle
daylight
6,500
94
35
UV-filtered
xenon lamp
Cold white
daylight
FL 2
4,230
64
70
Fluorescent
lamp CWF,
cool white
fluorescent
Bluish white
daylight
FL 7
6,500
90
80
Broadband
fluorescent
lamp
4,000
83
90
Three-band
lamp TL84
CIE
CIE illuminant abbreviation
CIE standard
illuminant
A, evening
light
A
White daylight FL 11
CIE simulator
22
2 Light Sources, Types of Colorants, Observer
half-width of the emitted intensity, the high degree of optical efficiency, and
the long working time. Disadvantages up to now have been the low illumination intensity in comparison to traditional light sources. Improvements in these
respects, at the time of this writing, are the subject of ongoing research and
development.
The term laser is an abbreviation of “light amplification by stimulated emission of radiation.” A laser is, therefore, an optical amplifier which is based on
the principle of stimulated emission of light. To initiate stimulated emission of
light2 , an irradiating field, in some sense, forces the emission of light in atoms,
molecules, or ions of gases, liquids, or solids. The incident field of frequency
f has photon energy according to Equation (2.1.2). The primary requirement
for stimulated light emission is that this photon energy is at least the natural
energy difference of the medium. In such cases, the medium that has some population in an excited state has some return to the ground state. This emitted
energy is incorporated into the incident field. In order to obtain an amplification
of radiation by stimulated emission, the energetically higher levels or bands of
a medium should maintain a state with a greater degree of filling. This greater
electron number or population in the upper energy state is usually maintained
using an energy supply such as flash lamps, other laser pump sources, currents
in semiconductor laser, or atom/electron collisions.
Typical classification of lasers is along the lines of the physical state of
the gain medium: solid state (crystals), semiconductor, liquid (usually organic
dyes), or gas lasers, for example. The ruby laser with emission wavelength of
λe = 694.3 nm is a solid-state laser. Semiconductor lasers are, for example,
indium-gallium-phosphide (In1-x Gax P) or aluminum-gallium-arsenide lasers
(Alx Ga1-x As); the emitted monochromatic wavelength of each usually lies in
the range 500 and 1,000 nm depending on the content x of the indicated element. Dye lasers are the dominant class of liquid lasers; typical laser mediums
are dyes such as coumarin (460 nm ≤ λe ≤ 560 nm) or rhodamine (535 nm
≤ λe ≤ 630 nm). The most well-known gas lasers are the helium–neon laser
(632 nm) and the argon-ion laser (wavelengths of highest intensity 488.0 nm
and 514.5 nm).
The advantages of lasers are clear, considering the outstanding features of
the emitted light: constant frequency, highly monochromatic, spatial and temporal coherence, high beam directivity, and adjustable energy density. In the
color industry, lasers have been successfully used for the determination of surface gloss, covering capacity and glittering of effect colorants, as well as size
distribution of pigment particles in powders, among other things. In the following section, we concentrate on specific properties of light sources which are of
special interest for colorimetric applications.
2 The opposite is
absorption, or, more precisely, stimulated absorption.
2.1
Optical Radiation Sources and Interactions of Light
23
2.1.4 Illuminants
In the previous section, the physical basics of light emission and the applications in technical light sources have been introduced. Now, we direct our
attention toward the special handling of light sources in colorimetry or color
matching. Unquestionably, the vast variety of technical light sources complicates the unambiguous visual assessment of colors: colored objects are exposed
to changing natural as well as artificial illuminations such as daylight, evening
light, or fluorescence light. The change in illumination can alter the visual color
impression (see below). The CIE has, therefore, recommended the most representative light sources to use for color assessment applications. For clearness
and better communication, four terms should be identified. These terms describe
the different kinds of light sources:
1. CIE illuminant: this corresponds to a theoretical source of a tabulated relative
spectral power distribution S(λi );
2. CIE standard illuminant: only two illuminants are standardized by the CIE,
illuminant A and illuminant D65;
3. CIE source: corresponds to a technically realized CIE illuminant;
4. CIE simulator: is a technical source which approximately corresponds to the
desired CIE illuminant.
The first and second terms need some further explanation. The CIE specified
several representative illuminants [7], among them are the following:
a. three temperature radiators designated D50, D55, D75 with color temperatures of 5,000, 5,500, and 7,500 K, respectively;
b. twelve fluorescent lamps designated from FL 1 to FL 12; the illuminants FL
1–6 emit line spectra, FL 7–9 broadband, and FL 10–12 narrowband spectra.
Among these, FL 2, FL 7, or FL 11 are preferably used in colorimetry. In
Fig. 2.5, only the spectral power distribution of illuminants FL 2 and FL 11
are shown;
c. in the end, five high-pressure lamps designated as HP 1–5, of which two are
sodium vapor lamps and three metal halide lamps; these are normally not
significant in colorimetry but rather in lighting engineering.
The two CIE standard illuminants are characterized by the following features:
the spectral power distribution S(λi ) of standard illuminant A is given by the
Planck law of radiation (2.1.1), whereas that of D65 is given by tabular values
[8, 9]. These values correspond to the UV-filtered emission of a high-pressure
xenon lamp shown in Fig. 2.4. Standard illuminant A is recommended for simulation of room light in the evening, D65 of midday light of color temperature
6,500 K.
24
2 Light Sources, Types of Colorants, Observer
The tabular values of a CIE illuminant are generally used for computation of color values. The corresponding simulation illuminant serves for visual
assessment of color patterns. In other words, the real light source which is
used to illuminate a color sample is, for the purpose of calculation, substituted by a theoretical simulation source, consisting of discrete wavelengths
and power emission. This can clearly be a reason for deviation between the
visual assessment and the colorimetric result. A further deviation can result
from the so-called CIE standard colorimetric observers. This is not discussed
until Section 2.4.6.
The five most commonly used illuminants in colorimetry are D65, A, FL 2,
FL 7, and FL 11; a selection of their properties is given in Table 2.2. While the
standard illuminant A is assigned a true color temperature, the illuminant D65
and the fluorescent radiators have only correlated color temperatures. These are
for the luminescence sources FL 2 –11: 4,230, 6,500, and 4,000 K, respectively.
In most cases, the change of illumination also results in a change of perceived
color. This can be caused either by the colorants themselves or by the light
source used. If the spectral power distribution is responsible for color changes,
this is attributed to the color rendering of the illuminating source. The yellowish light of the sodium vapor lamp HP 1, for example, bathes each chromatic
color in a pale yellow. This is because sodium emits only two closely spaced
wavelengths of 589.0 and 589.6 nm in the visible range. The CIE proposed the
dimensionless color rendering index Ra to characterize the grade of color rendering of light sources [10–12]. This index takes values in the range 0 ≤ Ra ≤
100. The sodium vapor lamp HP 1 has an Ra value of 20; this indicates that
colors are quite distorted. In contrast, the CIE standard illuminant A takes the
highest possible value of 100.
An additionally used characteristic, which has a meaning in terms of energy,
is the light efficacy of a radiator. This economic quantity is defined as the ratio
of emitted luminous flux of a light source to the input power of unit lm/W.3
As can be seen from Table 2.2, the displayed fluorescence lamps show a higher
light efficacy than temperature radiators of equal or lower color temperature.
From a comparison of the spectral power distributions shown in Figs. 2.4
and 2.5, it is possible to understand how the change of a source alters the color
impression. Consider Fig. 2.4: using source A, the color sample appears more
yellow and red compared with illumination of a D65 simulator. This is because
of the continuously increasing radiation energy characteristic of the source A
from yellow to red wavelengths with quite small values at short wavelengths.
Consider now Fig. 2.5: the same color sample is rendered bluish white with FL
2 source, or with FL 11 source, redder in comparison to D65 simulator. Colors
3 By definition, the unit lumen (lm) is the luminous flux which a point light source of emissiv-
ity 1 cd (candela) emanates evenly in all directions in a solid angle of 1 sr (steradian): 1 lm =
1 cd sr; 1 steradian corresponds to a solid angle Ω – of even circular cone with center point
in a sphere of radius 1 m – which cuts an area of 1 m2 out of the sphere surface, cf. Fig. 5.1.
2.1
Optical Radiation Sources and Interactions of Light
25
illuminated with a D65 or FL 7 source are rendered and perceived in a similarly
balanced way as under midday light. This is because of the nearly constant and
high values of the corresponding emission spectra in the visible range.
2.1.5 Geometric Optical Interactions
There are various possible interactions between incident light and atoms,
molecules, particles, or crystals. Of these interactions, we are primarily interested in the color appearances that result. In a plane electromagnetic wave, the
electric and magnetic vectors E and H are perpendicular to one another, and,
in addition, mutually perpendicular to the propagation direction. The so-called
wave vector k is oriented in the propagation direction. The electromagnetic wave
carries the energy flux density in the direction of k, given by vector S (named as
Poynting vector) and relation
S = E × H.
(2.1.4)
Figure 2.6 shows the connection between the three vectors E, H, and S. In
the figure, the electric and magnetic vectors are shifted a quarter wavelength
in phase with respect to one another.
E
S
H
Fig. 2.6 Electric and magnetic field of a stationary wave
The amount of energy flux density S carried by such waves, also termed as
flux density, or short flux, is the origin of interactions with the molecules or
particles of colorants to produce colors. Color production of non-self-luminous
colors can be caused by simple or multiple reflection, refraction, absorption,
scattering, interference, and/or diffraction.
When the wavelength of the light (order 0.4 to about 1 μm) is much smaller
than the size of the objects that it interacts with (i.e., macroscopic objects), the
light no longer behaves strongly as a wave, but rather propagates in straight
lines according to geometrical optics. Reflection, refraction, absorption, or scattering can occur simultaneously if the light is incident on macroscopic boundary
surfaces consisting of mediums with different optical densities. The polarization
26
2 Light Sources, Types of Colorants, Observer
of light can intensify normal color appearance. This can appear especially for
some absorption pigments and liquid crystal pigments.
Materials can be illuminated by directional, diffuse, or mixed light. Quite
simple, but of great importance, is the directional reflection – also denoted as
specular reflection. Directed reflection arises from directional light at smooth,
polished, or glossy surfaces, for example at organic binders, synthetic polymers, glasses, metals, as well as colorations with absorption and effect pigments.
According to the reflection law, the angles of the incident ϑi and reflected light
ϑ r , measured with respect to the normal of the reflecting surface, are equal:
ϑi = ϑ r . Additionally, both rays and the normal of the reflecting surface lie in
the same plane, that of the paper in Fig. 2.7. It is important to note that for visual
assessment of colorations of glossy surfaces one must strictly avoid observations
in the direction of the specular angle. For visual inspection of absorption colorations with collimated light, the surface should be illuminated from the side
and the observation performed perpendicular to the sample surface. In contrast,
the visual assessment of effect colorations requires a sophisticated procedure,
cf. Figs. 2.29 and 2.30.
ϑi
ϑr
Fig. 2.7 Depiction of the reflection law with incident and reflected beams, as well as angle
of incidence, and specular angle, each from normal to the surface
If the medium behind the glossy surface is transparent and of different refractive index than the first medium, the beam is additionally refracted into this
medium. The refracted ray deviates from the original direction, see Fig. 2.8a, b,
due to the different indices of refraction in the two media. The angle of refraction ϑ 2 depends on the angle of incidence ϑ 1 and the ratio of refractive indices
n2 /n1 of the adjoining mediums according to Snell’s law of refraction
sin ϑ1
n2
=
=n
sin ϑ2
n1
(2.1.5)
(original W. Snel van Royen, 1621). In general, the refractive indices are also
wavelength dependent, this normally results in violet light being refracted at a
steeper angle than red light. This property is called dispersion [2] and results in
prism effects.
2.1
Optical Radiation Sources and Interactions of Light
27
ϑ1
ϑ2
n1
n1
n2
n2
ϑ2
ϑ1
a)
b)
Fig. 2.8 Refraction of light at the boundary surface of (a) an optically thinner medium and
(b) an optically denser medium
The reflected fraction r(μ, n) of the directional beam at the boundary surface
follows from the Fresnel equation
1
μn − w 2
μ − nw 2
r(μ,n) =
+
,
(2.1.6)
2
μn + w
μ + nw
where
μ = cos ϑ ,
w2 = 1 − (1 − μ2 )n2
(2.1.7)
[13, 14]. Equation (2.1.6) can be derived from Maxwell equations of electrodynamics [14]. The reversal of light direction does not change the reflected fraction
nor the law of refraction. The reversibility of the light path without change of
effect is a general principle of geometrical optics [15]; this principle is used in
color measuring methods among other things (Section 4.1.2).
In the case of light incident perpendicular to the surface, the special reflected
fraction is given by
n−1 2
.
(2.1.8)
r(1, n) =
n+1
This follows from Equations (2.1.6) and (2.1.7) using μ = 1. For air with refractive index n1 ≈ 1.0, for example, and plastics or binders with a typical value n2
= 1.5, using n = n2 /n1 , the normal incidence reflected fraction is r = 0.04.4
In other words, under these conditions, 4% of the incident light is immediately
4 The cited refractive indices in this book represent values which – as usual – belong to the
wavelength of the sodium line of 589.0 nm.
28
2 Light Sources, Types of Colorants, Observer
reflected from the surface of a colored sample; this amount is not available for
further light interactions in the volume of a color sample.
The reflectance of pure metals follows from Maxwell’s equations as well,
provided that the complex refractive index n̂ is introduced:
n̂ = n(1 + iκ).
(2.1.9)
The quantity n̂ is divided into the real part n for the refraction and the imaginary
part nκ describing the light absorption at the interface. The quantity κ is √
named
attenuation coefficient. In Equation (2.1.9), i is the imaginary unit (i = −1).
For directional light incident perpendicular to the metal surface, the reflected
total amount is given by
r(n, κ) =
(n − 1)2 + (nκ)2
.
(n + 1)2 + (nκ)2
(2.1.10)
For κ = 0, this formula reduces to Equation (2.1.8). The product nκ is termed
as absorption coefficient; some measured values of n, nκ , and r(n, κ) for metals
used for metallic pigments are listed in Table 2.7.
A further sort of reflection occurs if a light beam enters an optically thinner
medium coming from an optically denser medium. Note that the refracted ray
cannot exceed an angle ϑ 2 = 90◦ ; see Fig. 2.9. For a refractive index n = 1.5,
the corresponding incidence angle is ϑ 1 = 41.8◦ . In general, from the law of
refraction (2.1.5), it follows that rays, with angles of incidence with γcr ≥ arcsin
(1/n), are totally reflected back into the optically denser medium. The quantity
γcr is called the critical angle of total reflection or in short critical angle. If
ϑ2
n1
n2
ϑ1
γcr
γcr
Fig. 2.9 Critical angle γcr at a boundary surface of different refractive indices
2.1
Optical Radiation Sources and Interactions of Light
29
the total reflected light cannot immediately leave a colored layer, it participates
further in the interactions with the color-producing particles until it is absorbed
or leaves the layer. Total reflected rays of angles γ ≥γcr are called partly directed
in this text.
For unpolarized light, a further property follows from the law of refraction
with regard to the refracted ray. In the case that the reflected and the refracted
rays make a right angle, the light of the reflected ray is linearly polarized, in
fact perpendicular to the plane of incidence; see Fig. 2.10. This special angle of
incidence is denoted as Brewster angle ϑB and is given from the law of refraction
(2.1.5) with ϑ 2 = 90◦ – ϑB :
tan ϑB = n.
(2.1.11)
Fig. 2.10 A reflected beam
of Brewster angle ϑB is
linearly polarized
perpendicular to the plane
of incidence
ϑB
n1
n2
ϑ2
The Brewster angle depends only on the ratio of the refractive indices at both
boundary surfaces. For a ratio of n2 /n1 = n = 1.5, the Brewster angle of ϑB =
56.31◦ results. The critical angle γcr and the Brewster angle ϑB are shown in
dependence on n in Fig. 2.11. Polarized light produces always more intensive
colors than unpolarized light; polarized light is generated in some absorption
colorants and especially in liquid crystal pigments.
In addition to that from Equation (2.1.6) and the above considerations, the
reflection coefficient of directional light depends on the direction of polarization
parallel to the plane of incidence. These properties also follow from Fresnel
equations [14]. This is shown in Figs. 2.12 and 2.13 for a refractive index value
of n = 1.5 in dependence on the angle of incidence ϑi . The outer reflectance
coefficient at the boundary of the optically thinner medium begins to differ from
one another for the two rectangular linear polarizations already for small angles
30
2 Light Sources, Types of Colorants, Observer
100
Angle / degree
80
60
γcr
40
ϑB
20
0
1.0
1.2
1.4
1.6
Refractive index n
1.8
2.0
Fig. 2.11 Critical angle γcr and Brewster angle ϑB in dependence of refractive index n
Outer reflection coefficient
1.0
0.8
Polarisation:
parallel
normal
0.6
n = 1.5
0.4
0.2
0
0
20
40
60
80
Angle of incidence ϑ1
Fig. 2.12 Outer Fresnel reflection factor as function of angle of incidence for polarization
parallel and perpendicular to the plane of incidence
of incidence (Fig. 2.12). This difference increases strongly with the angle of
incidence. The inner reflection coefficient at the inner boundary of the optically
thicker medium shows the same behavior but is compressed into the angle range
0 < ϑ2 < 41.8◦ ; see Fig. 2.13. The high increase of this reflection coefficient is
caused by the critical angle of total reflection.
Consider now diffuse illumination instead of directional light. This alters the
reflection character. The majority of natural and artificial light propagates diffusely. Because of this, it is, perhaps, most reasonable to measure and visually
2.1
Optical Radiation Sources and Interactions of Light
31
Inner reflection coefficient
1.0
Polarisation
0.8
parallel
normal
0.6
n = 1.5
0.4
0.2
0
0
20
60
40
Angle of incidence ϑ2
80
Fig. 2.13 Inner Fresnel reflection factor as a function of angle of incidence for polarization
parallel and perpendicular to the plane of incidence
judge color samples under diffuse illumination. Ideal diffuse light is in the forward direction inside an angle range of ±90◦ and of equal energy over the
entire range of these angles. Because of that the radiation power, the optical
interactions, and specially the reflection conditions at the boundary surfaces are
changed. The reflection coefficients for diffuse radiation follow from energetic
considerations leading to the relation
1 − rd∗
n22
=
1 − rd
.
n21
(2.1.12)
The quantity rd∗ denotes the reflection coefficient of diffuse light at the boundary
of the optically thinner medium with n1 and rd stands for the reflection coefficient of the optically denser medium. In Fig. 2.14, the reflection coefficients
for diffuse light are represented schematically by arrows for simplicity. For diffuse illumination from air of n1 ≈1.0 in a layer of refractive index n2 = 1.5, the
appropriate reflection coefficients rd∗ = 0.09178 and rd = 0.59635 come from
Fig. 2.14 Reflection
coefficients of diffuse
radiation at a boundary
surface of different
refractive indices
(schematically)
32
2 Light Sources, Types of Colorants, Observer
1.0
rd
Reflection coefficient
0.8
0.6
0.4
rd∗
0.2
r
0
1.0
1.2
1.4
1.6
Refractive index n
1.8
2.0
Fig. 2.15 Three sorts of reflection coefficients in dependence on refractive index n: r for
directional illumination perpendicular to the surface, rd∗ for outer diffuse illumination, and
rd for inner diffuse illumination of a material
the literature [13]. The reflection coefficients for diffuse light rd∗ and rd as well
as for directional light at perpendicular illumination r are shown in Fig. 2.15 in
dependence of the refractive index n.
The boundary surface reflection certainly complicates the visual and measuring assessment of colored samples: this surface reflection is superimposed on
the entire visual impression as well as the spectrometric measuring results. But
the essential and interesting parts of color sensation are generated by the light
interactions in the volume of a colored layer.
For the following, we define the reflection of an optical medium as the
amount of incident radiation energy which is backscattered from the
volume and this is superimposed by the surface reflection energy.
Correspondingly, the transmission is the amount of the incident light energy
which overcomes the interactions in the volume and exits the second
boundary surface of the optical medium.
The accompanying energies are called reflection and transmission energy; these
are abbreviated by WR and WT .
The electromagnetic field of a light wave can drive vibrations of suitable
charge carriers in atoms or molecules of absorption colorants. This additional
absorption of energy leads sometimes to emission of secondary radiation; this
process is denoted as scattering. The scattering is elastic if the wavelengths of
the incoming and scattered light are equal. This is the case especially within
non-self-luminous colors but also for Rayleigh and Mie scattering (Sections
2.1.2 and 5.1.3, respectively). Inelastic scattering, however, produces a change
of scattered wavelengths such as in Raman and Brillouin scattering [16].
2.1
Optical Radiation Sources and Interactions of Light
33
In addition to scattering, a part of the incoming light energy is normally
absorbed by the charge carriers of the colorant molecules and not scattered.
This causes an increased molecular vibration energy and, therefore, a temperature increase of the coloration. The absorption of energy of amount WA is finally
absent from the reflected, transmitted or scattered light. In the most colored layers, scattering and absorption occur simultaneously in different amounts, and
additionally dependent on wavelength.
The three mentioned energy components WR , WT , WA come from the incident
energy Wi . Therefore, the energy conservation law, in our case, amounts to
Wi = WR + WT + WA .
(2.1.13)
1 = R + T + A.
(2.1.14)
Division by Wi results in
The quantities R, T, A are denoted as follows:
R = WR Wi reflectance,
(2.1.14a)
T = WT Wi transmittance,
(2.1.14b)
A = WA Wi absorption.
(2.1.14c)
These quotients are, for simplicity, also denoted as reflection, transmission, and
absorption but also reflection factor, transmittance factor, and absorption factor,
respectively.
The law of energy conservation is an axiom of physics and is of fundamental
importance; in the above formulation, it plays a central role in the entire radiative transfer of optical systems. The energy conservation law is even valid for
each single wavelength, therefore, valid independent of the irradiated spectral
power distribution. Furthermore, this law is independent of any specifications
concerning the interacting particles of the optical medium. From that follows a
basic realization, which is of great importance for the further discussions in this
text:
The resulting values of reflection, transmission, or absorption are characteristic quantities of the optical medium; in our case, they are essentially
caused only by the colorants of the chromatic color.
Reflectance and transmittance are determined with suitable color measuring
instruments (Sections 4.2.1 and 4.2.2); absorption and scattering are characterized by corresponding optical constants which follow from optical models
(Sections 5.1.2 and 5.1.4). Absorption and scattering are generally the most
34
2 Light Sources, Types of Colorants, Observer
important quantities of absorption colorants. In effect pigments, however, the
dominant processes are wavelength dependent such as interference or diffraction. The basic optical laws responsible for color production of pearlescent,
interference, and diffraction pigments are discussed in the next two sections.
2.1.6 Interference of Light
The colors produced by absorption colorants and metallic pigments are essentially based on processes such as reflection, absorption, and scattering and are
occurring at the surface and in the volume of a colored sample. In contrast to
that, impressive color effects are generated by interference of light waves in
pigment particles composed of an appropriate sequence of layers. Interference
is an effect caused by superposition of suitable waves (of, e.g., liquids, gases,
electromagnetic fields, elementary particles). Interference of light is, for example, responsible for the colors of soap lamellas, oil films on water, or coated
lenses [17]; the colors of opals, natural pearls, insect wings, or bird feathers
are in addition based on interference. The colors of interference pigments result
from light waves, which are reflected at the inner and outer layer boundaries
and which superimpose with the incoming waves. The produced colors are controlled by the thickness and refractive index of the different layers among other
things. The layer thicknesses vary from about 10 nm to 1 μm; see Fig. 2.40 [18].
Interference colors can be distinguished from normal absorption colors by the
color change in dependence of the observation angle; this is in some way similar
to diffraction colors.
A necessary requirement for interference is the existence of coherence. Most
of temperature and luminescence radiators emit incoherent waves, because the
single atoms of the source oscillate independently from each other, only short
wave trains are produced; between the single waves exists no constant phase
relationship. Waves are coherent, if the time dependence of their amplitude is
the same irrespective of a phase shift. In the case of harmonic waves, this means
that the frequencies of the waves have to be the same; however, they can have
a constant phase difference. Coherent sine-shaped waves must, therefore, be of
equal frequency. Coherent waves can result, for example, from the reflection of
a radiative field at a mirror. From this perspective, laser light is of nearly perfect coherence because it is amplified during multiple reflections. Interference
pigments normally consist of at least two layers of different refractive indices to
produce a suitable reflection at the boundary layer, cf. Equation (2.1.6).
In Fig. 2.16, there is a simplified illustration of the reflection and interference of light at a plane parallel layer. The reflected waves of beams R1 and R2
interfere above the layer. The waves of R1 initiated by R1 take a longer way to
the surface and, therefore, have an optical path length difference G with regard
to the waves of R2 . In view of the different path lengths, the ratio of refractive
2.1
Optical Radiation Sources and Interactions of Light
R1
R2
35
R'1
ϑ1
R'2
ϑ1
n1
n2
d
ϑ2
n3
Fig. 2.16 Interference at a plane parallel layer of different refractive indices
indices n = n2 /n1 , the refraction law (2.1.5), and the phase jump of λ/2 caused
by reflection of the waves at the upper layer surface, the difference G is given by
G = 2d ·
λ
n2 − sin2 ϑ1 + ,
2
(2.1.15)
where d stands for the layer thickness and ϑ1 for the angle of incidence. At
some locations, the wave amplitude is increased by the so-called constructive
interference of the incident and reflected waves. This occurs if G is an evennumbered multiple 2z of λ/2, fulfilling the condition:
(2z − 1)λ = 4d ·
n2 − sin2 ϑz ,
z = 1, 2, 3, ... .
(2.1.16)
Destructive interference occurs for
G = (2z + 1)λ 2,
z = 0, 1, 2, ... .
(2.1.17)
The positive integer z is called interference order.
The amplifying light waves and, therefore, the corresponding colors can be
modified according to Equation (2.1.16) by the material quantities d and n; this
is used to a great extent for realization of different kinds of pearlescent and interference pigments. For color sensation, the additional change of color impression
in dependence on the observation angle ϑz can be quite strange. The quantity
ϑz belongs to the different interference orders z instead of the constant angle
ϑ1 . Generally, the intensity of the amplified waves decreases strongly with the
number of z.
36
2 Light Sources, Types of Colorants, Observer
Some special interference features result in the case that light is incident
perpendicular to the surface of a layer. Colors of pearlescent and simple interference pigments are visually characterized by observation perpendicular to the
colored surface; some important technical applications come out of this. From
Equation (2.1.16) with ϑ1 = 0 for the dominant first interference order (z = 1),
the simple result d = λ/4n follows. Furthermore, if the interference wavelength λ
and the refractive index n are constant, the layer thickness for order z, given by
d = (2z − 1)λ 4n,
(2.1.18)
leads to constructive interference. A stepwise increase of the layer thickness by
the quantity d leads to a distance of Δd = λ/2n between two adjacent intensity
maxima. The same distance holds for neighboring minima.
These considerations are especially used to reduce the reflection of optical
systems by destructive interference. With the so-called optical coating, the optical surfaces are coated with an inorganic layer by physical vapor deposition; the
refractive index nC of the coating has to satisfy the condition
√
(2.1.19)
nC = n1 n2 ,
where n1 and n2 are the refractive indices of air and of the optical material,
respectively. Unfortunately, the effectiveness of reflection reduction is limited
to a middle visible wavelength. To achieve a nearly regular reduced reflection
of wavelengths in the entire visible range, a multi-layered coating on both sides
of the optical element is necessary at the most 10 layers which are tuned with
each other. This is a type of dielectric coating called an anti-reflection coating.
The so-called dielectric mirror coating relies likewise on interference. For
this, multi-layer coatings of alternately higher and lower refractive indices nh
and n1 are produced; see Fig. 2.17. If each single layer has a constant optical
thickness dh = λ/4nh or dl = λ/4nl , then the reflected waves of first order interfere constructively with the incoming light caused by the additional phase jump
at the boundary of the optical denser medium. Therefore, a narrowband mirror
results; the reflectivity depends on the difference of the refractive indices of the
layers [17]. With change of the layer parameters, the width of the wavelength
interval can be controlled. These considerations are also used to achieve suitable
layer structures in pearlescent and interference pigments to produce a dominant
color component.
Interference colors can be further improved by multiple reflection of light
between two semi-transparent mirrors at distance d, similar to the placement in
a so-called Fabry–Pérot interferometer; see Fig. 2.18. One part of the reflected
light is transmitted through the second layer. Multiple reflection leads to a great
number of partial beams, which interfere behind the second layer. The layer distance d and the refractive index n of the medium between the layers are chosen
in such a way that only a small wavelength band is transmitted; this construction
2.1
Optical Radiation Sources and Interactions of Light
37
Fig. 2.17 Layer sequences
of a dielectric mirror with
high and low refractive
indices nh and n1
nh
nl
nh
nl
dh =
λ
4nh
dl =
λ
4nl
Substrate
operates as an interference filter. For fixed distance d, this construction is also
called an etalon. The deciding parameters for the interference efficacy are n and
d of the intermediate layer. Because adjacent beams have the same geometrical
optical path difference, constructive interference is given by
zλ = 2nd cos αz ,
z = ±1, ± 2, ... .
(2.1.20)
The intensified wavelengths become, therefore, smaller with increasing angle
of beam incidence α z . For a layer thickness d = 300 nm and refractive index
n = 1.5, the wavelengths of violet and red light (400 and 700 nm) are separated
for the first order by an angle difference of about 25◦ . Founded on this principle,
d
L
LQ
P
Q1
n
Q
αz
Fig. 2.18 Fabry–Pérot interferometer: the partial waves of points Q, Q1 produce interferences of “equal inclination”
38
2 Light Sources, Types of Colorants, Observer
in particular, is the angle-dependent color effect of multi-layered interference
pigments in liquid crystal structures; see Fig. 2.43.
2.1.7 Diffraction from Transmission and Reflection Gratings
When light is incident on objects or boundaries with dimensions on the order of
the wavelength of the light, the wave characteristics of light become very important. This is the situation, for example, at a diffraction grating. Upon passing
through the grating, some portion of the light is deflected and/or is fanned out
depending on the grating geometry and the wavelength. This phenomenon is
an example of Fraunhofer diffraction if the light beam is incident nearly perpendicular to the grating [19]. In addition to macroscopic structured materials,
diffraction pigments can be impressed with such grating structures. This leads
to color effects which are also depending on the angle of observation.
A simple macroscopic transmission grating is shown in Fig. 2.19, not to
scale. The geometry is simply achieved by scratching or etching of equidistant
grooves in a thin plane parallel glass sheet. With recent techniques, diffraction
pigments can be impressed with nanostructures. Each constant groove gap d,
also called grating period, contains a narrow light-transmitting slit. The reciprocal quantity of the grating period, g = 1/d, is denoted as the grating constant;
its units are given in lines per millimeter (l/mm). At each of the slits – which are
spaced with typically as much as 5,000 l/mm or more – the incident wave front
αz
αi
d
αi
G1
αz
G2
Fig. 2.19 Diffraction conditions of an optical transmission grating (schematically)
2.1
Optical Radiation Sources and Interactions of Light
39
is diffracted according to the Huygens principle, which means that each point of
a wave front is assumed to be the origin of a new elementary wave [19]. Because
diffraction occurs at all illuminated grating slits, a pattern of constructively and
destructively interfered waves develops behind the grating. The path difference
G1 + G2 of waves coming from two neighboring slits follows from Fig. 2.19 as
G1 + G2 = d(n1 sin αi + n2 sin αz ),
(2.1.21)
where n1 and n2 stand for the refractive indices in front and after the grating and
α i for the angle of incidence. The diffraction maxima occur for a path difference
G1 + G2 equal to an integer multiple z of the wavelength λ. With Equation
(2.1.21), the relation
zλ = d(n1 sin αi + n2 sin αz ), z = 0, ± 1, ± 2, ...,
(2.1.22)
follows.
The zeroth-order diffraction, equivalent to z = 0, contains all wavelengths of
the irradiated light. Higher diffraction orders for z = 0 are generated on both
sides of the zeroth order with symmetric intensity maxima and minima. The
wavelengths contained in the incident light fan out by the grating in such a
manner that the condition in Equation (2.1.22) is fulfilled. The grating deflects
large wavelengths stronger than shorter wavelengths; this is the converse of a
prism. Moreover, the diffraction spectrum of the first order is of higher intensity
compared to that of a prism spectrum. In order to avoid an overlapping of the
diffraction maxima of higher order, the incident angle α i and the grating period
d can suitably be tuned with each other (see below).
In addition to transmission gratings, reflection gratings are also commonly
used – these are especially realized in diffraction pigments. These can be formed
by vapor coating both sides of a nontransparent grating structure with an additional layer of a reflecting metal, cf. Fig. 2.20; this has the added bonus of a
possible improvement in the mechanical stability of the thin plates. The waves
reflected from the periodically arranged mirrors interfere with the incoming
waves from the opposite direction. Consequently, the diffraction pattern already
known from transmission gratings develops in front of the reflection grating.
The cross section of the grooves can be produced as rectangular, triangular, or
sine shaped. Reflection gratings are used in modern spectrophotometers and
optimized diffraction pigments, among other things. Examples of diffraction
particles are shown in Figs. 2.54 and 2.55.
Concerning the reflection grating in Fig. 2.20, the path difference G1 – G2 of
the reflected waves from adjoining grooves follows from the expression
G1 − G2 = d( sin αi − sin αz ) .
(2.1.23)
40
2 Light Sources, Types of Colorants, Observer
Fig. 2.20 Diffraction
conditions of an optical
reflection grating
(schematically)
αi
G2
αi
d
αz
G1
αz
In analogy to the transmission grating, the diffraction maxima are given by
zλ = d( sin αi − sin αz ) ,
z = 0, ± 1, ± 2, ... .
(2.1.24)
For z = 0, it follows α i = α 0 and the grating operates like a normal flat mirror,
that is, the wavelengths are not separated.
Generally, the use of gratings results in spectra of higher light intensity in
comparison to prisms, but the incident intensity is distributed among all diffraction orders. Among them, is the maximum for z = 0, which is of highest
intensity, and also generally not of interest (see Fig. 2.21). This disadvantage
can be bypassed using a so-called echelette grating5 ; see Fig. 2.22. On the
basis of the special geometry of such a grating, nearly the entire intensity of
the diffracted light can be concentrated into a particular diffraction order, as
required.
To achieve this aim, the cross section of the grooves has to meet the following
requirements:
1. The desired diffraction order zB is not zero; the reflecting grating elements
should be tilted by an angle α B above the grating base; this angle is called the
blaze angle, after the corresponding production method known as the blaze
technique.
5 echelette:
French, small ladder.
2.1
Optical Radiation Sources and Interactions of Light
41
Δα
Δβ
Fig. 2.21 Angle differences of diffraction maxima
2. The angle half-width α of the diffraction fringe, caused by this kind of
grating element, has to be matched with the angle distance β between two
successive diffraction maxima; see Fig. 2.21.
In view of the first condition, it is useful to consider the angles from the
grating base normal. The blaze angle is, therefore, given by the simple relation
αB = (αi − αz ) 2,
(2.1.25)
where α i and αz are the angle of incidence and the diffraction angle of order z,
respectively. In addition, these two angles are combined with Equation (2.1.24),
to give
zB λB = d · (sin αi − sin αz ) ,
Grating normal
zB = 0, ± 1, ± 2, ... .
Face normal
αB
αi
αz
b
αB
d
Fig. 2.22 Echelette grating with blaze angle α B
(2.1.26)
42
2 Light Sources, Types of Colorants, Observer
The quantity λB is called blaze wavelength and zB denotes the blaze order.
According to Equation (2.1.25), the blaze angle depends on the incident and
the diffraction angles. For this reason, echelette gratings can be realized with
different blaze angles. From the last two expressions, the condition
zB λB = d · [ sin αi + sin (2αB − αi )] ,
zB = 0, ± 1, ± 2, ...
(2.1.27)
follows. It is independent of a diffraction angle.
For improved understanding, we differentiate now between two types of light
incidence – from which consequently follow different blaze angles. In the first
case, we assume an illumination in the direction of the grating normal; see
Fig. 2.22. In this case, the angle of incidence is α i = 0 and it follows from
Equation (2.1.27):
zB λB
1
,
zB = 0, ± 1, ± 2, ... .
αB = arcsin
(2.1.28)
2
d
In the second case, the light is incident in the direction of the face normal, the
so-called Littrow or autocollimation configuration. In this case, then the incident
angle is equal to the blaze angle α i =α B given by
zB λB
(2.1.29)
,
zB = 0, ± 1, ± 2, ... .
αB = arcsin
2d
Note that because an echelette grating of sine-shaped cross section can be
approximated by a series of successive isosceles triangles, the outlined considerations are also applicable to that geometry.
From the second condition above, some further geometrical conclusions
result. With the designations given in Figs. 2.20 and 2.22, the relation
cos αz
b
=
d
cos (αz − αB )
(2.1.30)
can be derived. In other words, the triangle geometry depends on the blaze angle
as well as the angle αz of diffraction order z. Additionally, according to Equation
(2.1.30), the width b of a step is specified with the groove distance d.
If the illumination is carried out parallel to the grating normal, from Fig. 2.22,
we have the intermediate result α z = 2α B . The condition
b=d·
cos 2αB
cos αB
(2.1.31)
therefore follows. On the other hand, for illumination parallel to the face normal,
the condition α z = α B is given and the simple formula
b = d · cos αB
(2.1.32)
2.2
Absorbing Colorants
43
follows from Equation (2.1.30). In this case, the triangle of the echelette grating
is right angled.
The utilizable wavelength range of such kinds of gratings is roughly limited
to the interval 0.7λB ≤ λ ≤ 2λB . Absorption and scattering dissipation reduce
the efficiency of a blaze grating to about 70% [20]. Accordingly, the blaze technique enables the focusing of about 70% of the influx into a desired z = 0
diffraction order. Each diffraction pigment is normally optimized with regard to
the first diffraction order z = ±1. This diffraction spectrum can be observed
symmetrically with respect to the direction of illumination, and is followed
by further orders of lower intensity, cf. Section 3.5.5. These principles apply
not only to macroscopic gratings but also to diffractive pigment particles; see
Figs. 2.55 and 2.56.
2.2 Absorbing Colorants
After considering different light sources and basic light interactions in the
previous section, the second fundamental component for color producing of
non-self-luminous colors is the color sample containing the colorants. Colorants
can be divided into two groups, depending on the dominant mechanism of
color production: classical absorption colorants and modern effect pigments
(cf. Table 1.1). Industrially applied absorption colorants consist mainly of synthesized colors of inorganic and organic compounds, and in some rare cases of
modified natural colors. In this section, we characterize dyes and absorption
pigments, describe the most important color attributes and the accompanying coloristic properties as well. Some of these properties are correlated with
specific spectral features of the corresponding coloration.
Additionally, color-order systems will be outlined. In some application cases,
such systems offer an overview of the diverse-generated absorption colors. Each
of these color order systems is grouped according to preset characteristic criteria. On one such system is based a special CIE color space. It is also shown
that the color impression results from light interactions in the volume as well as
at the surface of a color pattern. Properties of effect pigments are described in
the next section, which show a typical color development in dependence of the
angle of observation, a dependence that is absent in absorption colorants.
2.2.1 Types and Attributes of Absorbing Colorants
According to a rough classification, colors can be produced by 15 different physical mechanisms [21]. In the case of non-self-luminous colors, these processes
are entirely attributable to energetic interactions of electromagnetic waves with
the bounded electrons of atoms, molecules, particles, or crystallites of the
color-producing material. With regard to absorption colorants, we first outline
44
2 Light Sources, Types of Colorants, Observer
some typical phenomenological properties of absorption pigments and afterward those of dyes. The color origin of absorption pigments can be reduced to
absorption and scattering processes. Such kinds of light interactions are called
selective if they are effective in a narrow range of wavelengths in the visible
spectrum. Light is scattered by pigment particles if at least two conditions are
met: first, the particle dimensions and the wavelengths of the irradiated light
are on the same order of magnitude; second, the colorant molecules show spatially separated electric charge distributions – the so-called multipoles. Details
of these are given in Sections 5.1.2 and 5.1.3.
Chromatic absorption pigments are also called colored pigments or sometimes merely pigments. They consist of inorganic and organic compounds
which, in either case, form crystallites of sometimes different types. The crystallite dimensions are typically of the same order of magnitude lesser as the
wavelengths of light. Because of the charge separations in multipoles, the morphological non-uniform crystallites sometimes conglomerate to form differently
shaped particles with sizes from 10 nm to as much as 1 μm in size.
All sorts of pigments – absorption as well as effect pigments – are insoluble in
a binder or any polymer matrix. The pigments are usually uniformly dispersible
in such materials although some need a suited additive for that. These colorants
are used not only, for example, for mass coloration of plastic materials, fibers,
paper but also for coloring of lacquers, pastes, and coatings of solids of quite
different surfaces. In synthetic high polymers, the pigments tend to congregate
in the amorphous regions and, therefore, additionally change the mechanical,
thermal, or even electrical properties of the compound. Of great importance
– with regard to color physical applications – are the covering capacity (also
called hiding power), color strength, and tinting power. Requirements for optimized incorporation of pigments are sufficient wettability, dispersibility, as well
as compatibility of the binding materials used, polymers, or additives, among
other things.
Inorganic pigments consist of oxides, sulfides, sulfates, silicates, chromates,
carbonates, and metal complexes, for example [22]. Compared to organic pigments, they are preferentially used on account of their distinct optical scattering
power and the typical high hiding power. In comparison with organic pigments, due to their simple and stable molecular structure, inorganic pigments
tend to have better rheological behavior as well as increased weather resistance. Characteristically, inorganic pigments are mostly dull colors with lower
color strength but with greater hiding power compared to organic colorants. A
multitude of absorbing colorations with desired color properties are, therefore,
achieved only with mixtures of inorganic and organic pigments.
With regard to the chemical structure, organic pigments are divided into azopigments, polycyclic pigments, and anthraquinone pigments. The outstanding
feature of organic pigments is their distinctive colorfulness or chroma in comparison to inorganic pigments. This generally comes with a high color strength.
2.2
Absorbing Colorants
45
Compounds of polycyclic structures, compared to molecules with azo-groups,
tend to disperse better in polymer binders, have a lower migration tendency, as
well as higher weather durability [23]. Table 2.3 shows the most commonly used
modern inorganic and organic absorption pigments, differentiated with regard to
the kind of the dominant color production mechanism.
White and black pigments assume a special role in industrial color physics.
White pigments stand out due to their nearly ideal scattering of light in the visible range. They are preferentially used for pure white, increase in the lightness
of any coloration, or covering of a background. On the other hand, the characteristic feature of black pigments is the dominant absorption. These pigments are
applied mainly in tiny amounts for black colors and for darkening of absorption
colors. With calibration series of white and black pigment mixtures, the calibration of the lightness scale is, therefore, carried out between minimal scattering
(pure black pigment) and maximal scattering (pure white pigment). An analog
consideration holds for the case of absorption (Section 6.1.1). It is further the
case that a really tiny amount of a black pigment improves the interference color
of transparent pearlescent or interference pigments; this is because the black
amount absorbs the complementary color produced of interference pigments.
Table 2.3 lists also fluorescence and phosphorescence pigments. These are
summarized by the term luminescence pigments. Both sorts absorb light normally at lower wavelengths in the range of X-rays, UV, or the visible spectrum;
they often also absorb energy from electron beams. After some short time, a
part of the absorbed quantum energy is reemitted but with longer wavelengths
(lower energy) according to Equation (2.1.2). Fluorescence radiation is emitted spontaneously and phosphorous radiation, in particular, has a delay in the
reemission. In contrast to phosphorescence (Section 4.2.6), fluorescence emission stops immediately after illumination.
Unlike absorption pigments, dyes are completely soluble in a solvent or in
a polymeric medium. The coloristic properties are essentially based on absorption. On account of the absence of scattering, dyes are normally transparent –
notable exceptions are dark dyes in high concentrations. Dyes consist nearly
exclusively of organic chemical structures. Typical groups of atoms with covalent bonds such as >C=C<, >C=O, or –N=N– (ethylene, carboxyl, or azo
group, respectively), called chromophores, are typically responsible for the coloration of the organic compounds. The π-electrons6 of these covalent bonds
absorb a fraction of the incoming light waves. The incorporation of further
molecular groups, the so-called auxochromes, causes a color shift either to
6 In chemical compounds π -electrons form a pair of electrons which belong together to two
different atoms.
Color production
Selective scattering/
selective
absorption
Pigment
Absorption pigment,
colored pigment
Oxides
Iron-II-oxide,
iron-III-oxide,
chromium-III-oxide,
chromium-IV-oxide,
chromium-VI-oxide pigments
Mixtures with oxide pigments:
cobalt blue, cobalt green, zinc iron brown
Chromate pigments
Chromium yellow, chromium orange, chromium
green; chromium titanate, molybdate red,
molybdate orange; copper chromate
Iron blue pigments
Iron cyanide blue
Cadmium, bismuth pigments, ultramarine pigments
Inorganic
Typical examples
Table 2.3 Typical modern inorganic and organic absorption pigments
Azo pigments
Mono-pigment, disazo-pigment,
β-naphthole pigment, naphthole
AS pigment, benzimidazolon
pigment, disazo condensation
pigment, metal complex pigment
Polycyclic pigments
Phthalocyanine, carbazole,
quinacridone, perylene, perinone,
pyrrolo/pyrrole, thioindigo
pigments
Anthraquinone pigments
Anthrapyrimidine, flavanthrone,
pyranthrone, anthanthrone,
dioxazine, triarylcarbonium,
quinophthalone pigments
Organic
46
2 Light Sources, Types of Colorants, Observer
Color production
Scattering
Absorption
Selective absorption,
emission within
10 ns
Selective absorption,
emission after
1 ms
Pigment
White pigment
Black pigment
Fluorescent pigment
Phosphorescent
pigment
Pure phosphors
Alkaline tungsten salts
Other phosphors
Alkali halogenoids, alkaline earth oxides,
alkaline earth sulfides, Barium oxide: doped
with Na, Mn, Ce, Sn, Cu, Ag; zinc phosphide,
cadmium phosphide, gallium sulfide, zinc
sulfide, cadmium selenide, gallium phosphide
Fluorite, uranylic salts, salts with metals of rare
earths
Carbon black, iron oxide black, copper chromate
Titanium dioxide (anastas, rutil), zinc sulfide, zinc
oxide pigments
Inorganic
Typical examples
Table 2.3 (continued)
Pure phosphors
Carbazoles
Other phosphors
Fluorescent organic substances,
embedded in crystalline matter
Oxinaphthaldazine, disazomethine
Aniline black
White plastic powders
Organic
2.2
Absorbing Colorants
47
48
2 Light Sources, Types of Colorants, Observer
higher wavelengths as with –NH2 and –OH groups (amino and hydroxyl groups,
respectively) or to lower wavelengths with –NH–CO–CH3 (ethylene-acid-amide
group), for example.
Dyes are subdivided into natural and synthetic compounds; see Table 2.4.
Dyes found in nature are generally known by common names like indigo, crimson, saffron, or alizarin, although they are prepared partial artificially today.
For reasons of product constancy, generally only synthetic dyes are applied.
Among synthetic dyes are azo-dye, anthraquinone dye, indigo dye, cationic dye,
phthalocyanine dye, polymethine dye, triphenylmethane dye, xanthene dye, and
fluorescence dye [24, 25]. Owing to their molecular double bond structures,
dyes show a poorer fastness to light and weather resistance in comparison to
pigments. The basic molecular interactions of fluorescence dyes and pigments
are described in the literature [26].
Table 2.4 Typical examples of natural and synthetic dyes
Dye
Typical examples
Natural
Indigo, crimson, saffron, alizarin
Synthetic
Azo-dye, anthraquinone dye, indigo dye, cationic dye,
phthalocyanine dye, polymethine dye, triphenylmethane dye,
xanthene dye, fluorescence dye
2.2.2 Pigment Mixtures and Light Transmittance
The wavelengths of the visible range which are not absorbed by colorants
make up a so-called complementary color. This color is the perceived color
of the absorbing dye or pigment; see Table 2.5. It can be seen in the table
Table 2.5 Spectral range of absorption, light color, and perceived complementary color of
absorption colorants
Rough spectral range of
absorption/nm
Light color of the spectral
range
Perceived complementary
color of the colorant
380–440
440–480
480–490
490–500
500–560
Violet
Blue
Green blue
Blue-green
Green
Yellow-green
Yellow
Orange
Red
Crimson
560–580
580–595
595–605
605–750
750–780
Yellow-green
Yellow
Orange
Red
Crimson
Violet
Blue
Green blue
Blue-green
Green
2.2
Absorbing Colorants
49
that the light and complementary colors reverse their roles at a wavelength of
about 560 nm. Over and above that, in Table 2.19 are given some pairs and
triples of complementary colors; some of them are partly demonstrated in Color
plate 1.7 These relationships concerning complementary colors are valid for
uniform spectral power distributions of the irradiated light similar to a xenon
discharge lamp. Complementary colors are arranged opposite (according to
Hering color opponent theory) in a color plane of the CIELAB system; see Color
plate 4.
As mentioned in the previous section, the realization of a desired color is
normally achieved with mixtures of different sorts of colorants. Apart from
coloristic aspects, concerns over the compatibility and color fastness of the components are in the forefront. Colorations of lacquers, plastic materials, or textile
fibers consist usually of mixtures with three up to six or more different colorants. Mixtures of different fluorescence dyes can be distorted by fluorescence
extinction if the quantum emission of one dye in the visible range causes a
fluorescence stimulation of a second dye in this range.
For the realization of a great number of different color shades, a selection
of at least 25 up to about 130 chromatic, white, and black absorbing pigments
has to be made and as much as of 110 effect pigments. Among the colored
absorption pigments, normally yellow and red should preponderate in comparison to violet, blue, or green shades; additionally, two to four brown colorants
are normally taken into consideration. Similar considerations should be taken
into account for dyes. The predicted color should match the reference color as
exact as possible. In the majority of cases, there are additional properties, such
as high color constancy or low metamerism, which need to be fulfilled. It is,
therefore, necessary to have a broad experience with the composition of the
colorant components and binding materials for mixing in order to achieve the
coloristic, processing, or basic performance conditions required with regard to
the reference color.
Color samples are termed as transparent, translucent, or opaque in dependence on their light transmittance properties. Requirements for transparent
colors are not only pure absorption and complete solubility of the used colorants
but also the refractive indices of the applied colorant matrix (e.g., solvents, binding agent, or plastic materials) have to agree with those of the used colorants.
Transparent optical media are characterized by the wavelength-dependent
absorption coefficient. This coefficient follows from the spectrometric measurements of the transmittance and a suitable approximation of radiative transfer in
optical media (Section 5.1).
A transparent chromatic layer is perceived by way of not only transmitted light but also reflected light. The accompanying reflectance comes merely
7 Color plates
are inserted between Chapters 3 and 4.
50
2 Light Sources, Types of Colorants, Observer
Table 2.6 Light transmittance and spectral quantities of color samples
Measuring
quantities
Determination
quantities
Examples
Transparent
Directed, diffuse
reflectance and
transmittance
Absorption
coefficient K
Liquids, inorganic,
organic glasses
Translucent,
translucent
nonopaque,
translucent
glimmering
Directed, diffuse
reflectance and
transmittance
Absorption
coefficient K,
scattering
coefficient S,
phase function p
Binders, foils of
partially
crystalline high
polymers, paper,
opal glasses
Opaque
Directed, diffuse
reflectance
Absorption
coefficient K,
scattering
coefficient S,
phase function p
Emulsion paints,
lacquers,
plastics, textiles,
ceramics, leather
Light transmittance
from reflection at the illuminated outer and inner boundary surfaces which is
caused by differing refractive indices. The magnitude of the reflected portion
follows from Equations (2.1.6), (2.1.7), (2.1.8), (2.1.9), (2.1.10) or (2.1.12). In
Table 2.6, three different sorts of color samples with regard to the degree of light
transmittance are listed along with some spectral measuring and determination
quantities.
Translucent color patterns such as turbid films, paper, or opal glass are
characterized by selective absorption and simultaneous scattering. Translucent
media are only light transmitting on a small scale; nonetheless, a colored
background is not completely covered. The light transmittance decreases with
increasing layer thickness, this is similar to transparent layers. Some organic
pigments of light yellow, orange, or red shade are translucent as are some
pearlescent and liquid crystal pigments. The scattering of light occurs at the
irregular surfaces or edges of the pigment particles and caused by the electromagnetic interactions with the multipoles of the pigment particles. In general,
scattering of translucent colors depends on the pigment sorts used, the chemical structure of the surrounds, the refractive indices, and the structure of the
boundary surfaces. Translucent colorations are particularly of interest for such
coloristic applications, in which the same hue is to be realized simultaneously
in a nearly transparent and almost opaque finish. In addition to reflectance
and transmittance, the characteristic quantities of translucent color samples are
turbidity and covering capacity (Sections 3.4.3, 3.4.4, and 3.4.5).
The theoretical modeling of radiative transfer in translucent systems can
actually be quite difficult. These complications are caused by the combined
processes of absorption and scattering, where the latter is anisotropic in some
2.2
Absorbing Colorants
51
cases. On the basis of the different optical effects, translucent materials can be
subdivided into the following groups:
ideal translucent: a directional ray is partly absorbed and diffuse scattered;
it exits the medium with lower intensity;
translucent diaphanous: the primary ray in the optical medium is surrounded by a halo8 ; the primary ray is more attenuated than in the ideal
translucent case;
translucent gleaming: the energy of the primary ray is spread out in an
intense halo; there is virtually no primary ray remaining at the second
boundary surface.
These different translucent states are best modeled with a multi-flux approximation. For this, in addition to absorption and scattering coefficients of the optical
medium, some additional optical quantities such as the phase function p, for
example, need to be taken into consideration (Section 5.1.5).
The majority of natural and artificial non-self-luminous colors are opaque;
they, therefore, appear impenetrable from the rear – a background is covered
completely by this kind of colors. In all opaque systems light scattering is
normally the dominant process, and it is accompanied by more or less distinct absorption. Scattering occurs isotropically without a preferred direction
or, the other extreme, anisotropic with a specific preferred direction. Increasing
scattering lowers the light transmittance and vice versa. The covering capacity of a coloration is, above all, caused by the scattering power of the pigment
particles. The single spectrometric measuring quantity of opaque materials is
the reflectance. The reflectance, in general, depends on the measuring angle
for many kinds of effect pigments. Extreme optical states result in mixtures
of absorption and effect pigments with different light transmittance. These are
most often implemented in lacquers or plastic materials for consumer goods.
2.2.3 Description of Color Attributes
Based on the discussion in the previous sections, it should be clear that the
color of absorbing colorants is caused by light interactions such as scattering
and absorption. On the other hand, the produced visual color sensation is by no
means completely characterized by those. The variety of different combinations
of wavelengths as well as the accompanying power distributions reaching the
eye results in many colors, which can be described by different color attributes.
For better understanding of the context, we use an analogy from acoustics.
8 This is a circular light spot encircling the primary ray; the halo of the Moon, for example,
results of light refraction at the ice crystals in the atmosphere.
52
2 Light Sources, Types of Colorants, Observer
A pure acoustic tone is unambiguous, physically described by its frequency
and amplitude. The same tone, produced from different music instruments, is
however surrounded by a typical sound spectrum. In a similar way, each nonself-luminous color is produced not simply by a single light frequency but also
from various spectral values of the visible spectrum.9
The different wavelengths simultaneously entering the eye are perceived as
a single color impression and not as separate single-colored wavelengths. This
entire color impression can be verbally described by characteristic terms. The
description or comparison of colors is used in color industry not only from physical or colorimetrical points of view but also according to coloristical attributes
[27]. The following enumeration, which is not to be considered complete, gives
some conventional terms for characterizing the color impression of non-selfluminous colors. The accompanying definitions and assemblies are, however,
not uniformly used in the literature:
hue, shade: the color property which is mainly described by adjectives such
as red, green, yellow, blue; hue and shade are terms equivalent to color
tone, or tint, see below;
relative color strength, relative tinting strength: the color economy of an
available colorant material relative to an arbitrarily chosen colorant of
equal or similar color;
color depth, color intensity: the color distinctiveness, which increases with
enhancement of the same colorant amount;
dullness: a characteristic color feature which can be described by an existing
amount of gray or black; it is the converse to brightness.
The quantitative determination of relative color strength is standardized
based on colorimetric criteria (Section 3.4.2). These instructions underlie the
formalism of the CIELAB or DIN99o color spaces. The following terms are
also used to denote a color point in color space:
lightness: a measure for the reflectance of a non-self-luminous colorant; the
reflection ratio of absorption colorants is standardized by the so-called
gray scale in which black is assigned to the value of 0 and white to the
value 1; fluorescent and effect colorants often have reflectance values
greater than 1, caused by the arbitrary fixing of the gray scale; selfluminous sources such as light sources or the sky are characterized by
the term brightness rather than lightness;
saturation: a quantity describing the colorfulness of colorants which does
not change by further increase of the colorant concentration;
shade, color tone: this corresponds to hue; equivalent terms are tint or tinge;
9 This metaphor is not to be confused with synesthesia, in which a physiological stimulus
induces a further stimulus, for example, colors are associated with music and vice versa.
2.2
Absorbing Colorants
53
chroma: an absorption colorant loses colorfulness with lower saturation;
chroma depends on both saturation as well as lightness because a tiny
amount of black reduces the colorfulness of a color.10
Common for characterization of color impressions are also adjectives and
their comparative forms; their meaning is somewhat equivalent to the terms
already given above. Here are listed properties in opposing pairs:
colored, chromatic: any color, such as yellow, orange, red, or green; it is
analogous to the term hue;
uncolored, achromatic: colors like white, gray, or black;
light, bright: a color with a high lightness amount; light colors have a high
reflectivity;
dark: colors of small or even zero reflectance;
brilliant, clear, pure: colors of both high hue and high lightness but missing
white amount;
pale, dirty, dull: colors of both minor hue and minor lightness.
A great number of non-self-luminous colors containing absorption colorants
can be directly manufactured with properties in the ranges of the last 12 listed
extreme color states. Some of the cited characteristics correlate also with typical special features of the corresponding spectral reflection or transmission
curve traces. The measured spectrum can sometimes be interpreted as a kind
of “finger print” of the accompanying color. Some of these properties can be
visualized by characteristic spectral reflection curves of absorption pigments,
for example, in Figs. 2.23–2.27. Some of these features can also be found by the
angle-dependent spectral reflection of effect pigments.
The spectral reflectance of a chromatic absorption color is generally characterized by either a significant maximum (e.g., violet, blue, green) or a steep
rise to higher wavelengths (e.g., yellow, orange, red) in the wavelength range
of the complementary color or rather natural color; see Fig. 2.23. The highest absorption exists in a wavelength range of a distinct reflection minimum;
backscattering, however, dominates in the range of maximal reflection or the
plateau region of the relevant pigment.
In contrast, an achromatic color shows a nearly constant spectral reflectance;
see Fig. 2.24. Ideally scattering white is represented in the visible range by a
constant reflection of 1.0 and ideal black of 0.0; gray takes intermediate values
depending on the content of white or black. The decrease of spectral reflection
for white or gray with shorter wavelengths is due to the tail of the UV absorption
of the underlying TiO2 pigment. The impression of white results exclusively
10 These four color terms can be visualized by geometrical quantities in both mentioned color
spaces and further ones; see Sections 3.1.3 and 3.1.4.
54
2 Light Sources, Types of Colorants, Observer
R(λ)
c
0.8
d
e
0.6
b
a
0.4
0.2
0
400
500
600
λ
700
nm
Fig. 2.23 Spectral reflectance curves of chromatic pigments: (a) blue, (b) green, (c) yellow,
(d) orange, and (e) red
R(λ)
a
0.8
0.6
b
0.4
0.2
c
0
400
500
600
700
λ
nm
Fig. 2.24 Spectral reflectance curves of achromatic colors: (a) white, (b) gray, and (c) black
2.2
Absorbing Colorants
55
R(λ)
2bt
0.8
2dk
1bt
0.6
0.4
1dk
0.2
0
400
500
600
700
λ
nm
Fig. 2.25 Spectral reflectance of bright and dark pigments: 1bt bright blue, 1dk dark blue,
2bt bright yellow, and 2dk dark yellow
R(λ)
0.8
a
0.6
b
0.4
c
0.2
0
400
500
600
700
λ
nm
Fig. 2.26 Spectral reflectance of different gray colors: (a) light gray, (b) middle gray, and
(c) dark gray
56
2 Light Sources, Types of Colorants, Observer
R(λ)
2br
0.8
2du
1br
0.6
0.4
1du
0.2
0
400
500
600
700
λ
nm
Fig. 2.27 Spectral reflectance of brilliant and dull pigments: 1br brilliant blue, 1du dull
blue, 2br brilliant yellow, and 2du dull yellow
from regular light scattering over the entire visible range. This is the case for
examples such as water vapor, clouds, or snow. Ideal black, on the other hand,
is caused by absorption of entire visible wavelengths.
Light (or dark) colors stand out either due to a high (low) reflection maximum
or a widened (narrowed) plateau region; a light (dark) gray shows a shift of the
reflection level to white (black); see Figs. 2.24 and 2.26. Most of the color-order
systems and the colored calibration samples for recipe prediction are based on
colored pigment mixtures with white and black colorants. It is remarkable that
the human eye provided by nature is more sensitive to color differences between
dark colors (violet, blue, green) in comparison to light colors (yellow, orange,
red). This is correlated with a low maximum respective high reflectance plateau
range.
The higher and steeper the rise of the curve to the plateau region or the
smaller the half-width of the reflection maximum, the more the color is perceived as brilliant, clear, or pure. Conversely, pale, dirty, or dull colors possess
a spectral reflection characterized by a lower and broader maximum or overlapping maxima, compare in Fig. 2.27 curve 1br with 1du for a blue pigment. The
spectral reflectance of a dull yellow, for example, shows a more flat peak profile
and a lower plateau range compared to a brilliant yellow, cf. curves 2br, 2du in
Fig. 2.27.
The terms outlined up to now are merely used to describe some typical coloristical properties of classical absorption colors or colorants. This vocabulary
2.2
Absorbing Colorants
57
cannot be directly carried over to effect pigments. Rather than absorption and
scattering, effect pigments produce new sorts of colors on account of different optical mechanisms; identical terms have, therefore, different meanings for
effect pigments than for absorption colorants. Metallic pigments, for example,
produce a characteristic metallic lightness, brilliance, or hue extinction. This
ambiguity is discussed in Sections 2.3.3 and 3.5.1.
2.2.4 Color-Order Systems
It is quite remarkable that the color sense of humans is capable of distinguishing
about 10 millions of colors. It is further important to note that, in addition to the
astonishing number of colors, a color can have different attributes; therefore, it
seems essential to have systematic classifications for such a tremendous diversity of colors. Such classification systems serve not only as an overview but also
as an improved communication about non-self-luminous colors, particularly
for their use in difficult applications. From each of the established color-order
systems, series of color samples exist for visualization. The antiquated color
classifications are certainly not ordered after uniform criteria [28, 29]. The
chronologically first systems were arranged based on features, which included
the actual knowledge about colors. Among the contemporarily used color-order
systems are to differentiate roughly two groups: systems on coloristic and on
colorimetric basis. In the following, we sketch the common four representative
examples of both groups.
The most important coloristic-order system is that of Munsell, established in
1905. It is simultaneously comprised of various companion features such as,
for example, precise nomenclature or systematic extension capability for additional colors [30]. The corresponding color patterns are ordered according to
the three properties hue H, value V, and chroma C in three dimensions in a
cylindrical coordinate system. The true significance of this collection are the
colored patterns which display a nearly constant color difference between neighboring colorations. This was developed without any colorimetric background
– an amazing for the beginning of the 20th century. In spite of the visually
nearly equal color steps, this color-order system was not accepted until 1976
as a basis of the CIELAB system. Experience with the Munsell system has
brought out critical disadvantages. Particularly unfavorable are the non-uniform
perceived color differences of bright and dark colors. In remedy of these shortcomings, the Munsell system was supplemented by an additional color pattern
in 1990.
The natural color system (NCS) was worked out in Sweden and is standardized there; it is based on the opponent color theory of Hering and is arranged
in pairs of the four chromatic colors red, green yellow, and blue as well as the
achromatic colors white and black [31]. The patterns are organized in color
58
2 Light Sources, Types of Colorants, Observer
spectra and color triangles after the three criteria blackness s, colorfulness c,
and shade Φ. They are grouped in the form of an atlas of 1,741 color patterns.
In spite of this great number, the NCS system is restricted in its applicability. It incompletely covers the color space, and additionally, colors with glossy
surface are inapplicably marked. Moreover, the arrangement pattern is visually
non-uniform. Without a measuring device, this color system is, therefore, only
suited for rough orientation in color space.
The so-called color index (C.I.) is suited for identification of colorants but
represents no real color-order system as in the discussion above. It simply consists of a list with unsystematically assembled dyes and absorption pigments.
These are partially denoted according to the origin (generic names) and according to the chemical constitution with natural numbers (constitution numbers)
[32]. This listing offers a certain aid only in a few cases, if, for example, some
of the colorants listed in the C.I. are to exchange with one another.
Strictly speaking, the widely distributed color registry RAL 840 HR in
Germany is also not a color-order system in a broader sense. This registry was
created to ensure that industrial colors are classified uniformly with defined
names and numbers for better communication between public agencies and producers of consumer goods. The color patterns were originally vaguely arranged
in view of coloristic criteria; in the meantime, a modification was undertaken
using the so-called DIN color chart, see below.
It should be added that contemporary color systems also consist of patterns
which change uniformly by a suitable technical parameter such as the concentration of the used colorants, for example. The corresponding inconstant changes
of hue, lightness, or chroma certainly make color perception and color comparison more difficult. A visual ascertainment of color differences is not ensured by
such systems.
In contrast to the order arrangements above, the DIN color chart is a
colorimetric-based color system [33]. It comes from the CIE chromaticity diagram; see Section 3.1.2 and Color plate 2. The color patterns are arranged with
regard to three properties, similar to the Munsell system. These color properties are denoted as darkness D, hue T, and saturation S. They correspond to the
∗ , and chroma C∗ of the CIELAB system (Section 3.1.3).
lightness L∗ , hue Hab
ab
The OSA-UCS system (Optical Society of America Uniform Color Scales) is
principally used in the USA. It consists of a total of 588 color patterns, from
which 12 colors at a time are positioned in the corners and one in the center
of a cubic octahedron [34]. With this system, a multitude of visual equidistant
color scales can be established; visually equidistant means that adjacent color
patterns always show the same visually perceived color difference independent
of color point in color space. This system cannot be directly transformed into
the CIELAB system; the same holds for the Munsell system, NCS system, and
the DIN color chart. A reliable determination of color differences is impossible
on the basis of the OSA-UCS system.
2.2
Absorbing Colorants
59
Accordingly, it is advantageous to fall back on a universal applicable colororder system, which, for chromatic as well as achromatic colors, has the implicit
metric of a color space. The RAL design system is organized on such considerations. It is based on the structure of the CIELAB system. The RAL design
system enables, with good approximation, the visual determination of color differences. The corresponding color collection is established as RAL design atlas
[35]. There exists also a collection of 70 RAL effect colors, which cannot be
classified as a definite color-order system.
2.2.5 Surface Phenomenon
The color attributes assembled in the next to last section are more or less an
expression of a subjective color perception. As already mentioned in Section
2.1.5, the entire color impression is certainly composed of at least two components: the light interactions in the volume and at the boundary surface of a
colored sample. In other words, the reflection or transmission from the volume
is superimposed on the boundary surface reflection. This reflection is caused
by different refractive indices at the boundary surface. Such kinds of boundary surfaces are present in paints, coatings, plastic materials, emulsion paints,
or ceramics. This distinction cannot be made for undefined surfaces such as of
textiles, uncoated papers, plasters, or suede leather.
The kind of surface reflection is also influenced by the structure of the
surface. A given color can exhibit a surface structure between two extremes:
matt: appears a rough (or structured) surface; this appearance is caused by
completely (or partly) diffuse surface reflection;
high-glossy: appears a very smooth reflecting surface; such a surface
induces only directed reflection, which is called specular reflection, specular gloss, or simply gloss. This behavior is described by the reflection
law.
Both the above surface properties should generally be interpreted as color
attributes.
For the illumination of a (color) pattern with directional light, the transition
between matt, half-matt, glossy, or high-glossy surfaces can be characterized by
the resultant diffuse or directed reflection with the aid of the reflection indicatrix. This is a plane polar diagram which represents the angle-dependent
intensity distribution of the light reflected from the surface. In reality, an indicatrix is in three dimensions. Four different indicatrices are shown schematically
in Fig. 2.28, each caused by a different sort of surface reflection. The diffuse
and directional reflection amounts are given by the shape of the envelope curve
and enveloping surface of the intensity distribution.
60
2 Light Sources, Types of Colorants, Observer
Fig. 2.28 Reflection indicatrices of different surfaces: (a) matt: purely diffuse reflection,
(b) half-matt: dominant diffuse, minor directed reflection, (c) glossy: predominant directed
and minor diffuse reflection, and (d) high glossy: exclusive specular reflection
A diffuse reflecting surface of high roughness is achieved by various treatments, for example, with the help of suited polymer matrices or ceramics or
pigment crystallites standing out non-uniformly from the boundary surface. In
addition, the use of embossing dies is possible with regular geometrical surface forms such as micro-spheres and micro-prisms or irregular linen and other
fabric structures. Further methods are sanding, etching, or physical vapor deposition (PVD). Certainly, the realization of ideal matt surfaces is exceedingly
difficult.
A matt surface appears normally somewhat lighter than a high-glossy surface
of the same material. This is caused by the higher reflection coefficient for diffuse light in comparison to that of directional and perpendicular incident light,
cf. Equations (2.1.8) and (2.1.12). The higher diffuse reflection is nearly independent of the absorption colorant sort. In the case of directional illumination,
however, the reflection is only influenced by the degree of surface roughness.
The matt surface of brilliant but dark-colored samples sometimes causes a minimal color shift. This phenomenon comes from the superimposed scattering of
pigments near the surface. The entire diffuse reflection at the surface of a colored
layer can, therefore, be composed of three components:
– immediate reflection at the boundary surface;
– scattering from particles near the surface;
– anisotropic or isotropic scattering from the volume.
The most of color physical problems are associated with the color component
originated from the volume because this shows the interesting light interactions
with the contained colorants. The result of a color measurement is, of course,
composed of the volume and surface components. This result must, therefore,
be corrected with regard to the surface boundary effect. This is achieved through
the implementation of the various theoretical concepts detailed in Sections 5.3,
5.4, and 5.5, among other things.
If the boundary surface contains no colorant particles, then the reflection
is given by the refractive index of the binder. The pigments can, however, be
2.2
Absorbing Colorants
61
located in or near the surface, for example, by high pigment volume concentration (PVC), blooming, or flooding. In such cases, the arithmetic mean of the
refractive indices of the involved materials is to be used. Such a surface boundary can have further color features, due to the fact that the refractive index of
most colorants is dispersive. This effect is named bronzing; it can be present
in printing inks, lacquers, plastic materials, or textiles, and can be avoided by
appropriate measures.
For unambiguous coloristic assessment of matt to high-glossy samples, it is
absolutely necessary to avoid the glare caused by specular reflection. Therefore,
the sample containing absorption colorants is always illuminated laterally at
an angle of 45◦ and viewed perpendicular to the surface; see Fig. 2.29a. The
reversed arrangement is also possible, but rarely used. In commercial light
booths with lamps of different illuminants (normally D65, A, FL 2, FL 11 simulators), the light sources are arranged laterally and glare-free as shown in the
mentioned figure. The color sample should be surrounded directly by a middle gray and the assessment should be performed by keeping the so-called CIE
reference conditions, cf. Section 3.2.2.
In contrast, the visual evaluation of the surface gloss is achieved with a fixed
light source and constant line of vision by tilting of the sample over a specular
Light source
Observer
Specular
reflection
a)
Color pattern
> 60°
b)
Fig. 2.29 Two different configurations of the three factors for color impression of absorption
colors: (a) for coloristical assessment and (b) for evaluation of surface gloss
62
2 Light Sources, Types of Colorants, Observer
reflection angle range; see Fig. 2.29b. A light booth should, therefore, possibly
have a tiltable support with angle scaling. The quantitative determination of
surface reflection is carried out separately using a gloss meter; the reflected
intensity is registered at several variable angles between normal to the surface
and greater than 60◦ .
In the case of curved substrate surfaces, for instance, car body components,
cans, bottles, or tubes, it is possible to pursue simultaneously gloss, color blending, and change of gloss in dependence of the observation angle. To achieve
comparable results, the radius of curvature of the substrate and the thickness of
the coating have to be the same for all color samples of a collection. In contrast,
coated curved substrate surfaces are absolutely unsuited for instrumental color
measurements.
The evaluation of the surface reflection of colorations containing effect pigments is particularly critical. The optical properties of a metallic paint coating,
for example, are essentially caused by specular reflection at the flake-shaped
metal particles. The flakes are primarily arranged parallel to the substrate surface. Therefore, specular reflection dominates, but it is superimposed by diffuse
reflection coming partly from the rough particle edges. For metallic pigments,
the angular distribution of the reflection depends also on the illumination angle
as well as the angle of observation.
As already explained in Sections 2.1.6 and 2.1.7, the color physical properties
of effect pigments are also extremely angle dependent. Compared to absorption colorations, the visual assessment of such colorations needs a much more
sophisticated procedure, cf. Fig. 2.30.
The observation for effect pigments is also normally performed using a fixed
light source, but the classical method needs two identical colorations, one kept
horizontal and the other rotated by an angle < 45◦ from this position; see
Fig. 2.30a. This procedure allows for the observation of the angle-dependent
change of lightness intensity. For flake-shaped metallic pigments, this angledependent change in reflected intensity is typical; it is the so-called lightness
flop.
The color changes of interference and diffraction pigments between the two
extreme observation angles is, however, termed as color flop. Figure 2.30b
shows the modern arrangement for visual evaluation of effect colorations. In
this configuration, the light source and the observer are fixed. Vertical movement of a color sample simultaneously changes both the angle of illumination
and angle of observation. Therefore, the observation of the color flop, for
example, needs only one color pattern and is carried out at the same surface
spot.
We have arrived thematically at the transition from absorption to effect pigments. These colorants have been used industrially since about 1970 and to an
increasing extent. In the following sections, we discuss the structure, morphology, and the spectral properties of the most important sorts of these modern
colorants.
2.3
Effect Pigments
63
Light source
Observer
a)
Effect Color pattern
b)
Fig. 2.30 Two different configurations for assessment of colorations containing effect pigments with fixed observer: (a) classical method (tilting): lightness flop and (b) modern
method (vertical movement): color flop
2.3 Effect Pigments
Effect pigments have broken new ground in color physics, especially with regard
to industrial-scale research, development, and application. The color production
of effect colorants is predominantly caused by anisotropic processes like single
or multiple reflection, interference, or diffraction. These processes are unrealized in absorption colorants. The generic term “effect pigment” is inadequate
because colors generated by absorbing colorants are also based on an optical
“effect”. However, flake-shaped pigment or shorter flake pigment is an accurate
expression for this sort of colorants. The generated color impression of effect
pigments is extremely angle dependent. This is a function of both the illumination and the observation direction. Effect pigments result in quite strange color
64
2 Light Sources, Types of Colorants, Observer
sensations for human color sense because our sense has evolved to perceive only
colors from absorption colorations. In a practical sense, effect colorants need
more extravagant manufacture methods in comparison to absorption pigments
and also a more extensive characterization, measuring techniques, application,
and processing.
All types of effect pigments consist of flake-shaped particles with a large
range of typical lateral dimensions between 1 μm and 1 mm. This is more
than 10 – 1000 times larger than that of absorption pigments. The flake thickness has values between 10 nm and 1 μm. On account of the flake form, the
resultant color effect is increasingly distinct with a more uniform morphology
and the more the particles are oriented in the binder parallel to the substrate
or surface. Like absorption pigments, effect colorants can be of inorganic as
well as organic nature. With regard to the processes of color production, they
are divided into four groups (cf. Table 1.1). For historical reasons, they are
named:
– metallic pigment;
– pearlescent pigment;
– interference pigment;
– diffraction pigment.
In the literature, pearl luster pigments are often subsumed to the interference
pigment classification [36]. The laws used to describe the optical properties of
metallic pigments are essentially geometrical optics; all other sorts of effect
pigments are generally described by wave optics.
Metallic pigments consist normally of a metal or an alloy of metals. The
typical metallic gloss is increasingly brilliant the more uniformly the flakes are
oriented parallel to the boundary surfaces of a coating. The so-called metallic
effect is mainly a consequence of the directional and diffuse reflection at the
surface and the edges of the flakes.
In contrast, pearlescent pigments consist of two or more layers with a high
index of refraction difference; the values normally range from 1.5 to 2.9.
The mostly used substrate is mica, but also metals or metal oxides are often
applied. The specific pearl luster depends on the permutation of the layers. This
luster originates from single or multiple reflections at the layer boundaries followed by interference of the light waves. Differing optical layers are behind
the general function of interference pigments; this does not require the use of
a mica substrate. An interference pigment subgroup is the so-called optically
variable interference pigments. The high ratio of refractive indices, in conjunction with different layer thicknesses, fans out the first or more interference
orders in such a way that a variety of interference colors are to observe angle
dependence.
2.3
Effect Pigments
65
The grating structure of diffraction pigments deflects the incoming light.
The resulting color effect can be attributed also to the wave nature of light.
The substrate consists of a highly reflecting or even ferromagnetic substance.
The substrate is vapor-coated symmetrically on both sides with several materials known from nanotechnology. The ferromagnetic particles can be oriented
with an external magnetic field before the crosslinking of a binder. The produced unusual but often impressive colors require that effect pigments undergo
a more subtle and closer examination and handling compared with absorption
colorants.
2.3.1 Types of Metallic Pigments
Metallic pigments, generally consisting of metal flakes, are employed mainly
on account of the metallic reflection from the flake-shaped particles. This kind
of reflection consists of superimposed specular and diffuse components which
produce unusual color effects compared with absorbing pigments. Conventional
metal flakes have mean lateral dimensions ranging from about 5 μm to nearly
50 μm, whereas the thickness varies between roughly 100 nm and 1 μm. In
some extreme cases, the particles have dimensions which are up to 10 times
higher. The ratio of thickness to diameter of the particle is called the form factor
and it extends from 1:50 to about 1:500. Metal flakes are used in paints, lacquers,
plastic materials, and inks; they are also employed in chemical products and for
sinter metals, building materials, explosives, or pyrotechnics, for instance, as
functional or chemically reactive particles.
In this text, we are mainly interested in the metallic reflection. This property
is caused, in simplified physical terms, by the fact that individual metal atoms
can easily release the bonding electrons. In lattice arrangements, the metal atoms
completely loose the valency electrons. These electrons form the electron gas
which is distributed among the remaining ions so that each ion is fixed on a
corresponding lattice position. On account of its interaction with the electrons,
an external light wave from a normal source cannot penetrate the very dense
electron gas. The majority of the light is rather reflected and the remaining
part is absorbed within a very small penetration depth. Reflection and absorption produce the typical metallic brilliance and characteristic natural color of
metals [14].
The change in electron gas density at the metal surface results in light
dispersion in the visible range, among other things. This causes a light-, gray-,
or low-colored metallic effect. The theoretical reflectivity of metals is given
by Equation (2.1.10). In Table 2.7, the indices of refraction n, absorption nκ,
reflection r(n,κ), and the melting temperature Tm are shown; these are for
metals that are most commonly used for metal pigments. In this listing, the
metals are arranged according to decreasing reflectivity. The given optical
66
2 Light Sources, Types of Colorants, Observer
Table 2.7 Reflectivity, refractive index, absorption index for perpendicular incident light at
wavelength of λ = 589.3 nm and T = 293 K as well as melting point of metals used for
metallic pigments [37]
Metal
Reflectivity
r (n, κ)
Refractive
index (n)
Absorption
index (nκ)
Melting
point Tm /K
Ag
Al
Au
Cu
Zn
Ni
Fe
Mo
Ti
W
0.99
0.912
0.888
0.804
0.768
0.664
0.586
0.575
0.565
0.524
0.052
1.181
0.280
0.493
2.74
1.71
2.91
3.40
2.09
2.83
3.91
6.99
2.91
2.80
5.77
3.61
3.58
3.56
3.11
3.02
1,235
933
1,336
1,356
693
1,726
1,809
2,890
1,933
3,683
quantities are for the middle of the visible Na wavelength of λ = 589.3 nm;
they will generally have different values for other wavelengths. The melting
temperatures of the given metals are higher than those of the highest flow
temperature of normal polymer melts. The refractive index is also subject to
dispersion; in cases of Ag, Au, and Cu it is valued n < 1. The phase velocity cp
is, on account of cp = c/n, inside these three metals higher than the velocity of
light c in vacuum; this is not in contradiction to the special theory of relativity
because only the group velocity – with which energy or signals propagate –
cannot exceed the velocity of light c. Clearly, the actual reflectivity is lower than
the theoretical one. The real reflectivity depends on the details of morphology
of the particles, especially the
– surface grade and edge roughness;
– particle size and particle size distribution;
– flake thickness;
– pigment orientation in the material of application.
In the context of metallic pigments, it is useful to emphasize the fact that
historical laxness in naming remains an issue. Terms such as aluminum bronze
or silver bronze instead of aluminum pigments, gold bronze or even the more
general metal bronzes, are still in widespread use today by pigment manufacturers, colorists, and even in modern literature [38–40]. Actually, aluminum bronze
consists of copper alloyed at most 12% aluminum; silver bronze is an alloy of
silver and tin; gold bronze is a solid blend of suitable amounts of copper and
zinc; genuine bronze, however, consists of copper alloyed with tin.
2.3
Effect Pigments
67
Apart from dispersion and particle size, the character of the metallic color
impression is influenced by further details. Among them are the chosen metal
or alloy, the manufacturing and processing method of the flakes, and the wettability in binders. In the following, we give a survey of the influence of these
parameters with regard to the visual perceived metallic effect.
First of all, the chosen metal is responsible for the brilliance of the natural
metallic pigment. The metallic colors change from light white (Ag, Ni), white
(Al – as a substitute for Ag), bluish white (Zn), orange-yellow (Au), and reddish
(Cu) to gray (Fe, Mo, Ti, W). These color attributes relate only to the metal
gloss and, therefore, have a different meaning from that which was outlined for
absorption pigments in Section 2.2.2. Additional natural metallic colors can be
realized using mixtures of metallic pigments: Ni flakes lighten and Fe particles
gray the metallic effect. Also alloys such as brass (alloy of Cu and Zn) are
suited for gold-yellowish to reddish color, for example. Metallic pigments are
manufactured with mixtures or alloys only if the required metallic effect is not
achievable using only conventional metal flakes.
The most commonly used metallic pigments from modern point of view are
given in Table 2.8. Uncoated metal flakes based on natural metals have the most
diversity. Particles with especially even surfaces can be manufactured using
the PVD method. For this, a polymer foil is vapor coated in vacuum with a
metal and afterward crushed at temperatures far below the glass transition temperature of the polymeric material. These flakes are termed as crushed PVD
films.
Due to modern developments, even colored metallic flakes can be manufactured. In these cases, a colored component is superimposed on the
Table 2.8 Classification of metallic pigments
Metallic pigment
Typical examples
Uncoated metal
flakes
Aluminum (“aluminum bronze”, “silver bronze”), copper, zinc,
copper/zinc alloys (70/30, 85/15, 90/10: “gold bronzes”),
copper/aluminum alloys (4–12% Al: aluminum bronze), iron
(austenitic steel, max. 11% Cr), nickel, tin, silver, gold, titanium
Crushed PVD films
Foils of polyethylene terephthalate, polystyrene, or polypropylene:
vapor coated with aluminum, chrome, magnesium, copper,
silver, gold (PVD procedure)
Flakes coated with
absorption
pigments
Inorganic or organic pigments in silicon dioxide or acrylate
coating fixed on aluminum or “gold bronze” flakes as substrate
(CVD procedure)
Partially oxidized
and oxide-coated
metal flakes
Partially oxidized from the surface aluminum flakes, copper
flakes, zinc/copper flakes (“fire colors”);
coated aluminum flakes: iron-III-oxide, tin oxide, zirconium
oxide, iron titanate, cobalt titanate
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2 Light Sources, Types of Colorants, Observer
metallic effect. There are two different methods for manufacturing. In the first,
absorption pigments are suitably fixed at the surface of the flakes by chemical
vapor deposition (CVD) [38, 39]. The second method is based on metal flakes
which are partly oxidized from the surface, or coated with metal oxides. Such
metal flakes produce an intense color effect, sometimes called “fire colors.”
These intense colors are caused by multiple reflections at the transparent outer
layers with varying refractive indices; the multiple reflected waves then interfere. Technically, such colorants are not metallic pigments in the strict sense,
rather just a multi-layered interference pigment on top of a metal substrate. In
most cases, the original metallic brilliance of the metal substrate is lost.
It must be noted that the chosen manufacturing method is of great influence
to the resultant coloristical properties of metallic pigments. For shaping of natural particles, the melt is pressed through a narrow nozzle of suitable geometry
with high pressure. Due to high flow velocities in the nozzle channel, often up
to 400 m/s, the velocity gradient leads to an atomizing of the melt into round
and contracting tiny droplets outside of the nozzle tip. After cooling, they are
transformed into flake-shaped particles; these are the resulting metal flakes.
The grinding of the solid particles is performed by two different processes.
The wet milling method of Hall uses white mineral thinner for liquid phase.
This simultaneously has the benefit of preventing dust explosions. In order to
prevent clumping or welding of the particles, long-chained fatty acids are often
added, typically 3–6% oleic or stearic acid. The dry milling method of Hametag,
however, works in a N2 atmosphere containing at most 5% O2 . For this method,
4–6% palmitinic acid or stearic acid is often used as separators.
The mentioned long-chained fatty acids, on the other hand, coat the entire
surface of the resulting flakes; this certainly changes their wettability especially
against binding materials. Because the end groups of the fatty acids are dependent of surface tension and behave either hydrophilic or hydrophobic, the metal
flakes flood or disperse uniformly in the binding agent. Figure 2.31 gives an
Metal flakes
Coating
Substrate
a) Leafing
b) Non–leafing
Fig. 2.31 Two different distributions of metallic particles in a painted layer: (a) leafing near
the surface and (b) non-leafing or nearly uniform distribution
2.3
Effect Pigments
69
illustration of two flake arrangements in a binder, the first is called leafing
and the second non-leafing. The tendency to form the leafing arrangement is
stronger with the lowering of the wetting with the surrounding polymer. Leafing
flakes result from coating with stearic or palmitinic acid; non-leafing particles
are usually obtained with oleic acid, for example. It is worth mentioning that
the sort of wetting is generally correctable afterward with suitable additives. If
the flakes are dispersed in the melt state of plastic materials, the leafing is generally avoided due to the high structural viscosity of the melt.11 A measurement
method for determining the leafing behavior is detailed in the literature [41].
Leafing pigments incorporated in transparent binding agents show high brilliance due to a uniform and constant reflection. The abrasion resistance of the
surface film is often reduced and, therefore, an additional top coat is usually
applied. In contrast, the parallel and compact flake arrangement often behaves
like an optical or mechanical barrier: in addition to visible wavelengths, it
reflects UV and IR radiation and can also inhibit the diffusion of gases or vapors.
Leafing flakes are, therefore, often used for reflection of UV and IR radiation
as well as corrosion prevention pigments. Further non-colored applications of
metallic pigments are given in Appendix 7.1.1.
2.3.2 Morphology of Metallic Particles
As already mentioned, the metallic character is especially influenced by the
morphology of the flakes. The wet milling procedure of Hall predominantly
produces particles of irregular and uneven surfaces along with high edge errors
– they are, therefore, quite accurately called cornflakes. Typical aluminum cornflakes are shown in Fig. 2.32. The picture was taken with a scanning electron
microscope (SEM). The irregular particle edges result from fracture from other
flakes during the milling process within the ball mill. The uneven surfaces are
caused by abrasion of the coarse edges of colliding and pressed particles. At
the particle surfaces shown in Fig. 2.32, it is possible to discern some remains
of broken edge zones and indentation traces of striking balls. Both the uneven
surface structure and the rugged particle edges are responsible for the typically
increased diffuse light scattering of cornflakes. The light reflected from such
flakes is composed of a directional and a superimposed scattering component.
The accompanying indicatrix corresponds to that of Fig. 2.28c. The amount of
diffuse reflected light is increased, therefore, with more uneven particle surfaces
and rugged flake edges. With increasing particle scattering, there is a reduction
of brilliance, that is, “it turns gray.”
11 Structural viscosity means that the viscosity has a nonlinear dependence on shear velocity;
this is in contrast to constant Newtonian viscosity.
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2 Light Sources, Types of Colorants, Observer
Fig. 2.32 SEM picture of typical cornflake particles of aluminum (source: Eckart Werke
GmbH, Velden, Germany)
Sophisticated grinding techniques with metal brushings or polishing pastes
have been used since about 1980 to reduce this brilliance loss. These techniques
allow for the manufacture of thicker metal flakes with relatively plane surfaces
as well as even or rounded edges. Particles of this kind are often called silver
dollars, of which an example is shown in Fig. 2.33. These sorts of flakes reflect
light with a dominant directional component accompanied by a considerably
lower scattering. A paint film with silver dollars and clear top coat is, therefore, lighter and more brilliant than the one with cornflakes of the same metal
and identical particle size distribution. Silver dollar pigments are preferentially
employed in high-quality systems such as automotive coatings, the so-called
metallics. They are also used in high polymer materials and printing inks.
Shear stable flakes of upward 10 times the particle thickness of cornflakes
can be realized in order to withstand processing techniques of high pressure or
high shearing stress (e.g., ring main pumps, injection molding, blow molding, or
extrusion). Particles with nearly plane surfaces and high brilliance can also be
manufactured by PVD coating of thin polymer foils. They do, however, exhibit
an undefined breaking edge. A representative example is shown in Fig. 2.34.
In addition, it is possible to produce metallic pigments of constant thickness and of geometric regular shapes. These sorts of particles are called glitter
flakes. To describe the glitter effect, the terms sparkle and glittering are also
used. Both expressions are often utilized simultaneously, although they have
somewhat different meanings.
2.3
Effect Pigments
71
Fig. 2.33 SEM picture of silver dollar pigments of aluminum (source: Eckart Werke GmbH,
Velden, Germany)
Fig. 2.34 Metallic pigments of PVD metal coated and broken polymer films (source: Eckart
Werke GmbH, Velden, Germany)
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2 Light Sources, Types of Colorants, Observer
Sparkle is the property that single flake particles are directly recognized visually due to their expanded planar reflection surfaces. This is typically the case
for mean particle sizes of about 30 μm and larger. The metal flakes are perceived separately on account of the surface reflection contrasting to the darker
surroundings. They behave as isolated microscopic mirrors. In contrast to glittering, see below, neither the morphology nor the lateral dimensions of sparkle
particles are necessarily uniform. The phenomenon of sparkle (also referred to
as sparkling, optical roughness, micro-brightness, glint, or diamonds) is present
in quite an assortment of effect pigments and is particularly observable with
directional light; see also Section 3.5.1.
In contrast, glittering is exclusively due to particles of uniform and regular
geometry. These particles are manufactured in the form of squares, rectangles,
rhombs, or circles by cutting or punching-out from metal foils or metallized
polymer foils. In Fig. 2.35 an example of nearly quadratic aluminum glitter
flakes cut from ribbons with a band knife is shown. Glitter flakes are of nearly
uniform lateral dimension compared with conventional manufactured metallic
pigments in ball mills. They are produced with sizes of 50 μm up to as much as
2 mm. They are generally at least 10 times thicker than usual cornflake or silver
dollar particles.
With regard to quadratic and rectangular glitter flakes, often specifications
such as “2 × 2” or “2 × 4” are used. These can be interpreted as follows:
Fig. 2.35 Almost quadratic glitter flakes cut with a band knife from foil strips of aluminum
[38] (source: Rapra Technology Ltd, Shawbury, UK)
2.3
Effect Pigments
73
multiplication of each of these numbers with one thousandth inch (2.54 ×
10–3 cm) gives the middle lateral extension of the corresponding particles. This
means, for the given examples, that the glitter flakes have dimensions of 50 ×
50 μm and 50 × 100 μm, respectively. It is also worth noting that with extreme
process control in the Hall technique, it is also possible to produce spherical pigment particles with diameters as large as 700 μm. Such particles have, however,
not the appearance of glitter flakes [38].
Colored metallic pigments offer an exceptional optical enlargement of usual
metal pigments. These consist either of metal flakes covered by absorption pigments or metal flakes partially oxidized from the surface or oxide-coated metal
particles. In the first case, the metal particles are coated with silicon dioxide or a
polyacrylate containing inorganic or organic absorption pigments. In Fig. 2.36,
there is an SEM photograph of aluminum flakes with a silicon dioxide coating
of embedded inorganic pigment particles. This picture shows not only the coarse
surface structure of the flakes but also the size proportion of the absorption
pigments having only a few nanometers to the around two orders of magnitude larger sized metal flakes. From this difference in size, the typically higher
scattering power of absorption pigments compared to effect pigments is also
understandable.
Colored metal effect pigments consist also of partially oxidized or oxidecoated flakes, which are manufactured using the CVD procedure. Partially
Fig. 2.36 Aluminum flakes coated with silicon dioxide and embedded inorganic pigment
particles (source: Eckart Werke GmbH, Velden, Germany)
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2 Light Sources, Types of Colorants, Observer
20
100
10
50
Cumulative frequency curve
Relative frequency %
oxidized flakes of aluminum, copper, or zinc/copper are generally preferred.
Iron-III-oxide-coated aluminum flakes are also common. All of these pigments
produce particularly impressive reddish colors – and are, therefore, also called
fire colors. These unusually striking colors are due to the combination of three
effects: first, absorption and scattering of copper, zinc, or iron-III-oxide; second, interference caused by the layer construction; third, metallic reflection of
the particles.
Already the concept of the glitter flakes suggests that the character of the
metallic effect is particularly dependent on the particle size. All particles,
however, are not of the same size; therefore, the metallic effect is in general
influenced by the particle size distribution. On the other hand, the size distribution can be controlled partly by the milling and sieving process; from these
manufacturing steps, an asymmetrical particle size distribution with respect to
the mean results. This distribution has a higher amount of smaller particles, cf.
Figs. 2.37 and 2.38. The mean, in this context, is usually denoted by the quantity
d50 or D[v; 0.5]. This quantity, for example, d50 = 25 μm, indicates that 50%
volume of all particles are higher or lower in size than this near center value.
The subtle properties of the metallic character even depend on the width of the
distribution.
In addition to the use of scanning electron microscopy, the laser granulometry
method has proven quite useful for the determination of the mean particle size
of effect pigments and the accompanying size distribution. The laser method is
founded on scattering and diffraction of the particles suspended in a suitable
liquid. This so-called laser granulometrical operation is suited only as a relative
method, this is, not as an absolute method.
d50
0
10–1
0
100
101
102
d /μm
Fig. 2.37 Curves of particle size distribution and of cumulated frequency of an aluminum
cornflake pigment with same value of d50 ≈ 20 μm as in Fig. 2.38
2.3
Effect Pigments
75
20
100
10
50
Cumulative frequency curve
Relative frequency %
The size distribution of effect pigments is characterized by the so-called
width W, which is given by the quotient W = (d90 − d10 )/d50 > 1. The quantities d10 and d90 mean that 10 and 90% volume, respectively, of the particles have
lateral dimensions of Φ ≤ d10 and Φ ≤ d90 . A narrow distribution with low W
produces a more brilliant metallic effect in comparison to a broader distribution
of equal d50 value; see Figs. 2.37 and 2.38. The concentration of small particles is lower in a narrow distribution than in a broad distribution. However, the
greater the number of small-sized particles present, the more gray and paler the
metallic effect appears. Of course, with smaller flakes edge scattering preponderates, and in addition, the parallel configuration of the flakes is more distorted
than with larger sized particles.
The metallic reflection of typically narrowly distributed silver dollar pigments is consequently more distinct than that of traditional cornflakes.
Cornflakes show a significantly broader particle size distribution. Among modern metallic pigments, silver dollar flakes of aluminum are the most light and
most brilliant particles. According to Figs. 2.37 and 2.38, there is always an
elevated number of particles smaller than 5 μm.12 This increased content of
fine particles is unavoidably caused by the grinding process and is quite typical
for the manufactured metal powders. The fine particles give rise to a scattering
component which reduces the metallic brilliance.
Finally, the production of the metallic effect is also influenced by the orientation of the particles in the polymeric surrounding medium. The particle
d50
0
10–1
100
101
102
0
d /μm
Fig. 2.38 Curves of particle size distribution and of cumulated frequency of an aluminum
silver dollar pigment with same value of d50 as in Figs. 2.37
12 Particles
smaller than 5 μm contribute to particulate (dusty) matter.
76
2 Light Sources, Types of Colorants, Observer
alignment is primarily determined by the processing techniques used. The maximum possible metallic reflection is achieved by complete flake parallelism to
the bounding faces of a plane parallel layer; this is equivalent to a mirror. Local
perturbations of particle alignment parallel to the paint coating can be caused by
turbulent motion of the solvent during evaporation; such kinds of heterogeneity
lead to mottling or flocculation. Both kinds of visible non-uniformities are also
known from coatings with absorption pigments. Lacquers with low solid-state
content display a more distinctive metallic effect than systems with higher solidstate content (so-called high solids). This is because the lower viscosity makes
the orientation of the flakes easier.
During processing of metallic or other flake-shaped pigments in printing inks,
the absorbability of the stock can influence the parallel orientation of the flakes.
But the slower the diffusion rate of the solvent, the more time available for
parallel alignment of the particles. In high polymer materials, the flake pigments
orient themselves according to the prevailing flow conditions. The alignment of
the particles direct after surface formation is nearly maintained during cooling
time and concurrent volume contraction. The collision of two melt fronts causes
a flow line, at which the particles orient – visibly – parallel to the flow fronts.
Flow lines can be avoided generally with suitable manipulation of the fusion in
the mold [38].
2.3.3 Coloristic Properties of Metallic Pigments
The geometry, morphology, and reflection of metallic pigments produce a variety of unusual color effects which need to be described in detail. The most
important coloristic characteristics of metallic pigments are given in Table 2.9.
From this apparent arbitrary division it is possible to discern two groups: in
the first group, the indicated effect properties increase with expanding lateral
dimension of the particles and for the second group, they decrease. This inverse
behavior and the complex color attributes of metallic pigments demand a
closer examination in comparison to the more simple properties of absorption
pigments.
First, the five special features of the first group will be discussed. The metallic
character or metallic gloss depends on the ratio of the directional to the diffuse
reflection. Both components are directly proportional to the quotient of the surface to the edge length of the metallic flakes. The higher this ratio, the more
distinctly developed the metallic character. Small particles normally give rise to
a higher edge scattering and, therefore, produce a poor and gray metallic effect.
Conversely, flakes with a lateral dimension greater than 30 μm show a striking metallic character. In general, the narrower the particle size distribution, the
more distinct the metallic luster.
2.3
Effect Pigments
77
Table 2.9 Correlation between particle size and coloristical properties of metallic pigments
(other used terms in brackets)
Assessment of characteristic
particle diameter d50 , non-leafing pigments
Characteristic of metallic
pigment
≤10 μm: fine pigments
Cornflakes
≥30 μm: coarse pigments
Silver dollars, glitter flakes
Metallic character (metallic
gloss)
Brightness (brilliance)
Reflection brightness
(whiteness)
Sparkle, glittering (optical
roughness)
Graininess (coarseness,
texture)
Insignificant, matt, gray
Quite distinct, brightened
Low
Minor
High
Enhanced
Invisible
Visually noticeable
Low
Visible
Lightness flop (flop, flip,
travel, two-tone)
Hue extinction
Covering capacity (hiding
power, opacity)
Distinctiveness of image
(DOI)
Light
Dark
Enhanced
Enhanced
Low
Low
High
Minor
The brilliance of metallic pigments is, in essence, caused by the directional
reflection component. Metallic flakes, therefore, appear all the more brilliant the
higher the directional reflected light amount and the lower the diffuse reflection
component. The brilliance, and consequently the directional reflected component, is reduced with smaller and more uneven surfaces of the pigments,
with broader particle size distributions and with greater irregularities in particle
orientation in the surrounding polymer material.
The reflection brightness or whiteness characterizes the lightness of the
metallic effect. This property is a measure of the total reflected light and is
composed of the directional and diffuse components. Consequently, reflection brightness differs from lightness of absorption pigments, which is due to
scattering and absorption. In connection with effect pigments, the term reflection brightness has, therefore, a quite different meaning from the lightness of
absorption colorants (although both quantities are determined with the same
measuring and evaluation system). In fact, the spectral reflection of metallic
pigments behaves similar to that of white/black mixtures of absorption pigments. Metallic pigments certainly show a key difference: the spectral reflection
depends on the angle of illumination and direction of observation.
This angle dependence is shown clearly, for example, by the reflectance of
an aluminum cornflake pigment in Fig. 2.39. In this illustration, the reflectance
78
2 Light Sources, Types of Colorants, Observer
R (%)
150
100
15
25
50
45
75
110
0
400
500
600
λ /nm
μas /degree
Fig. 2.39 Spectral reflectance of a cornflake aluminum pigment in dependence of the wavelength λ measured at aspecular angles of μas = 15º, 25◦ , 45◦ , 75◦ , 110◦ ; illumination angle
β = 45◦
R is plotted in dependence of wavelength λ for five standardized aspecular
measuring angles μas and an illumination angle of β = 45◦ .13 With increasing measuring angle, the reflectance behaves similar to that of light white and
middle or dark gray, cf. Figs. 2.24 and 2.26. For angles steeper than μas ≈ 75◦ ,
the reflectance remains at a low level, the metallic effect appears dark gray [42,
43]. On the other hand, the reflectance increases exponentially for the aspecular angle of μas = 0◦ . This drastic change in brightness in dependence on the
observation angle is characteristic for metallic flakes; it is termed as lightness
flop or short flop (see below).
The reflectance increase near the specular angle can be further raised, within
limits, with a narrower particle size distribution or altogether larger sized flakes.
Measured reflectance values higher than 100% are absolutely usual and produce
no inconsistency with conservation of energy. Because of the lack of suited
and corrosion-resistant metallic standards, the reflectance scale is based on the
reflectance of a white (scattering) standard which is interpreted as a reflectance
of 100% (Sections 2.2.3 and 4.1.2). Real effect pigments can have reflectance
values up to about R = 800%.
13 For
nomenclature and counting of angles, see Section 4.1.2, Figs. 4.5 and 4.6.
2.3
Effect Pigments
79
Metallic pigments of irregular lateral dimension greater than about 30 μm
produce a phenomenon termed as sparkle in the last section. This effect is also
called sparkling or optical roughness. For particle dimensions of this size or
larger, the naked eye can distinguish single flakes of nearly equal orientation
at the surface of a coating or plastic material. This is caused by the increased
intensity of directionally reflected light at the larger particle surfaces (similar
to parallelized crystals of an illuminated snow surface). As a consequence of
the distorted orientation of the flakes, sparkling changes in dependence on both
the illumination and observation angle. Leafing flakes develop no sparkling in
dependence of the particle size because nearly all flakes have an alignment parallel to the surface of the coating or the plastic material. Sparkle is not restricted
to metallic pigments and can be present in other sorts of flake-shaped pigments.
This striking feature depends, e.g., on the size, the sort, the surface curvature,
and the content of the effect pigment in a coloration.
If the illumination is switched from directional to diffuse, the sparkling disappears completely and turns into a kind of graininess of the particles. Under
this lighting condition, only a kind of fixed snowing picture is observable near
the surface of the coating. This phenomenon is also called coarseness, texture, or
vivid “salt and pepper” and is independent of observation angle. The impression
of graininess depends on the size and type of the flakes, orientation irregularities,
or clustering of the pigments during processing.
Now, consider the second group of properties listed in Table 2.9. The abovementioned lightness flop (also light to dark flop, flop, flip, travel, two-tone) can
be regarded as the most important and visually most striking property of metallic pigments. This term characterizes the decrease in lightness that a metallic
coloration shows under diffuse illumination between two extreme angles of
observation, especially at angles for perpendicular observation and an angle
greater than 60◦ with regard to the normal of the surface (cf. Fig. 2.30a).14
The lightness flop is influenced by three primary factors: first, the flakeshaped pigment morphology, second, the surface and edge formation, and third,
how well the flakes are ordered parallel to the surface boundaries of a layer.
During observation perpendicular to the surface, the light enters directly the eye
after interactions with the flakes. The observer registers the reference lightness.
Now, for angles nearly parallel to the surface, the light path through the layer is
longer. For this reason more interactions can take place with the particles of the
layer, that is, at the surface or edges of the flakes. Due to this, light is increasingly scattered or reflected out of the line of observation and, therefore, only a
small amount of the interacting light reaches the eye. This results in a registering
of a reduction of lightness in comparison to the perpendicular observation.
14 Perpendicular observation means, in practice, that observation angles of β = ±20◦ ,
ν
referred to the vertical, are permitted.
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2 Light Sources, Types of Colorants, Observer
This flop is termed as light if only a small lightness difference is observed
between both extreme observation angles. It is, however, called dark if a large
lightness difference is registered. For finer and irregularly shaped flakes (e.g.,
cornflakes), for broader accompanying particle size distribution, and for greater
particle disorder in the layer, the flop is lighter. Conversely, the flop is the more
dark, for greater evenness of the particle surfaces, for more rounded flake edges
(silver dollar flakes), for narrower size distributions, and for more consistent
parallel orientation of the particles to the surface boundary of the layer. The
lightness flop can be altered afterward to some degree by adding inorganic or
organic absorption pigments (see Table 2.10).
Table 2.10 Lightness and color flop of effect colorations
Flop kind
Flop character
Effect pigment/
absorption pigment
Lightness
flop
Light
Metallic pigment
Metallic pigment and
absorption pigment
Dark
Metallic pigment
Metallic pigment and
absorption pigment
Color
flop
Colored
Absorption pigment
Absorption and
pearlescent
pigment
Interference pigment
Diffraction pigment
Typical examples
Fine non-leafing cornflakes,
eventually with orientation
distortion medium
Scattering, inorganic, and
organic; for example, titanium
dioxide, chromium titanate
Coarse non-leafing silver dollar
flakes, normal silver dollar
flakes, PVD flakes
Transparent, inorganic, and
organic
Blue with green flop:
phthalocyanine pigments of
neutral color flop; blue with
red flop: α/-phthalocyanine
pigments
Combination of hiding
absorption and transparent
pearlescent pigments,
nano-titanium dioxide
Interference pigments with
extreme color flop: LCP, flakes
coated with silicon dioxide,
aluminum oxide,
iron-III-oxide, magnesium
fluoride
Aluminum or nickel substrate
PVD coated with
chromium/magnesium fluoride
or magnesium fluoride/silicon
dioxide
2.3
Effect Pigments
81
The phenomenon of lightness flop can be examined quantitatively by a gloss
meter. The usual measuring angles μν = 20◦ , 60◦ , 85◦ with regard to the normal of the surface are certainly not sufficient. This is already clear from the
angle-dependent reflectance measurements in Fig. 2.39. A reliable characteristic value describing the lightness flop of a single-layered metallic formulation
is the so-called flop index; however, for clear-over-base paints, the so-called
metallic value is used (Section 3.5.1).
As mentioned, some metallic systems are mixed with absorption pigments
for coloring or covering of the background. These systems have a more or less
colored flop; see Table 2.10. Mixtures with absorption pigments always result in
a lighter flop compared to the natural metallic pigment. This effect is generally
called color flop.
Mixtures of pearlescent and metallic pigments normally produce a lighter
flop than the corresponding single natural pigments. However, the brilliance is
usually raised at perpendicular observation. This behavior can be reversed with
suitable pigment combinations. The color flop of interference and diffraction
pigments is generally accompanied by a distinct color change. This change is
mainly due to the interference or diffraction maximum of first order (Sections
3.5.3 and 3.5.5).
A particular kind of color flop is given by a mixture of a metallic flakes
with titanium dioxide, provided that nanoparticles of the rutil modification are
used. The observable minor color shift caused by the nanoparticles is generated by the selective scattering of waves in the region of blue wavelengths; this
special phenomenon is called frost effect [44]. Such a layer has a yellowish
color at top view but for a flat angle of observation, a bluish color impression results. Accordingly, the shorter blue wavelengths are more scattered than
the other longer wavelengths, in agreement with Rayleigh’s law (2.1.3). This
comparatively low effect is also observed with other absorption or pearlescent
pigments of lateral dimensions in the nanometer range. Altogether, the color
flop of a formulation can be controlled within limits by adding small amounts
of nanoparticles. Certainly, the frost effect lowers the entire brightness of the
relevant coloration.
The next property of interest in Table 2.9 is the hue extinction. This feature characterizes the capability of a metallic pigment to change or to cover
completely the natural color of an absorption pigment incorporated into a formulation. In the literature [39], this ability is called “hue saturation,” which is
again misleading, because this term implies a saturation of the relevant absorption colorant. The extent of the hue extinction is related to the covering capacity
of the metallic particles. In this case, for metallic particles this term has the
same meaning as it does for absorption pigments (Section 3.4.3). Both the hue
extinction and the hiding power are improved with smaller cross sections of the
particles, broader particle size distributions, larger flake thicknesses, and denser
packing of the flakes.
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2 Light Sources, Types of Colorants, Observer
Finally, there is the so-called distinctiveness of image (DOI). In addition to
lightness flop and hue extinction, this property lists among the central characteristics of single as well as clear-over-base paints of metallic coatings. The DOI
value represents the uniformity of the observable metallic reflection. It depends
mainly on the particle size and orientation of the flakes in a layer. The distinctiveness of image is again improved by smaller particles and more highly
parallelized grade of the flakes. The DOI value of large-sized flakes nearly
correlates with the glittering effect. The determination of the DOI value by
measurements is outlined in Section 3.5.1.
2.3.4 Sorts of Pearlescent and Interference Colorants
The color production of pearlescent and interference pigments is essentially
based on constructive interference. Pearlescent pigments imitate the nacre luster
of natural pearls. The brilliant colors and unique luster are due to superimposed
light interactions such as absorption and multiple reflection at different boundary surfaces of the particles. Interference pigments generate substantially more
brilliant colors than pearl luster pigments. The terms pearlescent and interference pigments are often wrongly used as synonyms for both pigment sorts,
although only pearlescent pigments have the typical luster of natural pearls
coming from the depths to the surface.
The particles of pearl luster and interference pigments consist of layers with
different refractive indices. The layer thicknesses are on the order of magnitude
of visible wavelengths. The entire flake thickness varies from about 30 nm to
1 μm and the mean lateral dimension of the transparent to opaque pigments
extends – similar to metallic flakes – from about 5 to 300 μm. Pearlescent,
interference, and diffraction pigments can also exhibit sparkling. This sizedependent phenomenon is, in this case, generally darker than the sparkle of
metallic pigments because the reflection is caused only by the difference of
refractive indices instead of metallic reflection.
The color-producing properties of pearlescent, interference, or diffraction
pigments are dependent on the particle geometry, especially on the interfering
light interactions, and the color physical conditions in the particle surrounding. According to Equations (2.1.15), (2.1.16), (2.1.17), (2.1.18), (2.1.19), and
(2.1.20), the interference laws are functions of the wavelength λ, the refractive
index n at the interface, the thickness d of each single layer, and the observation or interference angle α z . These parameters can be tuned in such a way that
only the first interference order (z = 1) occurs in the range of normal observation angles. In this case, the higher orders can be neglected or are simply not to
observe.
The incoming light waves are partly reflected at each boundary surface of a particle, cf. Fig. 2.16. The constructive interference of the waves
2.3
Effect Pigments
83
produces the matt to high brilliant color appearance. The interference color is
observed at the specular angle on the illumination surface and the complementary color is transmitted by transparent flakes. Each single pigment, therefore,
behaves as an interference filter, which the incoming light waves split up into a
reflected interference component and a complementary transmitted or absorbed
component.
As a result of the different refractive indices at the interfaces as well as the
morphology of the particles, the following light interactions together contribute
to the color appearance of pearl luster and interference pigments:
– constructive interference produces the sometimes intense colors which change
in dependence of the angle of observation; the different colors and the angle
dependence are given by the refractive indices, the thicknesses, and the
number of layers;
– single reflection at interfaces causes part of the glossiness;
– multiple reflection at the different interfaces of the transparent or translucent
layers causes the typical luster “from the depths” of pearlescent pigments;
– scattering at the edges or rough surfaces of the particles leads to matt
interference colors;
– absorption reduces the brilliance; it depends on the layer material.
Table 2.11 shows the customary substances from which pearlescent and
interference pigments are composed. The materials are ordered according
to increasing values of refractive index nD . In comparison, air at a pressure of 1.0 bar at room temperature T = 298 K has a refractive index of
only n = 1.000272. The pigment particles consist of at least three different
Table 2.11 Refractive index n of substances used for pearlescent and interference pigments;
λ = 589.3 nm, T = 298 K [40, 45, 46]
Substance
Special terms
Refractive index n
Synthetic high polymers
MgF2
Proteins
SiO2
Alumina silicate
CaCO3
Al2 O3
Guanine, hypoxanthine
Pb(OH)2 2PbCO3
BiOCl
Fe3 O4
TiO2
α-Fe2 O3
Organic materials
Magnesium fluoride
Proteins
Inorganic glasses
Mica, muscovite
Aragonite
Aluminum oxide
Natural pearl essence
Basic lead carbonate
Bismuth-oxide chloride
Magnetite
Anastas/rutil
Hematite
1.35–1.70
1.384
1.40
1.458
1.50
1.68
1.768
1.85
2.00
2.15
2.42
2.5/2.7
2.88
·
84
2 Light Sources, Types of Colorants, Observer
materials. Because the relevant substances are anisotropic crystalline, the indicated n values represent a mean. The refractive indices of the substances given
in Table 2.11 are subject to dispersion.
Table 2.12 is arranged by pigment classes: pearl luster, interference, and
diffraction pigments. In other literature, these are often gathered arbitrarily under the collective name: special effect pigments [18, 40]. Our further
discussion relates to the pigment classification and terms given in Table 2.12.
This fixes a unified nomenclature for all sorts of pearlescent, interference, and
diffraction pigments.
Pearlescent pigments of the simplest structure are substrate free and form
flake-shaped single crystals. The flakes consist of natural fish scales (75–95%
Table 2.12 Effect pigments producing colors founded on wave properties of the light:
pearlescent, interference, and diffraction pigments
Sort of effect
pigment
Unsystematic
names
Pearlescent
pigment
Platelet-like single
crystals
Mica-based
pearlescent
pigments
Interference
pigment
Special interference
pigments
Liquid crystal
pigments (LCP)
Optical variable
interference
pigments (OVIP)
Extended
interference films
Diffraction
pigment
Grating pigments
Typical examples
Natural pearl essence, basic lead carbonate,
bismuth-oxide chloride, α-iron-III-oxide,
titanium dioxide, mixed-phase pigments of
aluminum oxide, manganese-iron-III-oxide
Substrates: natural or synthetic muscovite layers:
titanium dioxide (rutil or anastas),
iron-III-oxide, chromium-III-oxide, silicon
dioxide (multi-layer principle)
Substrates: aluminum oxide, silicon dioxide,
iron-III-oxide chromium,
silicon–aluminum–boron silicate;
Layers of iron-II-oxide-hydroxide, iron-III-oxide,
chromium-III-oxide, titanium dioxide,
chromium phosphate; chromium,
iron-II-/iron-III-oxide, iron titanate, silver,
gold, molybdenum
Polysiloxanes in cholesteric phase, cross-linked
in layers
Substrates: aluminum, aluminum oxide,
iron-III-oxide, silicon dioxide, glass flakes;
Layers: aluminum, chromium, iron-III-oxide,
magnesium fluoride, silicon dioxide, titanium
dioxide
Multi-layer film consisting of polyacrylates,
polypropylene with polyethylene terephthalate,
polystyrene, or polycarbonate
Al substrate with symmetrical PVD layers of
MgF2 or Cr/MgF2
Ferromagnetic: Ni substrate with symmetrical
PVD layers of MgF2 /Al or Cr/MgF2 /Al
2.3
Effect Pigments
85
guanine, 5–25% hypoxanthine), basic lead carbonate, bismuth-oxide chloride,
or α-iron-III-oxide, as well as mixed phases of aluminum oxide or manganeseiron-III-oxide. On account of the lack of a mechanically stabilizing substrate,
these pearl pigments will not easily survive shear and pressure flow of technical
processing. They are similar to ground shells and are, therefore, limited to a
small range of applications [40].
However, for the most part, the flake-shaped pearl and interference pigments
consist of a symmetrically coated substrate of at least one additional layer.
The most used substrates are natural or synthetic mica, aluminum, aluminum
oxide, chromium, iron-III-oxide, or synthetic silicon dioxide. The lamellate center should have a great difference in refractive index compared to that of the
coated layers.
Pearlescent pigments are mostly based on mica substrate. This is a native
depositing layer silicate, named muscovite, with total molecular formula
KAl2 [(OH, F)2 AlSi3 O10 ]. Instead of natural muscovite, also synthetic mica
is increasingly being used. The synthesized material shows a more uniformlayered structure and produces, therefore, more brilliant interference colors.
Apart from metal oxides, further coating substances are fluorides or silicon dioxide, also cobalt and iron titanate, chromium phosphate, silver, gold,
molybdenum, or chromium [18, 46–48]. The symmetric permutation of layers
of the flakes is achieved by normal chemical procedures or vacuum evaporation
coating by the PVD or CVD method [49, 50]. Examples of pearl luster pigments
based on natural muscovite are shown in Color plates 7 and 8.
2.3.5 Interference Pigments Consisting of Multiple Layers
Flake-shaped pigments based on muscovite or other substrates can be modified
to produce a variety of further impressive colors. Intensified interference colors
and simultaneously selective absorption, analogous to colored pigments, can be
achieved by coating mica with two or more metal oxides of different refractive
indices. Such kinds of flakes are also called combination pigments. Compared
to single-coated mica pigments, they show more brilliant and brighter interference colors, as well as a more distinct color flop. The color flop is called distinct
if a variety of interference colors are to observe. Conversely, the color flop is
less distinct if only few interference colors are angle dependent to perceive.
The color flop is again more distinct than with a mixture of the natural pearlescent and absorption pigments. Because of the underlying two different color
production mechanisms, combination pigments are also termed as two-color
pigments or color-flop pigments.15 In dependence on the observation angle,
15 Not
only combination pigments produce a color flop but rather interference pigments with
other layer combinations as well as diffraction pigments, cf. Table 2.10., Section 2.3.3.
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2 Light Sources, Types of Colorants, Observer
Fig. 2.40 Cross section of a symmetrical multi-layer pigment; permutation of layers from
the centered mica substrate: titanium dioxide, silicon dioxide, titanium dioxide; overall layer
thickness about 500 nm (source: Merck KGaA, Darmstadt, Germany)
either the gloss is composed of the absorption and interference color or the
non-self-luminous color of the absorption pigment is dominant.
The most important combination pigments are TiO2 -coated mica flakes
vapor-coated with further oxides such as α-Fe2 O3 (hematite modification),
Fe3 O4 , or Cr2 O3 . As shown in Fig. 2.40, the muscovite substrate can be covered
with two different oxide layers of TiO2 and SiO2 . On account of the six boundary layers with different refractive indices, 15 interference combinations are
possible. These produce extreme interference colors which are superimposed
by the absorption colors of both oxides.
Mica pigments vapor-coated with TiO2 and top-coated with other metal
oxides such as TiO2–x , TiOx Ny , FeTiO3 , or nanocarbon particles embedded
in TiO2 generate silver gray or black pigments of improved compatibility with colored pigments. Transparent mica pigments can be produced in
form of nano-sized particles by a suitable precipitation method of oxides or
oxide hydrates; these colorants are called transparent colors. Moreover, modified process engineering allows for the manufacture of pigments of minor
gloss [41].
The top-coat of an interference pigment can also consist of a pure metal. A
substrate of a metal (Al or Cr) or metal oxide (Al2 O3 , Fe2 O3 , SiO2 ) is coated
with a glassy layer of another refractive index (TiO2 , MgF2 ), as well as an
evaporated semitransparent metal top-coat (Cr, Ni, or Al). The inner and outer
reflecting layers form together a Fabry–Pérot etalon, cf. Fig. 2.18. This structure causes increased interference intensities and a sharp color flop by multiple
reflection. An interference pigment showing a distinct color flop is generally
named as optical variable interference pigment (OVIP).
An example of such an OVIP of layer composition MgF2 /Al/MgF2 is shown
in Fig. 2.41. In this SEM picture, it is particularly interesting to see the quite
2.3
Effect Pigments
87
Fig. 2.41 SEM photograph of an optical variable interference pigment with symmetrical
layer composition of MgF2 /Al/MgF2 ; cf. Color plate 9 (source: Flex Products Inc, Santa
Rosa, CA, USA)
even surfaces and the sharp edges of the pigment particles. The even surfaces
indicate also internally even surface boundaries and, therefore, brilliant interference colors followed by a distinct color flop. The sharp edges indicate that
the flakes are broken at low temperatures and sifted out. The particles shown in
Fig. 2.41 have a mean lateral dimension of d50 ∼
= 20 μm and a thickness of about
100 nm. An impression of the color flop produced by this pigment is given by
comparing the two pictures of Color plate 9. Both photos show the same image
field of a light microscope in bright- and dark-field illumination; bright field
means illumination from the top of the surface and dark field means interference from the side of the color sample. In this case, the colored flop changes
from green to violet (see also Section 3.5.3).
Interference pigments of special shish-kebab layer structures and consisting of organic polymers are termed as liquid crystal pigments (LCP). A liquid
crystal state is arranged without exception of rod- or elliptical-shaped polymer molecules consisting of suitable dipole moments or polarizing groups. The
corresponding textures are optically anisotropic and are, for example, used in
seven segment displays for more than four decades. The accompanying texture
is called liquid crystalline or mesomeric phase because the molecular conformation corresponds neither to a random liquid nor to an ordered crystalline
state.
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2 Light Sources, Types of Colorants, Observer
There exist altogether three different liquid crystalline textures. The corresponding molecular configurations are termed as nematic, smectic, and
cholesteric:
– nematic: the molecules are aligned parallel to their longitudinal axes, are arbitrary slidable in the axial direction, and are rotatable around the longitudinal
axes independent of one another;
– smectic: the molecules are oriented with their long axis perpendicular to each
monomolecular sheet; the movement of the molecules is restricted to rotations
around the longitudinal axes;
– cholesteric: the molecules are arranged parallel to one another and grouped
in layers; the layers are systematically turned toward each other by a specific
angle; the mobility of the molecules is the same as in the nematic phase.
These molecular configurations are schematically sketched in two dimensions
in Fig. 2.42, but are to interpret as three-dimensional textures.
Nematic
Smectic
Cholesteric
Fig. 2.42 Schematic representation of rod-shaped polymer molecules in nematic, smectic,
and cholesteric phase
The manufacture of liquid crystalline pigments of suitably layered structures
normally starts with polymer molecules in the nematic phase. This state is converted into layers of cholesteric texture – for example, with silicones – at higher
temperatures in the presence of a chiral additive. The single parallel layers are
then cross-linked and fixed using UV radiation; see Fig. 2.43. Each layer is
twisted by a constant angle relative to the adjacent layer. The nearly identical
molecular conformation with regard to the initial layer is attained after passing
the so-called pitch height p of about 100 nm. On account of the systematically twisted molecular conformation inside the pitch, the transmitted light is
circularly polarized by this structure. The pigment particles have thicknesses
2.3
Effect Pigments
89
Fig. 2.43 Parallel and
cross-linked layers of
polysiloxane molecules in
cholesteric texture forming
a half pitch of a liquid
crystal pigment
(schematically)
of about 5 μm, the lateral dimension normally ranges from about 7 to 90 μm.
Liquid crystalline sparkling pigments can be realized up to about 500 μm.
An entire pitch works optically like a Fabry–Pérot etalon [51]. The partial
reflection at the pitch surfaces and the rotated molecular arrangement causes
several optical effects which greatly affect the interference behavior of these
pigments:
– a kind of gloss coming from the depths, which is attenuated in pearl luster
pigments because the light must pass through various pitches and layers;
– on account of reflections between adjacent pitch surfaces, the interference
wavelength λ changes according to Equation (2.1.20) for z = 1 and p = 2d;
the wavelength decreases with increasing angle of observation from the vertical; an example of transparent liquid crystal pigments is shown in Color plate
10;
– caused by a low pitch value, only one single interference order is observable
within ±90◦ ; it is accompanied by a distinct color flop;
– the reflected polarized light increases the brilliance of the interference color;
– because the particles are transparent, the total color impression can be
influenced by the background color or mixed absorption pigments.
Furthermore, modern developments use even pure metals, metal alloys,
metal oxides, or borosilicate glass for substrates of interference pigments; see
Table 2.13. An example of an uncoated glass substrate and coated with TiO2 is
shown in Fig. 2.44. The differences in refractive indices at the interfaces cause
not only unusual brilliant and pure interference colors but also sparkle effects
which are even colored. Pigments of other compositions, thicknesses, and permutation of layers cause impressive color flops. These occur nearly throughout
the entire visible spectrum (see Section 3.5.3).
Finally, there are the so-called extended interference films (cf. Table 2.12,
previous section). The manufacturing is carried out by co-extrusion of transparent polymer foils with different refractive indices (1.48 ≤ n ≤ 1.60). The
films are partly colored with absorption pigments. The original low interface
reflectivity is improved by semitransparent silvering of some internal foils. The
full foil sequence has a thickness of up to 400 μm and contains a maximum
90
2 Light Sources, Types of Colorants, Observer
Table 2.13 Some optical variable interference pigments
Substrate
Coating
Peculiarities
Al2 O3
Depending on coating
thickness d
TiO2
Fe2 O3
Lateral dimension
5 μm ≤ φ ≤ 30 μm
Colors:
“Silver,” yellow over blue-green until blue;
“Bronze,”, “Copper,” red interference colors;
sparkle pigments for φ ≥ 30 μm
Ca–Al
borosilicate
TiO2 , Fe2 O3 , SiO2 :
SiO2 /TiO2 in
multi-layers:
d ≤ 1 μm,
20 μm ≤ φ ≤ 200 μm
Substrate of high transparency,
“pure” interference colors without scattering,
multicolored sparkle effect
SiO2
TiO2
Colored flop: “gold-silvery” to greenish,
green-blue to dark-blue; more distinct with rutil
compared to anastas
Fe2 O3
Layer configuration:
Fe2 O3 /SiO2 /Fe2 O3 /
SiO2 /Fe2 O3
Colored flop: violet to orange-“gold”; top coating
of Fe2 O3 , corrosion resistant
Metals and
metal
alloys
Mono-layers:
Al, Zn, Cu–Zn alloys;
SiO2 /Al/SiO2 ,
α-Fe2 O3 /Al/α-Fe2 O3
Multi-layers:
From the surface
partially oxidized and
oxides of metal flakes
Fabry–Pérot etalons; cf. Table 2.8
Fig. 2.44 (a) Uncoated borosilicate substrate, (b) coated with titanium dioxide layers; total
flake thickness of about 300 nm (source: Merck KGaA, Darmstadt, Germany)
of 70 films. The multi-layer films are crushed at temperatures below the lowest glass transition temperature of the polymers used and are sieved in different
fractions.
2.3
Effect Pigments
91
2.3.6 Spectral Behavior of Pearlescent and Interference
Colorants
Pearl luster and interference pigments are either nearly transparent or opaque.
The most important representatives of both groups are shown in Table 2.14. In
this section, we limit ourselves to describing only transparent particles because
these colorants have more interesting color shades. First, we discuss the dependence of the color impression on the background color; thereafter, we explore
methods for covering coatings. As already mentioned, the interference color
appears in the direction of the specular angle; this corresponds to the interference angle of first order. The complementary color is transmitted by the
transparent particles and absorbed by opaque flakes.
Table 2.14 Examples of nearly transparent and opaque pearlescent and interference
pigments
Light transmittance
Examples
Nearly transparent
TiO2 pigment, Fe2 O3 combination pigments on mica substrate;
Fe2 O3 coating of Al2 O3 substrate; coated SiO2 flakes; liquid
crystalline polysiloxanes
Opaque
Reduced TiO2 on white mica; multi-layer pigments: Al flakes
coated with SiO2 , Fe2 O3 ; Al or Cr platelets vapor coated with
MgF2 , Cr, or Ni
The total color impression of transparent interference pigments is strongly
influenced by the chosen background; this is clearly shown in connection with
Fig. 2.45. Because a black background absorbs the complementary color, only
the interference color is observed above the coating. The interference color corresponds to the mass tone of the pigment. On account of the additional light
scattering, which is generated to a greater or lesser degree by the corners or
edges of the pigment particles, the surface of such coatings appears in fact dark,
but rarely absolute black.
On the contrary, a white background scatters, to a large extent, the transmitted complementary color and is only slightly absorbed. The interference color is
then superimposed upon by the scattered amount of the complementary color in
direction of the specular angle. In all other directions, only the scattered complementary color is observed. Consequently, over a black background, the natural
colors of an interference pigment are observed and over a white background,
the covering capacity. These uncolored background surfaces allow also for the
determination of the reflectance and transmittance of a transparent or translucent
layer from reflection measurements (Sections 3.4.3 and 4.2.4).
In the case of a colored background, the interference color is clearly superimposed upon by that color. Because the interference and absorption colors can
92
2 Light Sources, Types of Colorants, Observer
Interference
color
Complementary
color
Black
White
Colored
Fig. 2.45 The color impression of colorations with transparent interference pigments is
affected by the chosen absorbing or scattering background
be either identical or different, a variety of color flops are possible. At curved
surfaces (which are always to be avoided for color measurements), the interference and the absorption color can be observed simultaneously. Transparent
interference pigments mixed with colorants of complementary mass tone result
in a white color according to the laws of additive color mixing. Mixtures of
transparent interference pigments with other pigments of similar color produce
more dull colors like the single colorants.
As an alternative to a white background, a scattering silver-colored metallic
or pearlescent pigment of d50 value less than 10 μm can be used. Such parameters for the pearlescent pigment normally ensure a high DOI value. Preferred
bright silvery pigments for this purpose are mica flakes coated with TiO2 or
aluminum cornflakes. For light gray layers FeTiO3 -mica pigments are suitable.
On the basis of the scattering contribution or broad particle size distribution,
the gloss is reduced. Aluminum pigments have also the tendency to reduce the
chroma of pearlescent and interference pigments. This is in analogy to white in
mixtures of colored absorption pigments.
In the following, we consider in more detail the color systematic and the
corresponding spectral reflection which result from thickness changes and composition of the layers. For this, we restrict ourselves to the pigments with layer
compositions which were already discussed in the previous section, among other
things. They are as follows:
– titanium dioxide evaporated mica particles;
– mica flakes coated with iron-III-oxide;
2.3
Effect Pigments
93
– two mica-based combination pigments of titanium dioxide in rutil modification: top coated with iron-III-oxide or with chromium-III-oxide;
– liquid crystal pigments consisting of polysiloxanes.
These pigments are typical representatives of other pearlescent and interference
pigments. This goes especially for the accompanying colorimetric behavior of
these pigments which show astonishing colorimetric parallels (Section 3.5.3).
2.3.6.1 Titanium Dioxide Evaporated on Mica Substrate
An example of a pearlescent pigment on a mica substrate coated with rutil is
shown in the upper half of Color plate 7. This picture was taken under bright
field illumination. From the top view, the particles produce a yellow color
impression over a black background. The non-uniform colors of the particles
are caused by different layer thicknesses and by flakes tilted with regard to the
image plane. This is further elucidated with the example of the red pearl luster
pigment in Color plate 8. In this case, the particles in the same field are recorded
in using bright and dark field illumination.
The comparatively high-valued refractive index of titanium dioxide (n = 2.5
or 2.7) together with the low value of muscovite (n = 1.5) offers suitable conditions for developing neatly ordered interference colors. However, if the mica
substrate is already flake shaped, TiO2 crystallizes in a thin film which is only
suited for interference. Among the three possible crystal modifications of titanium oxide – rutil, anastas, and brookit – the rutil structure is preferred in this
case.
The dependency of the interference color on the titanium-dioxide-layer thickness is given in Table 2.15 (cf. Table 2.5). Each color impression over black
background changes with increasing layer thickness from metallic “silver” over
copper-red to green. These are no spectral colors because the accompanying
colors are, in each case, composed of several adjoining interference wavelengths. The different wavelengths are selected by varied layer thicknesses of
the metal oxide and by particles tilted differently toward the image plane (see
Color plates 7 and 8).
Under diffuse illumination, these pearl luster pigments produce the spectral
reflectance over black background shown in Fig. 2.46. With increasing layer
thickness, the peak shifts to longer wavelengths and simultaneously broadens.
In the figure, this begins in the violet region. The reflectance minimum also
moves to longer wavelengths, in the figure starting from the yellow range. The
spectral reflectance of the “silver” pigment corresponds to that of a light gray
hue or to that of aluminum cornflake pigments. This suggests the substitution of
the metallic aluminum pigment by the cheaper pearlescent pigment in suitable
cases.
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2 Light Sources, Types of Colorants, Observer
Table 2.15 Interference colors depending on layer thickness of titanium dioxide on mica
substrate (cf. Table 2.5)
Layer thickness
titanium dioxide/nm
Platelet
thickness/nm
Interference color –
inherent color over
black background
Transmitted
complementary color
40–60
60–80
80–100
90–110
120–130
100–140
120–160
120–140
140–160
230–250
250–270
280–300
310–320
370–390
“Silver”
Yellow
Red
Copper-red
Violet
Blue
Green
“Silver”
Blue
Green
Blue-green
Yellow-green
Yellow
Red
Now, assume that the peaks in Fig. 2.46 can be interpreted as interference
wavelengths of first order. Clearly, this is not exact, but sufficient for the following estimations. If we use the values of the relevant refractive indices of
Table 2.11 and assume perpendicular observation, then Equation (2.1.18) delivers an approximate value for the thickness of the titanium oxide layer. For the
R (%)
Layerthickness in nm
80
a: 40 – 60
b: 60 – 80
c: 80 – 100
d: 120 – 130
e: 100 – 140
f : 120 – 160
60
40
b
a
c
d
20
e
f
0
400
500
600
λ
nm
Fig. 2.46 Spectral diffuse reflectance of mica pigments of different TiO2 coating thicknesses; measurements over black background, de:8 geometry16
16 The corresponding de:8 measuring geometry (see Section 4.1.2) simulates diffuse illumination conditions in closed rooms.
2.3
Effect Pigments
95
last five flakes indicated in Table 2.15, this approximate calculation results in
values which are in the given thicknesses intervals. The systematic changes
in spectral reflectance are characteristic features of the basis pigment series:
the spectral reflectance curves measured under diffuse illumination are “fingerprints” of the relevant pearl pigments. This is an analog to absorption colorants.
These fingerprints are sometimes utilized for analyzing mixtures with further
pigments.
Using directional illumination and angle-dependent reflectance measurements, particularly important information about the properties of the relevant
interference pigments can be obtained. For the moment, we restrict the discussion to only one illumination angle although the colors of pearlescent,
interference, and diffraction pigments depend on the illumination as well as
the observation angle. The five spectral reflectance curves in Fig. 2.47 were
measured with the green pearlescent pigment, which has a peak at 507 nm in
Fig. 2.46, curve (f). The film of pearl luster pigments over a black background
is illuminated at an angle β = 45◦ and the spectral reflectance is measured
at aspecular angles μas = 15◦ , 25◦ , 45◦ , 75◦ , and 110◦ . As can be seen, the
peak reflectance reduces dramatically with increasing measurement angle and it
shifts to slightly shorter wavelengths. For observations near the specular angle,
the reflectance exceeds values higher than 1.0 or 100%. The chosen five measuring angles are by no means sufficient to gather the entire color dynamics of
pearlescent and interference pigments [52, 53].
2.3.6.2 Iron-III-Oxide on Mica Substrate
Crystalline α-Fe2 O3 has the highest refractive index of n = 2.88 among the substances listed in Table 2.11. As mentioned in the previous section, the total color
impression of the layer composition with mica results from superposition of
the layer-dependent interference color and the absorption color of the hematite.
Iron-III-oxide produces a red to reddish-brown absorption color which is further modified by the thickness of the outer layer, see lower picture of Color
plate 7. The color impression changes with increasing layer thickness from
bronze colored to copper to purple or even reddish-green at the highest layer
thickness. This is clear from the spectral reflectance curves shown in Fig. 2.48.
In the cases of bronze, copper, and red, the reddish-brown absorption color is
even amplified by the corresponding, nearly equal interference color like yellow, copper, and red. We return to the hue dependence of the layer thickness in
Section 3.5.3.
The superposition of interference and absorption leads to brilliant colors in
the vicinity of the specular angle. Near this angle, the purple and reddish-green
pearlescent pigments have a violet or green interference color caused by the
relative high layer thickness of the hematite. With regard to comparable outer
96
2 Light Sources, Types of Colorants, Observer
150
R (%)
100
μas =
15°
50
25°
45°
0
400
75°
500
600
110°
λ
nm
Fig. 2.47 Spectral reflectance of the green interference pigment from Fig. 2.46 at five
aspecular measuring angles μas ; measurement over black background, illumination angle
β = 45◦
layer thickness, the TiO2 -mica pigments produce a broader variety of interference colors, whereas the iron-III-oxide produces diverse types of red hues.
The distinct brilliance of the α-Fe2 O3 pigments comes from the slightly higher
refractive index of the hematite in comparison to that of titanium dioxide. The
increased covering capacity is again a consequence of the typically increased
scattering of the inorganic oxide.
2.3
Effect Pigments
97
R (%)
a: Bronce
b: Red-golden
c: Copper
d: Purple
e: Red-green
80
Fe2O3Layer
thickness
60
a
b
c
40
d
e
20
0
400
500
600
λ
nm
Fig. 2.48 Diffuse spectral reflectance of mica pigments coated with Fe2 O3 of different layer
thicknesses; measurement over black background, measuring geometry de:8
2.3.6.3 Combination Pigments
Interference with more brilliant colors and higher absorption is generated by
coating the substrate with two or more different metal oxides. A multitude
of combination pigments are based on titanium dioxide-mica flakes, where
the flakes are additionally vapor coated with Fe2 O3 or Cr2 O3 . These sorts of
combination pigments show, in comparison to the original single-coated mica
pigments, higher brilliance and a more distinct color flop.
In the following, we consider the reflection behavior of mica combination
pigments composed of layers of titanium dioxide in rutil modification coated
with iron-III-oxide. The optical interactions between both metal oxides lead to
many brilliant golden colors reaching from pale yellow-gold to rich red-gold
to green-gold. With the addition of an oxide layer, a clear color extension with
regard to the simple Fe2 O3 -mica particles is achieved. Furthermore, the change
of the layer thicknesses of the two metal oxides generates a wealth of superimposed interference and absorption colors. The thicknesses of all three layers
can be tuned with each other in such a way that the interaction of the interference and absorption components leads to a demanded coloristical effect, within
limits.
Similar features result from the substitution of the outer Fe2 O3 layer by
Cr2 O3 . The combination of Cr2 O3 with TiO2 in anastas modification results in
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2 Light Sources, Types of Colorants, Observer
R (%)
Fe2O3
TiO2 Rutil
80
60
Fe2O3
TiO2 Rutil
40
Cr2O3
TiO2 Anastas
Cr2O3
20
TiO2 Anastas
0
400
500
600
λ
nm
Fig. 2.49 Diffuse spectral reflectance of two combination pigments Fe2 O3 /TiO2 (rutil),
Cr2 O3 /TiO2 (anastas) on mica substrate of different layer thicknesses; measurement over
black background, measuring geometry de:8; the curves of Fe2 O3 /TiO2 are shifted 20 units
toward higher reflectance values for better overview
high-luster blue-greenish to moss-green colors. Figure 2.49 shows the spectral
reflectance curves measured under diffuse illumination of Fe2 O3 /TiO2 pigment
and Cr2 O3 /TiO2 -mica pigment. Each has two different outer layer thicknesses,
but the total coating thickness is constant in each case. The greater thickness of
the outer oxide layer reduces the reflection. This is clearly caused by increased
absorption due to greater layer thickness. In the case of a higher layer thickness
of Cr2 O3 , this pigment additionally develops a clear peak in comparison to the
quite broad peak belonging to the thinner outer layer. The increased influence
of the Cr2 O3 layer on the interference development can be ascertained from the
reflectance curve (f) in Fig. 2.46 for the green pearlescent pigment together with
the two lower curves in Fig. 2.49. Altogether, titanium dioxide is responsible
for the brilliance of the colors and the outer layer thickness for the interference
color. The included absorption colors of iron oxide or chromium oxide exist
otherwise under all observation angles.
Nearly equal-colored oxide layers create a pearl luster effect of intensive
colors which, at nearly all observation angles, show a noticeable color shift.
However, if the color of an absorption colorant corresponds to that of the complementary color of the interference pigment, then a distinct two-colored effect
is achieved, especially in the oxide combination of Cr2 O3 /TiO2 . Further inorganic absorption pigments such as Prussian blue, cobalt blue, Fe3 O4 , or carbon
2.3
Effect Pigments
99
black generate, in combination with titanium oxide on mica substrate, unusual
color effects as well.
2.3.6.4 Liquid Crystal Pigments
The color flop of liquid crystal pigments consisting of polysiloxane depends
on the pitch height p and causes, for example, the color pairs violet/blue,
blue/turquoise, blue/green, green-blue/gold, and green/copper-red. Flakes with
blue/green-flop are shown in Color plate 10 at bright and dark field illumination
over black background. The noticeable sparkle particle there is already green
from the top view because of the higher pitch height compared to the other
flakes. To the present day, mixtures of the transparent particles with absorption
or other effect pigments produce unequaled and extremely brilliant colors.
As mentioned at the beginning of the section, further shades can be obtained
with a suitable background color. With regard to liquid crystal pigments, this
concept is underlined by the example in Fig. 2.50. The reflectance curves correspond to background colors of white, red, and black as well as each top coated
with a transparent film of the same liquid crystal pigment. The reflectance
peak over black at 512 nm corresponds to the green color impression from
the top view. The red background leads to a minimal blue-tinged red and the
R (%)
Background alone
White
80
Layer over background
Red
60
40
20
Black
0
400
500
600
λ
nm
Fig. 2.50 Spectral reflectance of a transparent liquid crystal pigment with d50 = 30 μm over
white, red, and black background, as well as backgrounds alone; wavelengths of maximum
reflectance over background: 512 nm (red), 531 nm (black); measuring geometry de:8
100
2 Light Sources, Types of Colorants, Observer
white background creates a very light pink. The flat maximum of the white
background at a wavelength of 490 nm is caused by fluorescence emission of
the contained optical brightening agent (Section 4.2.6).
Figure 2.51 shows the directional reflectance over a black background for
illumination angle β = 45◦ and aspecular observation angles μas = 15◦ , 25◦ ,
45◦ , 75◦ , 110◦ . With increasing measuring angle, the wavelength of the peak
shifts from 483 to 520 nm. Simultaneously, the peak height decreases from R =
108% to about R = 2%. The angle dependence of the interference wavelength
corresponds to the cosine function in Equation (2.1.20).
R (%)
μas = 15°
β = 45°
d50 = 30 μm
100
25°
50
45°
75°
0
400
500
λ
nm
110°
600
Fig. 2.51 Spectral reflectance of a liquid crystal pigment with d50 = 30 μm for five aspecular
measuring angles; measurements over black background, illumination angle β = 45◦
The brilliance of liquid crystalline pigments depends also on the average
lateral dimension of the flake particles. This can be seen from the reflectance
maxima in Fig. 2.52. The reflectance curves are measured for three different
particle size distributions over the same black background and at constant illumination and aspecular angle of β = 45◦ and μas = 15◦ , respectively. The flakes
have size distributions which correspond to the ratios of d50 /d99 = 30/90, 23/60,
and 18/50 μm/μm. The reflectance maxima in Fig. 2.52 correspond to the ratios
30:23:18 of accompanying d50 values. In addition, this result is confirmed by
measurements over red and blue background. The height of the reflectance maximum of liquid crystal pigments is, therefore, directly proportional to the mean
flake size. Clearly, large-sized LCPs orient better to the background surface, in
analogy to metallic flakes. These larger particles then show increased brilliance
2.3
Effect Pigments
101
R (%)
β = 45°
μas = 15°
d50 = 30 μm
100
23 μm
50
0
400
18 μm
500
λ
600
nm
Fig. 2.52 Directional reflectance at constant aspecular measuring angle μas = 15◦ of a liquid
crystal pigment in dependence on particle size d50 ; measurements over black background,
illumination angle β = 45◦
compared to smaller sized flakes. The colorimetric properties of the most important pearl luster and interference pigments are outlined in Sections 3.5.3 and
3.5.4.
2.3.7 Opaque Films Containing Absorbing and Effect Pigments
From discussions up until now, it is clear that the creation of new colorations by
mixtures or films consisting of modern effect and classical absorption pigments
represents quite a challenge. Especially needed to meet this challenge are hiding layers which consist of transparent effect pigments and covering absorption
pigments. A coating is called covering or hiding, if any colored background can
no longer be observed from above the film (Section 3.4.3).
Covering layers with coarse metallic, transparent pearlescent, interference, or
even diffraction pigments are produced by mixtures of colorants which generate
suited scattering or absorption. It is also important to consider the change of
the originally desired color effect with the addition of further colorants and also
the compatibility with the pure effect pigment. Experience shows that covering
coatings with effect pigments can, in the most cases, be manufactured with three
different colorants: carbon black, suitable absorption pigments, and fine metallic
pigments [54].
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2 Light Sources, Types of Colorants, Observer
A small amount of carbon black turns out to be quite effective for this. The
resulting dark and sometimes even intense colors are caused by absorption of
the complementary color with carbon black already inside the layer. Only a
small volume amount < 1.0% of carbon black is normally sufficient. For larger
concentrations, the interference color often appears too dark and the color travel
(respectively, color flop) is too small or suppressed.
The selective absorption and scattering of mixed in absorption pigments also
result in covering layers of additionally impressive colors. Small amounts cause
mostly brilliant interference colors. Larger amounts, however, can obliterate the
pearl luster and interference effect: on the one hand, the interference intensity
is increasingly masked and on the other hand, the complementary and part of
the interference color are absorbed depending on the chroma of the absorption
pigment.
Finally, in the third method, the transparent pearl or interference pigment is
mixed with a small amount of a special fine and, therefore, strongly scattering
metallic pigment. In this case, the covering formulation is, however, accompanied by reduced brilliance, color saturation, and gloss. In all three mentioned
cases, it is important to pay attention to the compatibility of the added components. Furthermore, the added amounts should be as small as possible in order
to result in a coloristic effect changed only slightly.
Altogether, the level of pigmentation of effect pigments in recipes depends
on the desired color effect, the spreading rate of the pigment, and the molecular
surroundings. For a few applications the pigment volume content is shown in
Table 2.16. Apart from the application, the processability, the light, temperature,
or weathering resistance, etc., additionally determine the total pigment amount
of a coloration; see also Section 3.4.6.
Table 2.16 Pigmentation level of effect pigments in various fields
Pigment level %
Employment
Metallic pigments
Pearlescent, interference pigments
Lacquers, emulsion paints
Thermoplastics, thermosets
Printing inks
Cosmetics
Toiletries
0.5–2
0.5–3
1–45
1–15
0.05–1
0.5–20
0.5–2
1–30
1–50
0.05–1
From color physical point of view, mixtures of effect pigments together or
with absorption colorants obey the laws of additive or subtractive color mixing (Section 2.4.3). Mixtures or layers of effect pigments show additive color
mixing if the colors of the single pigments are based on the superposition of
wavelengths; see Table 2.17. But, as soon as the light interacts only with one
2.3
Effect Pigments
103
Table 2.17 Additive and subtractive color mixing of effect and absorption pigments
Pigment combination
Color mixing
Cause
Interference pigment mixed
with interference
pigment
Interference pigment mixed
with diffraction pigment
Additive
Interference pigment on
absorption pigment
Additive and subtractive
Interference pigment mixed
with absorption pigment
Subtractive
Absorption pigment mixed
with absorption pigment
Subtractive
Superposition of reflected
interference and transmitted
complementary color
Superposition of interference,
diffraction, and transmitted
complementary color
Superposition interference color,
absorption of complementary
color and selective absorption
of the colored pigment
Colored pigment absorbs parts of
the complementary and natural
color of the interference
pigment
Each colored pigment absorbs
parts of the influx light
Additive
absorption pigment together with any further pigment sort, the resulting color
impression is based on subtractive color mixing; see also the literature [54, 55].
Additive color mixing is fundamental in the human color sense and the based
on colorimetry of versatile industrial applications.
Finally, we return to optical properties of interference pigments which
depend on the particle size and morphology. Smaller particles show a reduced
pearl luster effect in comparison with those of larger sized. This is because the
higher edge scattering reduces the luster. In the case of dominant scattering,
the pearl luster and gloss of interference pigments can even disappear completely. An increasing lateral size dimension up to 200 μm improves not only
the brilliance but also the sparkle of the pearlescent and interference pigments;
furthermore the color travel passes more wavelengths. However, with increasing
flake geometry, the hiding power and DOI are reduced. The pigment properties
shown in Table 2.18 correlate with related properties of metallic pigments listed
in Table 2.9. In other words, comparable color properties of metallic, pearlescent, and interference pigments change in the same direction depending on the
flake size.
We have, thus far, still neglected opaque multi-layered pigments (Table 2.13).
A considerable part of their color physical properties correspond to those of
transparent effect pigments. An advantage of these pigments is the fact that the
color effect is not distorted by additional colorants, but the absorption and selfscattering of the particles softens the original color. Further similarities between
different effect pigment sorts are uncovered in Section 3.5.3.
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2 Light Sources, Types of Colorants, Observer
Table 2.18 Assessment of some properties of pearlescent and interference pigments in
dependence of the particle size
Particle size Φ/μm
Property
Φ<5
5 ≤ Φ ≤ 25
10 ≤ Φ ≤ 60
30 ≤ Φ ≤ 200
Brilliance
Color flop
Covering capacity
DOI
Low
Reduced
Excellent
Very good
Silky
Low
Very good
Good
Very well
Striking
Good
Low
Sparkling
Distinct
Low
Very low
2.3.8 Colors of Diffraction Pigments
Although the diffraction of light waves has been known since the beginning
of the 19th century, this phenomenon has only been used in color physics for
a few years [56]. Waves are diffracted, analogous to interference, when they
interact with structures of dimensions on the same order of magnitude as the
wavelengths. Polychromatic light is split up by diffraction into the spectral
components. Reflective diffraction pigments are the sorts that is of interest in
industrial color physics. These consist of a metal substrate with a grating of
embossed periodic grooves. In addition, the substrate is coated with inorganic
substances; see Table 2.12. Each particle works as a reflection grating.
The nano-engineering method of interference lithography can be used to
produce periodic grating structures on surfaces. This method is based on the
interference of two laser beams; see Fig. 2.53. With the two coherent waves
from the same source, each of wavelength λL , an interference fringe pattern of
parallel fringes of distance d results (Michelson configuration). This distance is
given by the relation
d = λL · sin ϑ,
λL
(2.3.1)
d
2ϑ
λL
Fig. 2.53 Generation of parallel structures with two coherent light rays using the Michelson
configuration (schematically)
2.3
Effect Pigments
105
where ϑ denotes the half of the divergence angle. The periodic laser fringe
pattern is directed onto a metallized thermoplastic film or photoresist film so
that this pattern is transferred into the film as an exposure. After removing
the organic backing layer by thermal or chemical procedures, the remaining
metal foil of projected groove geometry is evaporated in vacuum with further
substances which are also used in nanotechniques. The substrate is coated symmetrically so that the diffraction always develops at the illuminated surface of
the reflection grating.
The films of up to 1 μm in thickness can be broken up into particles with lateral dimensions between 10 and 300 μm using ultrasound. The resulting flakes
can be sifted by pigment size. Flakes with mean diameters of d50 = 20±2 μm
are preferably used for print media and coatings [56]. The regular grating patterns consist not only of parallel but also rectangular, diagonal, or hexagonal
lines. Presently, diffraction pigments are manufactured with 100 up to 5,000
equidistant parallel lines per millimeter (l/mm). The cross section of the grooves
can be chosen in such a way that the first diffraction order corresponds to the
geometrical direction of reflection (blaze techniques, Section 2.1.7).
The diffraction particles shown in Fig. 2.54 have a grating constant of
1,000 l/mm. The substrate consists of highly reflective aluminum of about 80 nm
thickness and periodic folding. Using PVD techniques, the metal film is coated
on both sides with MgF2 of about 450 nm thickness; see cross section at fracture
in Fig. 2.55. Diffraction pigments have been produced industrially since 2002,
although symmetric grating cross sections have been used in technical optics
since about 1980.
The spectral reflectance of diffraction pigments with three different grating constants measured by diffuse illumination and de:8 geometry is shown
in Fig. 2.56. For pigments with 1,400, 2,000, or 3,000 l/mm, the reflectance
Fig. 2.54 Diffraction pigments with periodic grating dividing of parallel lines; grating
constant 1,000 l/mm (source: Flex Products Inc, Santa Rosa, CA, USA)
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2 Light Sources, Types of Colorants, Observer
Fig. 2.55 Cross section at fracture of a diffraction particle with periodic grating dividing;
the surfaces of the aluminum substrate are vapor coated with MgF2 (source: Merck KGaA,
Darmstadt, Germany)
R (%)
3,000 l/mm
80
70
60
2,000 l/mm
50
1,400 l/mm
40
30
400
500
600
λ
nm
Fig. 2.56 Spectral reflectance of diffraction pigments of magnesium fluoride/aluminum of
three different grating constants; the middle and upper curves are shifted 5, respectively 10
units toward higher scale values
is between R = 0.4 and R = 0.7. This quantity depends on the reflectivity of
the metal layer, the number and thickness of the non-metallic vapor-deposited
films, the accompanying refractive indices, as well as the mean particle size. The
pigment with 1,400 l/mm produces a silver metallic color impression at observation perpendicular to the coating surface. The nearly flat spectral reflectance
2.3
Effect Pigments
107
shown in Fig. 2.56 is known from silver-colored metallic or pearlescent pigments. Under diffuse illumination, particles of grating constant 2,000 l/mm
appear bluish and those of 3,000 l/mm produce a yellow-orange color
impression.
The almost equal form of the reflectance curves in Fig. 2.57 indicates that
the thickness of the aluminum substrate between 80 and 240 nm is, as to
expect, of no influence with regard to the color impression. For a fixed grating constant of 1,400 l/mm, the height of the reflectance – and, therefore, the
brightness – is only slightly increased with aluminum thickness. With substrate
thicknesses greater than 240 nm, the surface roughness increases and, therefore,
also the interface scattering. This scattering reduces, however, the intensity of
diffraction.
R (%)
240 nm
70
160 nm
80 nm
60
50
400
500
600
λ
nm
Fig. 2.57 Spectral reflectance of MgF2 /Al pigments with aluminum layer thicknesses of 80,
160, and 240 nm; grating constant 1,400 l/mm; the middle and upper curves are shifted 10
units toward higher scale values
Reflective diffraction pigments consisting of a ferromagnetic substrate allow
for the orientation of the particles according to an external magnetic field.
Preferred ferromagnetic materials are nickel, iron, cobalt, but also elements of
the lanthanide series. For better understanding of the orientation of ferromagnetic particles in an external magnetic field, it is useful to make a short excursion
into magnetostatics.
The ferromagnetic state in solids is caused by non-compensated electron
spins of the unsaturated 3d- and 4f-electron shells of metal ions. The unbalanced
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2 Light Sources, Types of Colorants, Observer
angular momentums of the electrons behave, therefore, like magnetic elementary dipoles which, in the crystal state, respond to two different forces. The first,
the anisotropic force causes an alignment of the dipoles parallel to an external
bounding face and the second, the exchange force forces the dipoles to parallelize to each other in the volume. In a magnetic material, anisotropic and
exchange forces produce zones of equal magnetization direction. These zones
have linear extensions between 1 μm and 1 mm which are called domains
or Weiss areas, after their discoverer P.E. Weiss. An external magnetic field
can drive two geometrical processes in the domains: a change of the threedimensional extension as well as a rotation from the original position at constant
volume.
Both effects are represented schematically in Figs. 2.58a–c. Figure 2.58a
represents the original position of four domains in a ferromagnetic substance.
A weak external magnetic field causes a shift of the domain walls; see
Fig. 2.58b. An even higher external magnetic field strength turns the molecular magnets more into the direction of the external field, accompanied by a
further extension of the domain volume, Fig. 2.58c. In general, domain wall
shifts occur at moderate magnetic field strengths and domain rotations only at
higher strengths.
The basic driving mechanism for the orientation of ferromagnetic domains
or particles parallel to an external field is the tendency of such systems to seek
a state of minimal total energy. This is achieved by an internal demagnetization
field which counteracts the external field. A sufficiently high external magnetic
field strength causes a total rotation of the domains. If the lateral dimensions of
free particles are on the order of magnitude of the domains, then the rotation
into magnetic field direction is performed by the entire particle. This effect is
H
a)
b)
H
c)
Fig. 2.58 Schematic representation of Weiss domains in a ferromagnetic material: (a) without external magnetic field, (b) with weak magnetic field, and (c) with strong external
magnetic field H
2.4
Observer
109
known from iron filings, which align along the lines of an external magnetic
field. Also ferromagnetic diffraction pigments are subject to such rotations. With
the help of an external magnetic field, a nearly uniform orientation of diffraction
pigments of ferromagnetic substrate can, therefore, be fixed before and during
crosslinking of a binder.
The both diffraction pigments given in the last line of Table 2.12 are ferromagnetic. With an additional Ni layer for the substrate, their composition
corresponds to the two- and three-layered diffraction pigments one line higher
in the table. The ferromagnetic particles consisting of the three different layers MgF2 /Al/Ni and grating constants of 1,400, 2,000, or 3,000 l/mm produce,
under diffuse illumination, a nearly uniform silver-colored impression. A further PVD coating with chromium causes a gold-yellow color. The spectral
reflectance curves of ferromagnetic diffraction pigments are of the same shape
as the curves of non-ferromagnetic particles with grating constants of 1,400 and
2,000 l/mm; see Fig. 2.56. Certainly, on account of the particle orientation in a
magnetic field, an angle-dependent colorimetrical behavior results, one which
had not been observed before (Section 3.5.5).
After a detailed description of the optical operation modes of industrially
used colorants, we can conclude: between the rock and cave paintings of natural
colors and the modern produced and applied colors there was, without doubt,
an impressive historical development. This is accompanied by broad research
as well as process and application technology in color industry. In spite of this,
all presently known and also newly developed or modified colorants are merely
orientated toward the color perception of humans. The human color sense is,
therefore, discussed in some detail in the next section.
2.4 Observer
In addition to the importance of the light source and the color pattern, the
most important and final crucial factor for the emergence of color perception
is the observer. His/her subjective color sensation comes from the remaining
light waves that reach the retina of the eye after source light interacts with
the colorants. Nearly all efforts in processing and applying natural, modified,
and synthesized colorants are oriented toward the capability of human color
sensation. Long ago, Newton emphasized the fact that color production is ultimately based on neural processes. This means that outside the visual cortex,
colors do not exist, but only electromagnetic waves. In the following, we give
a brief overview of the modern physiological and neurological understanding
of color sensation [57, 58]. These connections lead directly to the fundamental
Grassmann laws of additive mixing of colors. The standardized CIE color values
of the years 1931 and 1976 as well as the broad color physical and colorimetrical
applications are based on these laws.
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2 Light Sources, Types of Colorants, Observer
2.4.1 Color Perception and Color Theories
As already mentioned in the introduction of this text, color perception is produced by psychophysical and neural processes. Color sensation is, therefore,
not directly measurable with normal physical methods. The first important element contributing to overall color perception is the eye. The essential optical
components of the human eye for image formation are shown in Fig. 2.59. The
cornea is only 0.5 mm thick and of fixed focal length of 25 mm, the iris has a
lightness-dependent aperture ratio of 28:1, and the crystalline lens is of variable
focal length. This focal length amounts about 50 mm for the resting eye when
relaxed for distant vision. For an eye of normal vision, these optical elements
provide a clear and focused image on the retina in the area of the fovea. In the
retina are located two types of photosensitive receptors: first, the rods responsible for dusk vision and achromatic colors for luminance less than 0.01 cd/m2
(scotopic vision); second, the cones for color vision for luminance higher than
10 cd/m2 (photopic vision).17 If the eye is fully adapted to darkness, just nine
photons are required before a light stimulus is detected. In cases of middle illumination for luminance in the range of 0.01 and 10 cd/m2 , rods and cones are
simultaneously active (mesopic vision).
The retina of the human eye contains altogether about 125 million visual
cells, but only 5% consist of cones. In the small area of the fovea for visual
angles of about ±0.5◦ , there are only cones present. Here they are of maximum
density and enable focused vision only at this spot of the retina. The majority of
lris
Crystalline lens
Cornea
Fovea
Macula
Optic axis
Blind
Spot
{
Optic nerves
Retina
Fig. 2.59 Horizontal section of the human eye
17 For
definition of unit cd (candela) see footnote 1 in Section 2.1.3.
2.4
Observer
111
the rods are, however, distributed outside of the macula in an area of visual angle
greater than ±5◦ (for visual angle, see Fig. 2.65). At the place of the blind spot
of missing visual cells, the cord of the optic nerves continues to the brain.18 The
different density distributions of rods and cones in the human retina are shown
in Fig. 2.60.
Four different photosensitive pigments are contained within the outer zones
of the visual cells: one pigment in the rods and three pigments in the cones.
The photosensitive pigments consist of a protein molecule denoted as opsin to
which a derivative of vitamin A1 molecule is bound. This chromophoric group
is common to the four pigments. The absorption spectrum of a photosensitive
pigment depends on the kind of protein as shown in the normalized representation in Fig. 2.61. The pigment in the rods, called rhodopsin, shows an absorption
maximum at the wavelength of 498 nm, the tails of the maximum project into
the spectral absorption ranges of the cones. The absorption maxima of the three
cone pigments occur at wavelengths 437, 533, and 564 nm. These wavelengths
are perceived as blue, green, and red and the corresponding cones are, therefore,
called blue, green, and red receptors. In the English-speaking medical literature
they are denoted as S-, M-, and L-cones, indicating the selective sensitivity at
short, middle, and long wavelengths of the visible spectrum. The three cone
types are not equally distributed throughout the retina. The relative distribution for blue:green:red is about 1:20:40. From the similar shapes of absorption
Number of retinal receptors × 103/mm2
Blind spot
Rods
Cones
150
100
50
0
–80°
–40°
0°
Angle from fovea center
40°
Fig. 2.60 Density distribution of rod and cone receptors across the human retina
18 In modern neurology,
the retina is interpreted as a part of the brain.
80°
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2 Light Sources, Types of Colorants, Observer
λ max
437
498
533
564
nm
Relative absorption
1.0
0.5
Cones
Rods
0
400
500
600
λ
nm
Fig. 2.61 Normalized spectral absorption of the four different photo receptor types in the
human retina [57]
curves in Fig. 2.61, it is possible to conclude that the spectral absorption mechanisms of the three cone types are basically identical, although the curves seem
to be shifted along the wavelength axis.
Up until now, we have assumed normal color perception, called trichromacy
on account of the three different cone receptors. Some sort of color vision deficiency with at least one defective color receptor occurs in about 0.5% females
and about 7% males [58–60]. Although some animal species show an evolutionary caused tetrachromacy [61], this property has almost disappeared completely
of human beings. In only extremely rare cases of women a fourth color receptor
was proven; such a receptor shows a maximum sensitivity in the range of yellow
wavelengths [62].
The unusually varying description of defective color vision in the literature
is a consequence of the fact that previous generations of researchers used the
constrained color perception for indications of the neural color sensation. The
following kinds of anomalous color vision can be distinguished:
– color asthenopy: fast onset of tiredness during color vision;
– color amblyopy: selectively reduced ability to distinguish colors;
– color anomaly: caused of defective or missing color receptors.
The color anomaly can be divided further into:
– anomalous trichromasy: the characteristic feature is a reduced perception of
one color during simultaneous observation of several varied colors. In this
2.4
Observer
113
case, there are three color receptors available but one does not work normally.
More concretely, there are red-, green-, and blue-yellow weakness;
– dichromasy: is present if a certain color is not perceived at all; dichromasies
are the most frequent anomalies in humans and can be passed on gender
specifically. Dichromates have only two color receptors, leaving red-, green-,
and blue-yellow blindness;
– achromatopsy: this term is a synonym for complete color blindness. Affected
people do not possess any of the three well-operating color receptors; such
people can only differentiate lightness levels.
Although the after retinal occurring neural processes are only vaguely understood for normal color vision – and surely will remain for a long time at this
level understanding – we follow at least roughly the path of the neural signals in
the brain. This discussion is also carried out here to indicate to the reader how
difficult the search of an adequate color vision theory is. About 50 ms after photon absorption in the photo pigments, retinal signals reach the optic nerve behind
the eye. Each left and right half of the retina of both eyes form a nerve fiber; see
Fig. 2.62. At the position of the optic nerves crossing over, the so-called chiasma
or optic chiasma, each nerve fiber coming from the left and right half of both
retinas is shared to the related brain lope. In the optic chiasma, however, there
is no mixing of the incoming neural signals from both eyes. The subsequent
optic tract ends at the region of the so-called lateral geniculate nucleus, where
Lateral geniculate nucleus
Optic radiations
Optic tract
Visual cortex
Chiasma
Optic nerve
Fig. 2.62 Top view of the head to the human brain with indicated path of neural signals
between the two retinas and the visual cortex; the visual cortex is in no way a sharp restricted
region of both brain lopes, but individually different expanded
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2 Light Sources, Types of Colorants, Observer
the separate incoming neural impulses from both eyes are united into groups.
Along several optic radiators, the transformed signals directly reach the region
at the back of the brain lopes. This is the location of the center of our visual
perception, called the visual cortex. In one special zone of the visual cortex, the
actual color perception is produced, just about 100 until 150 ms after photon
absorption in the retina.
On the basis of this incomplete knowledge, it is necessary to have at least an
adequate theory of human color perception. Although the trichromatic color
theory of Young–Helmholtz and the opponent color theory of Hering have
been shown to be true on physiological basis, neither theory can concretely
explain the mechanism in the visual cortex for producing color perception
(cf. Chapter 1). Likewise the modern retinex theory of Land, based on studies of color constancy, delivers no usable ideas about the emergence of color
impression in the visual cortex.
According to the zone theory, proposed by Müller [63] and Judd [64],
the first zone contains the three independent S-, M-, and L-color receptors
of the trichromatic theory. In the second zone, the generated nerve impulses
are transformed according to Hering’s theory into an achromatic signal and
two opponent chromatic signals. The visual cortex represents the third zone.
The arriving neural signals initiate the color impression including the memory.
Accordingly, the zone theory merely brings together the verified and accepted
basics of both theories mentioned above. On the basis of current knowledge,
it is possible to distinguish 30 different zones of the brain responsible for
vision. Merely five of them are assigned to the color sense, of these only one
dominates for color perception. The neural processes between photon absorption in the retina and induced color impression in the visual cortex remain
unclear.
It is not surprising, therefore, that only the physiological confirmed theories
of Young–Helmholtz and Hering lead to scientific color applications such as
colorimetry. The lacking of a theory which accurately describes the human color
sense turns out to be disadvantageous, in particular for quantification of visually
perceived color differences. As shown in Sections 3.1 and 3.2, only empirical
formulas are given to express a color difference numerically. This unsatisfactory
situation has existed since the beginnings of colorimetry.
2.4.2 Color Perception Phenomenon
In the previous section, we have roughly outlined how humans perceive color.
Now we direct our attention at some remarkable color phenomena of the complex processes of color sensation. Among these are the so-called simultaneous
contrast, negative, or positive after-images or phosphene perception. These
effects are important in different color applications and need to be taken into
2.4
Observer
115
consideration during color assessment. These are, therefore, considered briefly
here.
The term simultaneous contrast describes the phenomenon that the lightness
and the color of the surroundings influence the color impression. We should
differentiate between simultaneous lightness contrast and simultaneous color
contrast. A middle gray, for example, appears darker in a white neighborhood
than in a black one; this is lightness contrast. In a similar manner, differences
between dark chromatic colors are resolved worse with bright-surround field
than with dark-surround field; this is color contrast. For visual assessment of
color differences, it is, therefore, necessary to always use the same achromatic
surrounding color (Section 3.2.2). Phenomenon of simultaneous color contrast
is more varied than simultaneous lightness contrast. In both cases, the contrast
is amplified just at the edges of color areas. The so-called lateral inhibition
is responsible for the altered color perception. This term means that the neural
signals in adjacent receptors within the retina interact with one another. Changes
that are caused by lightness or color alone are, therefore, felt lesser strongly;
contrasts, on the other hand, are perceived amplified.
An additional quite remarkable ability of human color sense is the fact that
many object colors are unchanged in spite of illuminant change. For example,
a blue color is still perceived as the same blue, although the spectral energy
distribution of the illuminant is varied.
Another property of the visual sense is combined with the so-called afterimage. This after-effect occurs, if a single-colored area of high color saturation
is seen with fixed eyes during about 1 min, and without movement of the eyes
or head. If the eyes are afterward adapted to a white area, the color impression
remains for some time. This negative after-image is produced in the complementary color. The reason for this is that the most of the corresponding receptors are
desensitized during the fixing of the chromatic surface; the remaining sensitized
receptors continue to have a reinforced effect during the white impression.
The contrary phenomenon becomes apparent if the eyes are closed for some
minutes, and then for a short time directed toward a contrasting object and then
closed again. The resulting positive after-image shows that the color sensation
actually lasts longer than the original action of the light. A longer continuing
involuntary persistence occurs on chromatic adaption.
After-images are in particular of importance for colorists if color shades
are to be judged after a bright lighting phase with monochromatic sources.
Therefore, before assessment of critical hues, for example, is important to look
at a large, plane, and achromatic area for several minutes in order to avoid
influences of after-images.
A further time-dependent characteristic of color perception is associated with
a short viewing of a color stimulus. For a viewing time of less than 0.1 s, most
hues appear progressively desaturated. In the case of very short stimuli of about
3 ms duration, monochromatic light in the range from 490 to 520 nm appears
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2 Light Sources, Types of Colorants, Observer
achromatic white or gray. These effects are attributed to the property that the
response time of the receptors is clearly shorter for achromatic colors than for
chromatic colors.
Colors can be perceived, quite astonishingly, also without an outside stimulus; this phenomenon is called phosphene. After the eyes are accommodated
to darkness for a sufficient time, it is normal to observe light or colored spots.
The effect of outside pressure on one or both eyes results in time-dependent
changing light areas or colored schlieren. Phosphene occurs in addition without
dark adaption by sudden pressure or electric current. In these cases, the influence from outside the closed eyes evokes disturbances in circulation and neural
transmission.
There are further phenomena of color perception which depend on spatial
conditions or movement of the colored object. These are not of interest to color
physics and are beyond the scope of this book. With exception of phosphene,
the above outlined effects enable us to perceive a world of stable colors and
lightness, although we are surrounded by an even greater variety of electromagnetic waves of different frequencies and changing intensities. But these
electromagnetic waves are responsible for further color effects such as additive
color mixing, which is effective especially in the human eye, or subtractive color
mixing which, for example, is present in absorption colorants. Both phenomena
are subjects of the following section.
2.4.3 Subtractive and Additive Mixing of Colors
A deeper insight into the human color sense has been obscured as a consequence of subjective color judgment and, up to now, the inability to detect
directly the chromatic signals at each position from the retina to the visual cortex by objective measurements. Therefore, Grassmann tried an indirect way to
come closer to the human color sense [65]. In order to describe color impressions quantitatively, he avoided some of the briefly mentioned problems by
using three monochromatic light sources of different wavelengths; see Fig. 2.63.
Consequently, color stimuli are generated under defined conditions and color
effects can be observed and registered. Non-self-luminescent colors are unsuited
for such investigations, because the colors of these light sources are required to
be produced quite simply, reproducible, and additionally, they need to be mixed
trouble-free with one another. For better understanding of the results achieved
by Grassmann, it is useful to go into details of subtractive and additive color
mixing, both of which are basic properties of color physics.
Subtractive color mixing is present, for example, after polychromatic light
has passed through an optical selective filter: one part of the incident light is
absorbed by the filter, and, therefore, denoted as subtracted. In Table 2.19, some
2.4
Observer
117
Red
Green
Blue
White
screen
Observer
Black
partition
Incandescent lamp
Fig. 2.63 Configuration for producing light colors for additive color mixing
examples of subtractive color mixing are listed, cf. also Color plate 1, overlapping upper colors. In the case of several simultaneously used filters, the resulting
transmitted color is independent of the order of the filter. Subtractive color mixing dominates in all sorts of absorption colorants and their mixtures; the color
result of a colorant mixture is, therefore, independent of addition sequence.
Subtraction of light waves occurs also in special cases of mixtures with effect
pigments, as well as during developing of color pictures, among other things.
In contrast, additive color mixing occurs by superposition of colored lights.
The likely most important example is the human color perception. Additive
color mixing is subject to photons of visible light, provided they enter the
retina at the same time. Superimposed, the waves or photons are denoted as
added. If the retinal photo pigments are stimulated simultaneously by polychromatic light, merely one single color stimulus is induced. In this context
the synonymous term “additive color mixing of light” is correct.
Further examples of additive color mixture are computer or television
screens. For such screens, addressable groups of closely packed red, green,
and blue pixels of diameter less than 0.1 mm (of phosphorus, liquid crystals,
or inert gas cells) are stimulated simultaneously to produce color points. Color
pixels of such small lateral dimension cannot be perceived separately by the
eye at sufficient distance; therefore, only a single color stimulus is produced. A
macroscopic example is shown in Color plate 1, lower overlapping colors, cf.
Table 2.19.
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2 Light Sources, Types of Colorants, Observer
Table 2.19 Examples of subtractive and additive mixing of colors; cf. Color plate 1,
overlapping color segments
Subtractive mixing of colors
Additive mixing of colors
Initial colors
Mixed color
Initial colors
Mixed color
Magenta, yellow
Yellow, cyan
Cyan, magenta
Magenta, yellow, cyan
Red
Green
Blue
Black
Green, blue
Blue, red
Red, green
Green, blue, red
Cyan
Magenta
Yellow
White
From the position and shape of the curves in Fig. 2.61, it is clear that the light
absorption of the red, green, and blue color receptors occurs in different and partially overlapping spectral regions, although only one color stimulus is evoked
in the retina. The color stimulus Φ clearly depends on wavelength λ. If the photons of the source directly reach the retina, the color stimulus Φ(λ) equals the
spectral energy distribution S(λ) of the source. For non-self-luminous colors,
Φ(λ) is given by the product of S(λ) and the reflection R(λ) or transmission
T(λ) of the illuminated layer:
Φ(λ) = S(λ) · T(λ),
(2.4.1)
Φ(λ) = S(λ) · T(λ).
(2.4.2)
Using several illumination sources simultaneously, each individual color stimulus is summed up to form an aggregate stimulus, exactly the same procedure
as in the retina or in screens. All further color physical themes dealt within this
book, such as color vision, colorimetry, color measurement, or color recipe prediction, are based on the fundamental empirical laws of additive color mixing
formulated by Grassmann in 1853.
As briefly mentioned at the beginning of this section, for his investigations, Grassmann used three monochromatic light sources emitting constant red,
green, and blue wavelengths, respectively. With a similar configuration to that
shown in Fig. 2.63, but without the incandescent lamp, a new light color is mixed
on a white field by superposition of these three wavelengths. The experimental
results show that any additive color mixing is characterized by three arbitrarily
chosen primaries R, G, B, in this case lights, which are given by the corresponding color values R, G, B. They correspond to the relative luminance of the light
sources used. Of importance is that each of the three color values R, G, B is not
necessarily restricted to a fixed wavelength in the red, green, or blue range; they
are optional. The three color values R, G, B are combined in the so-called color
2.4
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119
stimulus specification C, which is written as a vector in three dimensions19
C = (R, G, B)T .
(2.4.3)
Furthermore, the primaries R, G, B can be interpreted as the unit vectors of a
three-dimensional space
R = (1, 0, 0)T ,
G = (0, 1, 0)T ,
B = (0, 0, 1)T .
(2.4.4)
Using terms such as color values, color stimulus specification, and primaries,
Grassmann summarized his results in the following three empirical laws of
additive color mixture:
1. For identification of a color stimulus specification, three independent primaries, which cannot be matched by additive mixture of the other stimuli,
are necessary and sufficient.
2. The result of an additive color mixture is influenced only by the color
stimulus specifications, not by their spectral compositions.
3. All producible color mixing series change continuously.
Now, we consider the consequences of the Grassmann laws. According to his
first law, each color stimulus specification C is represented by an equation of the
form
C = RR + GG + BB.
(2.4.5)
It is called the color equation. Equation (2.4.5) is of central significance to
all of color physics. It is valid for arbitrarily selected primaries R, G, B. The
three color values R, G, B provide the contributions of the three primaries to
the color stimulus specification C. In other words, the color values describe
the entire color impression. This is synonymous with the statement that every
color impression is given in quantitative form by three color values R, G, B.
The numerical quantities of R, G, B are, therefore, representatives of a color
impression.
The second law of additive color mixing turns out, for example, to be applicable to all cases of color matching; it is the basis of color recipe prediction. For
any color impression, it is irrelevant of which individual colorant components
the corresponding coloration is composed. The same holds for the mixture of
lights of different spectral distributions. If, for example, two arbitrarily given
color stimulus specifications C1 and C2 are matched by three primaries R, G, B,
then from the first Grassmann law, it follows
19 The exponent
T symbolizes a transposed vector.
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2 Light Sources, Types of Colorants, Observer
C1 = R1 R + G1 G + B1 B ,
(2.4.6)
C2 = R2 R + G2 G + B2 B.
(2.4.7)
According to the second law, the additive mixture of both color stimulus specifications is given by the sum of the corresponding individual color values
C = C1 + C2 = (R1 + R2 )R + (G1 + G2 )G + (B1 + B2 )B.
(2.4.8)
The additive color mixing produces a new color stimulus specification C, from
which is not possible to discern whether or not it consists of several individual
color components (i.e., color values).
The third law of additive color mixing implies that if one or more components of the mixture are gradually changed, then the resulting color values
also change gradually, that is, as opposed to changing in a discontinuous fashion. Therefore, if we assign the color stimulus specification to a point in
three-dimensional space, all additively mixed color stimuli generate an own
continuous and coherent color solid, the color space.
Grassmann has formulated originally four laws, which in modern literature
are summarized to the three given above. In the next section, we pursue the
industrially important question, how we can use color values to treat color
impressions objectively?
2.4.4 Tristimulus Color-Matching Experiments
According to the laws of additive color mixing, a given color is characterized
by three color values R, G, B. For handling of these laws, it is useful to establish
the optional primaries R, G, B in such a way that at least the requirements that
follow are fulfilled. The primaries should
– be definite, reproducible, and computable from color measurements;
– have always a positive sign;
– correspond to photopic vision;
– achieve numerical color differences corresponding to the visually perceived
color differences.
The system introduced from the CIE in 1931 meets, to a large extent, the
listed first three criteria [7]. The final listed requirement is as yet not satisfactorily solved (see, e.g., Section 3.2). The CIE 1931 system rests on the results of
tristimulus color-matching investigations of Wright [66] and Guild [67], which
used ten and seven people, respectively. For these experiments, the complete
configuration used is shown in Fig. 2.63. With a source of nearly monochromatic
2.4
Observer
121
light, a test stimulus of ±2.5 nm wavelength accuracy was generated by illuminating a bipartite white screen which was shielded against the other half. On this
second field, the additive mixture of three primaries was projected. These were
the matching stimuli of the three monochromatic lights. By using adjustable
light controllers, the observer subjectively adjusted the light flux of the three
primaries to obtain a color match between the two separated fields. Wright and
Guild used three monochromatic light sources of wavelengths 700.0, 564.1, and
435.8 nm. In the case of a match, the test stimulus was characterized by the three
luminance values of the primaries.
Before the actual matching experiments were performed, the intensities of the
three primaries were adjusted to obtain an additive mixture of achromatic white.
This procedure is termed as white balance; an example is shown in Color plate 1,
see lower overlapping color circles. The color values are, therefore, normalized
with regard to the radiant energy density of the primaries for white balance: the
accompanying color equations are valid for the so-called equienergy spectrum.
Colors differing only in their lightness belong to the same chromaticity.
The color stimulus specification of the test stimulus at wavelength λi is
termed as Ci . The matching color values of the three primaries are called colormatching values and are assigned by ri , gi , bi ; they are valid especially for the
chosen primaries R, G, B [68, 69]. Due to the subjectively different color sensation of the observers, the ri , gi , bi values fluctuate. Their mean values are
denoted by r̄i , ḡi , b̄i .
In the case of match, the color equation
Ci = r̄i R + ḡi G + b̄i B
(2.4.9)
is fulfilled according to the first Grassmann law. However, the matching procedures certainly show that not every given spectral color can be matched with
the preset primaries. For example, a blue-green color of wavelength 490 nm
does not match by mixing the blue or green primaries alone. In this case, the
color match of equally saturated color fields is only achieved if an amount r̄io of
the primary R is directly added to the given test stimulus specification Ci . This
procedure is called outer mixture and is represented by the color equation
Ci + r̄io R = ḡi G + b̄i B.
(2.4.10)
By adding the quantity −r̄io R to each side of color equation (2.4.10), an equation
analogous to Equation (2.4.9), but with negative amount −r̄io on the right-hand
side, results. This is a less than satisfactory situation to which we return in the
next section.
For continuous wavelengths λ, the mean color-matching values r̄i , ḡi , b̄i
turn into the color-matching functions (CMFs), which are assigned to r̄(λ),
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2 Light Sources, Types of Colorants, Observer
Color matching function
0.4
–
r (λ)
–
b (λ)
0.3
g–(λ)
0.2
0.1
0
546.1
435.8
700.0
–0.1
400
500
600
λ
nm
Fig. 2.64 Color-matching functions r̄(λ), ḡ(λ), b̄(λ) of the equienergy spectrum using
wavelengths of 700.0, 546.1, and 435.8 nm for primaries R, G, B
2°
10°
50
1.8
9.1
Fig. 2.65 Visual angles of 2◦ and 10◦
ḡ(λ), b̄(λ), and shown in Fig. 2.64. The color match on both color fields is carried out with a visual angle of 2◦ by the observer; see Fig. 2.65. Under this
observation angle and at normal viewing distance of 50 cm, a circle area of
1.8 cm in diameter is perceived. In the same angular range, the fovea of the
retina contains only cones (Fig. 2.60). An observer, which fulfills these conditions, is called 2◦ standard observer, abbreviated 2◦ observer, and is represented
by the three CMFs r̄(λ), ḡ(λ), b̄(λ).
As shown in Fig. 2.64, the CMFs have unequal peak heights. This represents the different sensitivities of the corresponding three retinal color receptors.
Among the CMFs, only the function r̄(λ) has a negative amount with the dip
minimum at about 522 nm. The negative proportion is a consequence of the
outer mixture. If the reference color stimulus specification corresponds to the
2.4
Observer
123
wavelength of a primary, the other two primaries are not required and their corresponding CMFs are zero. This can be taken from Fig. 2.64 for wavelengths of
435.8, 546.1, and 700.0 nm.
Finally, it needs to be pointed out that the trichromatic matching experiments
were achieved only with few people, under photopic vision with an observation angle of 2◦ and dark surroundings. Insights for scotopic or mesopic vision,
bright surroundings, or large colored fields have, up to now, not been performed.
2.4.5 Determination of Tristimulus Values
In view of color measuring methods and colorimetric applications, we will use
discrete wavelengths λi in the following. A trichromatic stimulus is induced,
according to the explanations in Section 2.4.3, by additive mixture of all
monochromatic color stimuli Φ i = Φ(λi ). In the case of non-self-luminous colors, the color stimulus Φ i follows, according to Equations (2.4.1) and (2.4.2),
from
Φi = S(λi ) · R(λi )
(2.4.11)
Φi = S(λi ) · T(λi ),
(2.4.12)
or
because a non-self-luminous color is to illuminate with a source of spectral
power distribution S(λi ). Each retinal color stimulus Φ i is represented by a corresponding color stimulus specification Ci . If there are simultaneously i = 1,
2, . . . , N stimuli Ci , the total color stimulus specification is given by additive
mixture:
C=
N
Ci .
(2.4.13)
i=1
Applying Equation (2.4.8) with N ≥ 2,
C=
N
i=1
Ci =
N
i=1
Ri R +
N
Gi G +
i=1
N
Bi B
(2.4.14)
i=1
follows. The color values Ri , Gi , Bi correspond, on the other hand, to the product
of the color stimulus Φ i , one of the respective CMFs r̄i , ḡi , b̄i , and the technically given wavelength interval width Δλ of the used illuminant. From this, it is
possible to write the equations for the color values:
Ri = Φi r̄i Δλ,
(2.4.15)
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2 Light Sources, Types of Colorants, Observer
Gi = Φi ḡi Δλ,
(2.4.16)
Bi = Φi b̄i Δλ .
(2.4.17)
If we insert these relations into Equation (2.4.14) and compare the new equation
with Equation (2.4.5), finally the color values R, G, B of a non-self-luminous
color follow from expressions:
R=
N
Φi r̄i Δλ,
(2.4.18)
Φi ḡi Δλ,
(2.4.19)
Φi b̄i Δλ.
(2.4.20)
i=1
G=
N
i=1
B=
N
i=1
If the emitted wavelengths are quite closely spaced together so that infinitesimally small wavelength intervals dλ can be assumed, the discrete color stimuli
Φ i can be written as the color stimulus function Φ(λ). Then, the color-matching
values r̄i , ḡi , b̄i also become the CMFs r̄(λ), ḡ(λ), b̄(λ). Accordingly, the sums
in Equations (2.4.13), (2.4.14) and (2.4.18), (2.4.19), (2.4.20) should be substituted by integrals and the integration limits correspond to the lower and upper
cutoff wavelengths of the visible range.
In this text, the sum notation is generally preferred. Two straightforward reasons for this preference are as follows: first, the spectral power distribution
S(λi ) of the most used illuminants in color industry and the CMFs of the 2◦
standard observer are tabulated for interval widths Δλ of 5, 10, and 20 nm
[70–72] and second, all industrial spectrophotometers are designed to measure
in one of these wavelength interval widths. Therefore, the color values R, G, B
of a given color sample can be calculated from Equations (2.4.18), (2.4.19),
and (2.4.20) if the accompanying reflection or transmission is known from
measurement.
To summarize, we emphasize that owing to additive color mixture, a given
color can be described by three corresponding numerical color values R, G,
B. These are merely representatives of the corresponding color and are by no
means absolute values. On the basis of the experimental connections, they can
be interpreted as the red, green, and blue components of a color shade. In the
following section these results are finally modified for practical applications in
colorimetry.
2.4
Observer
125
2.4.6 CIE 1931 and CIE 1964 Standard Colorimetric Observers
Among the indicated color values, the red component R of a color shade has a
region of negative values of the CMF r̄(λ) shown in Fig. 2.64: this is extremely
unreasonable. Depending on color stimulus Φ i , the color value R can show,
according to Equation (2.4.18), a positive or negative sign and, therefore, cannot
be clearly interpreted in a coloristic sense. More confusing is, for example, a red
coloration with a color value of R = 0. The occurrence of negative color values
is due to the choice of the three real primaries R, G, B. Negative color values
cannot be altogether avoided with the spectral energy distribution of technical
light sources.
In order to achieve only positive or zero CMFs and color values, respectively,
the CIE introduced in the year 1931 – after the conclusions of Wright [66] and
Guild [67] – the so-called virtual primaries X, Y, Z. These follow from a suitable numerical transformation of the previous real primaries R, G, B [7]. The
virtual primaries X, Y, Z are chosen in such a way that the following criteria are
fulfilled:
– X, Y, Z are by definition independent of each another, and are, therefore, not
producible by mixing (the same requirement as for the real primaries R, G,
B);
– the new CMFs x̄(λ), ȳ(λ), z̄(λ) always take values ≥ 0 and follow from the
previous CMFs by an appropriate transformation (see below);
– the virtual primaries X, Y, Z are adjusted in such a way that the corresponding tristimulus values X, Y, Z are equally valued for the chromaticity of the
equienergy spectrum: X = Y = Z;
– the two virtual primaries X and Z are chosen in such a way that only the color
value Y is proportional to the lightness of a color.
The new color quantities X, Y, Z are called standard color values. The new
CMFs x̄(λ), ȳ(λ), z̄(λ) are named standard color-matching functions (SCMFs)
and are given with the previous CMFs r̄(λ), ḡ(λ), b̄(λ) by the empirical matrix
equation
⎛
⎞ ⎛
⎞ ⎛
⎞
r̄(λ)
x̄(λ)
2.768892 1.751748 1.130160
⎝ ȳ(λ) ⎠ = ⎝
1
4.590700 0.060100 ⎠ · ⎝ ḡ(λ) ⎠ .
z̄(λ)
0
0.056508 5.594292
b̄(λ)
(2.4.21)
These SCMFs belong to the 2◦ observer, called CIE 1931 observer; the corresponding graphs are shown in Fig. 2.66 [7]. Discrete values of these functions
are used to calculate the standard color values X, Y, Z, see below.
126
2 Light Sources, Types of Colorants, Observer
In practice, all color samples for visual assessment have a larger sized colored
area compared with the 2◦ field at the normal vision range of 50 cm (Fig. 2.65).
A considerable reason for such small-sized samples is that an observation angle
of 2◦ covers only the area of the fovea. Although there is the highest cone density, the induced color stimulus from this spot is insufficient for an adequate
color assessment. Because of that, the CIE introduced in 1964 the so-called 10◦
observer, also termed as CIE 1964 observer, based on investigations of Stiles
and Burch as well as Speranskaja with 49 and 27 people, respectively [73–75].
Recent tabular values of the SCMFs for the 10◦ observer have been given in the
literature [70–72].
Whereas the primaries of the 2◦ observer are related to the wavelengths
700.0, 546.1, and 435.8 nm and the primaries of the 10◦ observer have the
corresponding wavelengths 645.2, 526.3, and 444.4 nm. For the normal vision
distance of 50 cm, the visual angle of 10◦ covers a circle area of 8.8 cm in diameter, cf. Fig. 2.65. In this area, the retina certainly contains rods. For this reason,
the SCMFs were corrected to eliminate the influence of the rods [7]. The CIE
recommended the 2◦ observer for visual angles between 1◦ and 4◦ , and the 10◦
observer for visual angles > 4 ◦ . The 4◦ limit was arbitrarily established although
there exists no discontinuity of color perception at this angle.
The SCMFs of the 10◦ observer x̄10 (λ), ȳ10 (λ), z̄10 (λ) are distinguished
from those of the 2◦ observer by the subscript 10. The values follow from
a transformation similar to Equation (2.4.21) using the corresponding CMFs
r̄10 (λ), ḡ10 (λ), b̄10 (λ) according to the equation
⎞ ⎛
⎞
⎞ ⎛
r̄10 (λ)
0.341080 0.189145 0.387529
x̄10 (λ)
⎝ ȳ10 (λ) ⎠ = ⎝ 0.139058 0.837460 0.073160 ⎠ · ⎝ ḡ10 (λ) ⎠ .
z̄10 (λ)
0
0.039553 1.026200
b̄10 (λ)
⎛
(2.4.22)
The numerical values of the components of the matrices in Equations (2.4.21)
and (2.4.22) are unequal because they belong to different primaries and different observer fields. The SCMFs of both observers are together represented
in Fig. 2.66. The maxima of the functions ȳ(λ) and ȳ10 (λ) are normalized at
λ = 555 nm to 1.0. Due to the different visual field of the observers, the corresponding curves do not match perfectly. For one and the same color, the standard
color values corresponding to each observer are also not identical. From the
nonlinear wavelength dependence of both CMFs follows that the corresponding standard color values cannot be converted into one another. Although the
10◦ observer is used to an increasing extent in color industry, in order to avoid
ambiguity, the observer must be clearly indicated with the results.
For the last adjustment criterion of the four listed above, it should be
stated that the graph of the function ȳ10 (λ) agrees with the measured luminous
efficiency V(λ) of the human eye
2.4
Observer
127
2°
10°
Standard color matching function
2.0
z (λ)
1.5
x (λ)
y (λ)
1.0
x (λ)
0.5
0
400
500
600
700
λ
nm
Fig. 2.66 Color-matching functions of the 2◦ and 10◦ standard observers (CIE 1931 and CIE
1964 observers, respectively)
ȳ10 (λ) = V(λ),
(2.4.23)
see Fig. 2.67.20 The standard color value Y is, on account of this adjustment,
a measure for the lightness of a coloration. The curves of V (λ) and V(λ) in
Fig. 2.67 correspond to the sensitivity of the eye for scotopic and photopic
adaption, respectively. The curves are shifted with respect one another by about
40 nm. This is described by the so-called Purkinje effect. From the half-widths
of 150 nm, it follows that the middle wavelengths of the visible spectrum are
perceived with particular sensitivity under both adaption conditions.
Now, the CIE standard color values X, Y, Z are simply given from the
previous quantities R, G, B by substituting the discrete color-matching values
r̄i , ḡi , b̄i of the 2◦ observer in Equations (2.4.18), (2.4.19), and (2.4.20) by the
corresponding quantities x̄i , ȳi , z̄i :
20 Since
V(λ).
2005, the CIE’s altered recommendation [71]; since 1931 it was accepted ȳ(λ) =
128
2 Light Sources, Types of Colorants, Observer
V(λ)
Relative luminous efficiency
V '(λ)
1.0
0.5
0
400
500
600
700
λ
nm
Fig. 2.67 Relative luminous efficiency of the human eye in scotopic adaption V (λ) and
photopic adaption V(λ)
X=
N
Φi x̄i Δλ,
(2.4.24)
Φi ȳi Δλ,
(2.4.25)
Φi z̄i Δλ.
(2.4.26)
i=1
Y=
N
i=1
Z=
N
i=1
The standard color values for the 10◦ observer follow from the same considerations using x̄10, i , ȳ10, i , z̄10, i instead of x̄i , ȳi , z̄i and are denoted by X10 , Y10 , Z10 .
According to the last three relations, the standard color values of a coloration can be explicitly calculated if the retinal color stimuli Φ i are known
from Equation (2.4.11) or (2.4.12). The spectral power distribution S(λi ) of the
light source used is known from CIE tables. This means that the spectral power
distribution of the real source is substituted by a corresponding artificial source
for the determination of color values. The same is the case with regard to the
observer: the individual observer is substituted by one of the standard observers.
In addition, the measured reflection or transmission of a given color sample can
differ in different color measuring devices. The retinal color stimulus values
above are, therefore, idealized quantities and it is, therefore, not astonishing
that color values can differ from the individual visual assessment.
Nevertheless, a given coloration is unambiguously characterized by three corresponding numerical standard color values. Colors of equal standard values are
References
129
perceived as equal, even if they consist of different sorts of colorants (e.g., dyes
or absorption pigments). Because of this, it is not possible to infer the constituent colorants from the numerics of the standard color values. At best, with
experience, one can estimate the lightness, chroma, or hue of the color. On the
other hand, a single color value alone is not of main interest in color physical
applications. Of much greater importance is the color difference between two
or more similar color shades. Such questions and answers to them for nearly all
sorts of colors are discussed in the sections of the following chapter.
References
1. Strocka, D: “Are Intervals of 20 nm Sufficient for Industrial Colour Measurement?”,
Colour 73, Adam Hilger, London (1973) 453
2. Pedrotti, FL, Pedrotti, LS, Pedrotti, LM: “Introduction to Optics”, Person Prentice Hall,
Upper Saddle River, NJ (2007)
3. Bellan, PM: “Fundamentals of Plasma Physics”, Cambridge University Press,
Cambridge (2006)
4. Taylor, AH, Kerr, GP: “The distribution of energy in the visible spectrum of daylight”, J
Opt Soc Am 31 3–8 (1941)
5. Albrecht, H: “Optische Strahlungsquellen”, Grafenau (1977)
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M: “Fundamentals of light sources and lasers”, Wiley-Interscience, Hoboken, New
Jersey (2004)
7. CIE No 15.3: “Colorimetry”, 3rd ed, CIE, Bureau Central de la CIE, Wien (2004)
8. ISO 11664-2:2007: “Colorimetry – Part 2: CIE Standard Illuminants”, International
Organization of Standardization, Genf, CH (2007)
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