**2.2 Tyndall diffusion in nature**

Tyndall scattering has long been recognized to be responsible for blue coloration of the sky (Tyndall, 1869) and the color of blue eyes (Mason, 1924). It appears when small particles or voids with dimensions of the order of the wavelength of blue light (about 500 nm) are present in the propagation medium. In that case, the small wavelengths of the incident white light will be scattered and the longer wavelengths will pass undisturbed through the medium. Thus, the red and yellow wavelengths are transmitted and the blue and violet colors are scattered by the composite medium, giving out a non-iridescent light blue diffusion spectrum.

In this phenomenon, the particle's sizes and refractive indexes control the coloration. As shown here above, the intensity of the reflected light by such a system is inversely proportional to the 4th power of the wavelength. The amplitude of the reflected light and its angular distribution will depend on the particle's sizes.

For incoherent Tyndall or Rayleigh scattering to occur, it is necessary that the diffusers are separated by more than the coherence length of sunlight (about 600 nm). Under this distance, coherent interaction occurs, even if the diffusive particles are randomly arranged and one can no more talk about Tyndall or incoherent scattering. This misleading fact is at the origin of several wrong interpretations of blue coloration in animals.

In living organisms, Tyndall blue is almost always present in association with underneath pigments. The underlying pigment granules absorb the incident light that penetrate through all the structural tissue and prevent desaturation by wavelengths scattered by inner tissues. They allow structural colors to be generated with a limited number of scatterers. In most cases, the pigment granules are made of melanin (Fox, 1976) but carotenoids, antocyanins and pterins (Lee, 1991; Stavenga et al., 200; Walls, 1995) can also be present, giving rise to various coloring effects.

Since the early 20th century, much work has been devoted to discovering the origin of dull blue colorations seen in animals. At first, it was common to distinguish two cases: the *iridescent* blue, synonym of coherent scattering and the *non-iridescent* blue, assumed to be incoherent Rayleigh or Tyndall scattering (Fox, 1976; Mason, 1926; Mason, 1927). At that time, the difference was based on the visual observation and not from the microscopic distances between scatterers.

things also become more complicated. When the distance between the particles is much larger than the coherence length of the illuminating light, the collective scattering is incoherent, which means that the diffused intensity is merely the sum of the intensities diffused by each scattering center. The incoherent scattering by "Rayleigh particles (in the range of diameters smaller than 50 nm)" and by "Tyndall particles" (in the range 50-900 nm) can still be considered as mechanisms of "Rayleigh" or "Tyndall" scattering, respectively. If the particles are closer, we encounter a case of coherent scattering and we must add vector amplitudes with respective phases rather than intensities. The multiple scattering on nearby particles provides further opportunities for standing waves and resonances and we again lose the inverse fourth power law. The intensity and scatter directions then depend on the spatial distribution of the particles and in particular, the

Tyndall scattering has long been recognized to be responsible for blue coloration of the sky (Tyndall, 1869) and the color of blue eyes (Mason, 1924). It appears when small particles or voids with dimensions of the order of the wavelength of blue light (about 500 nm) are present in the propagation medium. In that case, the small wavelengths of the incident white light will be scattered and the longer wavelengths will pass undisturbed through the medium. Thus, the red and yellow wavelengths are transmitted and the blue and violet colors are scattered by the composite medium, giving out a non-iridescent light blue

In this phenomenon, the particle's sizes and refractive indexes control the coloration. As shown here above, the intensity of the reflected light by such a system is inversely proportional to the 4th power of the wavelength. The amplitude of the reflected light and its

For incoherent Tyndall or Rayleigh scattering to occur, it is necessary that the diffusers are separated by more than the coherence length of sunlight (about 600 nm). Under this distance, coherent interaction occurs, even if the diffusive particles are randomly arranged and one can no more talk about Tyndall or incoherent scattering. This misleading fact is at

In living organisms, Tyndall blue is almost always present in association with underneath pigments. The underlying pigment granules absorb the incident light that penetrate through all the structural tissue and prevent desaturation by wavelengths scattered by inner tissues. They allow structural colors to be generated with a limited number of scatterers. In most cases, the pigment granules are made of melanin (Fox, 1976) but carotenoids, antocyanins and pterins (Lee, 1991; Stavenga et al., 200; Walls, 1995) can also be present, giving rise to

Since the early 20th century, much work has been devoted to discovering the origin of dull blue colorations seen in animals. At first, it was common to distinguish two cases: the *iridescent* blue, synonym of coherent scattering and the *non-iridescent* blue, assumed to be incoherent Rayleigh or Tyndall scattering (Fox, 1976; Mason, 1926; Mason, 1927). At that time, the difference was based on the visual observation and not from the microscopic

average distance between them.

**2.2 Tyndall diffusion in nature** 

angular distribution will depend on the particle's sizes.

the origin of several wrong interpretations of blue coloration in animals.

diffusion spectrum.

various coloring effects.

distances between scatterers.

It is interesting to mention that, in the twenties, Mason attributed all the non-iridescent blue colorations seen in bird feathers to Tyndall scattering but was aware that, in some insects, such coloration could arise from other phenomena (Mason 1923, Mason 1927). As new experimental and imaging techniques developed, new insights showed that blue in bird feathers could also be produced by constructive interference of light waves. Interfaces between keratin and air in the spongy medullar layer of the barbs act as coherent scatterers in that case (Prum et al., 1998; Prum et al., 1999). Blue Tyndall skins also appear in birds. For example, the extinct dodo head skin was found to be showing a diffuse blue color. This skin reveals randomly arranged, fine particles, about the size of the blue light wavelength (Parker, 2005).

Fig. 1. The male dragonfly *Orthetrum caledonicum* (Libellulidae). The blue coloration of the body comes from Tyndall scattering in a waxy layer over the black cuticle (Parker, 2000). (reproduced from GNU free documentation)

Scattered blues have early been assigned to insects. The scattering occurs in the epidermal cells beneath a transparent cuticle. In the odonate order such as aeschnids, agrionids and libelluloids (*Libellula Pulchella*, *Mesothemis Simplicicollis*, *Enallagma Cyathigerum*, *Aeshnea cyanea*, *Anax walsinghami*) the bright blue diffuse coloration on their body or wings (Mason, 1926; Parker, 2000; Parker, 2005; Veron, 1973) originates from scattering centers under the cuticle. Dragonflies (Mason, 1926) and some other adult insects can also develop a waxy bloom on the surface of their cuticle. The Tyndall effect is then produced by this waxy material and coloration can be destroyed by washing it with a wax solvent (Parker 2000): see Fig. 1.

Some butterflies have also been thought to be colored by this mechanism, such as *Papillio zalmoxis* or lycaenids (Huxley, 1976; Berthier, 2006). However, recent research shows that *coherent* interferences could also explain the various observed colors in these butterflies (Wilts et al., 2008; Prum et al., 2006). Tyndall blue has also been recorded in the cuticle of the

How Nature Produces Blue Color 9

 Fig. 3. Blue skins in mammals: Male mandrill facial blue skin (left) and male vervet monkey

Pigmentary coloration is based on a spectrally selective absorption of the incident whitelight. For a pigment to be useful, the light which has not been absorbed must be diffused in all directions, providing the same color in all directions. This means that a sheet of material colored by absorption and diffusion will appear with roughly the same color in reflection and transmission. This contrasts structural colors obtained by interference, without

The physical description of a selectively absorbing material illuminated by a single frequency needs to extend the concept of the refractive index to include refraction and absorption. A simple way to do this is, at a fixed frequency, to accept to replace its real value by a complex number *n n ik* . A frequency-dependent complex refractive index (or, equivalently) a frequency-dependent complex dielectric constant can explain the optical response of dyes in a homogeneous material. But pigments require to produce diffuse scattering and this will only take place in a random inhomogeneous material or when the absorbing material appears in the form of concentrated granules. This helps providing a

In plants, blue coloration is quite rare. However, it can be seen in some leaves, flowers or fruits. The blue is produced by modified anthocyanin pigments. A wide variety of mechanisms for modifying anthocyanin pigments has been observed in order to get blue or violet colorations. In flowers, they form complexes with flavonoids pigments and are in solution in cellular vacuoles. In leaves, they take place in chloroplasts. The structuration of

absorption, where back- and forward scattering colors tend to be complementary.

with blue scrotum (right) (reproduced from GNU free documentation)

**3. Pigmentary coloration 3.1 Theoretical background** 

distinction between dyes and pigments.

**3.2 Pigmentary coloration in plants** 

larvae of some tent caterpillars (Byers, 1975), due to the presence of inhomogeneous transparent cuticular filaments.

Fig. 2. The male grasshopper *Kosciuscola tristis* at 30°C (left) and 5°C (right). The blue coloration accuring at high temperature comes from Tyndall scattering (from K. D. L. Umbers, with permission, Umbers, 2011)

The male grasshopper *Kosciuscola tristis*, also called "chameleon grasshopper" has the ability to change from black to bright sky blue. It has been shown that the mechanism of this color change is completely reversible and regulated by temperature changes (Filshie et al., 1975; Umbers, 2011). It is currently admitted that the blue color arises from Tyndall scattering of light on a suspension of small granules, intensified by the underlying dark background. Intracellular granule migration can explain the color change. However, recent discussion may lead to the conclusion that coherent scattering may play a role much more important than expected (Umbers, 2011).

Tyndall scattering has also been observed in molluscs (Fox, 1976; Herring, 1994) and in nudibranch mollusks (Kawaguti & Kamishima, 1964). These are obtained by small diffusive granules displayed over a pigmentary melanophore layer. Octopus and squids are sometimes able to control the blue hue of their body patterns. This adaptive blue is achieved by varying the melanophore's grains distances in order to change the underneath absorbing screen density (Fox, 1976).

Several blue mammals skins, especially in the primates family were thought to be Rayleigh or Tyndall scattered (Fox, 1976; Price et al., 1976). However, recent research on several structurally colored mammal skins pointed out that these colorations should come from coherent scattering from quasi-ordered arrays of collagen fibers (Prum & Torres, 2004).

As far as we know, it is hard to find in nature true incoherent Tyndall scattering. Diffusive layers are often made of randomly arranged particles too close from each other to assume incoherent scattering. This condition for incoherent diffusion is often misunderstood in papers that attribute to Tyndall scattering an array of disordered particles of the size of the wavelength, whatever the distance between them.

larvae of some tent caterpillars (Byers, 1975), due to the presence of inhomogeneous

Fig. 2. The male grasshopper *Kosciuscola tristis* at 30°C (left) and 5°C (right). The blue coloration accuring at high temperature comes from Tyndall scattering (from K. D. L.

The male grasshopper *Kosciuscola tristis*, also called "chameleon grasshopper" has the ability to change from black to bright sky blue. It has been shown that the mechanism of this color change is completely reversible and regulated by temperature changes (Filshie et al., 1975; Umbers, 2011). It is currently admitted that the blue color arises from Tyndall scattering of light on a suspension of small granules, intensified by the underlying dark background. Intracellular granule migration can explain the color change. However, recent discussion may lead to the conclusion that coherent scattering may play a role much more important

Tyndall scattering has also been observed in molluscs (Fox, 1976; Herring, 1994) and in nudibranch mollusks (Kawaguti & Kamishima, 1964). These are obtained by small diffusive granules displayed over a pigmentary melanophore layer. Octopus and squids are sometimes able to control the blue hue of their body patterns. This adaptive blue is achieved by varying the melanophore's grains distances in order to change the underneath absorbing

Several blue mammals skins, especially in the primates family were thought to be Rayleigh or Tyndall scattered (Fox, 1976; Price et al., 1976). However, recent research on several structurally colored mammal skins pointed out that these colorations should come from coherent scattering from quasi-ordered arrays of collagen fibers (Prum & Torres, 2004).

As far as we know, it is hard to find in nature true incoherent Tyndall scattering. Diffusive layers are often made of randomly arranged particles too close from each other to assume incoherent scattering. This condition for incoherent diffusion is often misunderstood in papers that attribute to Tyndall scattering an array of disordered particles of the size of the

transparent cuticular filaments.

Umbers, with permission, Umbers, 2011)

than expected (Umbers, 2011).

screen density (Fox, 1976).

wavelength, whatever the distance between them.

Fig. 3. Blue skins in mammals: Male mandrill facial blue skin (left) and male vervet monkey with blue scrotum (right) (reproduced from GNU free documentation)
