Structural coloured feathers of mallards act by simple multilayer photonics

2.1. Animals

Moulted mallard feathers were collected in a location known to be inhabited by a duck community, and were taken from a road kill and a specimen provided by a local huntsman.

2.2. Light microscopy

Photographs of barbules in an intact speculum feather were made with an Olympus SZX16 stereomicroscope, and images of the upper- and undersides of an isolated barbule were made with a Zeiss Universal Microscope (Zeiss, Oberkochen, Germany).

2.3. Transmission electron microscopy

The barbule anatomy was investigated by TEM using standard methods [18]. Briefly, a feather piece was subjected to a series of dehydrations in increasing concentrations of EtOH : H₂O mixtures, embedded in EPON resin and cut to approximately 50 nm sections using a diamond ultramicrotome. Sections were stained using 2% aqueous uranyl acetate solution and examined with a Hitachi 7100 TEM.

2.4. Spectroscopy

Reflectance spectra of both sides of isolated barbules attached to the tip of a glass micropipette were measured with a microspectrophotometer (MSP), which consisted of a Leitz Ortholux microscope (Leitz, Wetzlar, Germany) connected to an AvaSpec 2048–2 CCD detector array spectrometer (Avantes, Apeldoorn, The Netherlands) and a xenon arc light source. The microscope objective was an Olympus 20×, NA 0.46 (Olympus, Tokyo, Japan). Owing to the glass optics, the MSP spectra were limited to wavelengths greater than 350 nm. The area measured with the MSP was a square with edge length of 5–10 µm. The reference was a white diffuse reflectance tile (Avantes WS-2); when the measured object is not diffuse but directionally reflecting this causes severely overestimated reflectance values (by about a factor of 4). Transmittance spectra of isolated barbules, immersed in immersion oil (refractive index 1.515), were also measured with the MSP. Reflectance spectra from intact feathers were measured with a bifurcated reflection probe (Avantes FCR-7UV200), using also the white diffuse reflectance tile as a reference. The light source was a deuterium-halogen lamp (AvaLight-D(H)-S). The bifurcated probe illuminated an area with a diameter of about 1 mm, and captured the light reflected in a small spatial angle with aperture about 20°.

2.5. Imaging scatterometry

For investigating the spatial reflection characteristics of the barbules, we performed imaging scatterometry. A small feather piece attached to a glass micropipette was positioned at the first focal point of the ellipsoidal mirror of a imaging scatterometer. The scatterograms were obtained by focusing a white light beam with a narrow aperture (less than 5°) onto at a small circular area (diameter approx. 13 µm) of the feather piece, and the spatial distribution of the far-field scattered light was monitored. A flake of magnesium oxide served as a white diffuse reference object (for further details, see [19–21]).

2.6. Modelling

Using parameter values inspired by anatomy, we calculated the reflectance and transmittance spectra of model barbules with a transfer-matrix program, written in Matlab, based on classical optical multilayer theory [20]. The model barbules contained two stacks of melanosomes, embedded in a keratin matrix and enveloped by a keratin cortex. We sliced the melanosome stacks into 1 nm thin layers and calculated the volume fractions of the components keratin and melanin, f_k and f_m, of each layer, with f_k + f_m = 1. The real parts of the wavelength-dependent refractive indices of the two components, n_k and n_m, were calculated with the Cauchy formula n = A + Bλ⁻² (λ is the light wavelength), using for keratin A_k = 1.532 and B_k = 5890 nm⁻² and for melanin A_m = 1.648 and B_m = 23 700 nm⁻²; the imaginary component of the refractive index of keratin was assumed to be negligible in the wavelength range of interest, but that of melanin was taken to be k_m = a_mexp(−λ/b_m), with a_m = 0.56 and b_m = 270 nm [10,13]. The effective refractive index of each 1 nm layer was calculated with the volume fractions of the components:

Effective medium theory predicts for TE- and TM-polarized light incident on parallel rods weighting factors: w = −2 and 2 [22,23]. We found that w-values between −2 and +2 yielded virtually identical reflectance spectra, and therefore we used in the final calculations w = 1. We compared the results with calculations performed with Lumerical FDTD solutions 8.16, a commercial-grade Maxwell equation solver. Being based on fundamental Maxwell theory, FDTD simulations enable the detailed simulation of the light flux in any complex-structured material with arbitrary refractive index and spatial arrangement. With the same parameters as those used in the multilayer modelling, simulations were performed in a simulation box with a volume of approximately 3 × 3 × 5 µm³.

2.7. Photoreceptor sensitivity spectra

Mallards have four main photoreceptors: VS (violet-sensitive), SWS (short-wavelength-sensitive), MWS (middle-wavelength-sensitive) and LWS (long-wavelength-sensitive) [23,24]. The absorption spectra of the photoreceptors can be calculated with the absorption spectra of the visual pigments and their density in the outer segments. The absorption spectra were obtained with the peak wavelength of the visual pigments, 415, 452, 506 and 567 nm, and peak density of the photoreceptors 0.3, using a template [24–26]. In front of the SWS, MWS and LWS photoreceptors oil droplets are located that contain a high concentration of various carotenoids and thus act as spectral filters. Hart & Vorobyev [25] approximated the transmittance of the oil droplets with the expression

and assessed for the SWS, MWS and LWS oil droplets b = 0.098, 0.090 and 0.061, respectively, and λ₀ = 457, 519 and 580 nm. The transmittance spectra obtained with equation (2.2) can be well understood by assuming in the three oil droplets the carotenoids galloxanthin, zeaxanthin and astaxanthin, respectively, with peak density 5, 20 and 25 [5]. Furthermore, incident light is filtered by the ocular media in front of the retina. The absorption spectrum of the ocular media (fig. 5 in [26]) converted to the transmittance spectrum, normalized and fitted by equation (2.2) yielded b = 0.064 and λ₀ = 364 nm. The spectral filters cause strongly narrowed absorption bands of the photoreceptors. Normalizing the resulting absorption spectra yielded the sensitivity spectra of the four photoreceptors.

3.1. Colours and anatomy of head and speculum feathers

The common mallard, Anas platyrhynchos, is well known for its sexual dichromatism. The head of the male is marked by a prominent green sheen, highly contrasting with the white and orange-brownish coloration of the body (figure 1a). The female has an overall brown colour (figure 1b). The only colour correspondence of the two sexes, most notable during flight, is the blue colour of the speculum. The head and speculum colours are iridescent, i.e. the hue varies upon a change in direction of the illumination or inspection.

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The head and speculum feathers not only differ in colour, but also strongly in size and organization. In the approximate 1 cm long head feathers of the male (figure 1c), only the distal part is structurally coloured. Interestingly, the proximal part is rather colourless, because it is overlapped by adjacent feathers in situ (figure 1a,c). The overlap extends to the black middle part of the head feather, which has a contrast-enhancing function for the exposed distal part that displays the green colour. Somewhat differently, the approximate 10 cm long speculum feathers overlap sideways, but again only the exposed feather part is coloured (figure 1a,b,d). The distal and proximal boundaries of the displayed sides of adjacent feathers together create highly contrasting black and white bands of the speculum (figure 1a,b).

Inspection with a light microscope shows that the iridescence originates in the barbules (figure 2a,b). The barbules are coloured at only one side of the barb (figure 2c,d). The barbules consist of long rows of brightly coloured individual cells, each with an area approximately 20 × 30 µm² (figure 2e–g). The colour of the cells slightly varies across the speculum, and the colour appears to be not uniform even locally within a single cell (figure 2a–f). Interestingly, when observing an isolated barbule from both the upper- and undersides, a similar colour is seen (figure 2c–f). Notably, however, the underside of the cells features a pale centre, indicating the remnant of a cell nucleus [13,14,27]. The colours dramatically differ when observed with transmitted light. The barbules then appear to be heavily brown-black pigmented, clearly indicating the presence of melanin pigment (figure 2g).

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TEM demonstrates that the melanin of the barbule cells is concentrated in rod-like structures, the so-called melanosomes [6,7], that are oriented along the barbule's longitudinal axis (figure 3a), causing the striped pattern seen with transmission light microscopy (figure 2g). Cross sections show a highly symmetric pattern where a cortex, with thickness approximately 270 nm, envelopes two stacks of melanosomes, tightly packed into a lattice of five to six rows, with in-between randomly arranged melanosomes (figure 3b). The size of the individual melanosomes somewhat varies; in the specific case of figure 3c, the length is 1.5–2.0 µm and the diameter approximately 130 nm. The spatial arrangement is also somewhat irregular, clearly deviating from an ideal hexagonal stacking, especially at the side of the stacks facing the barbule's axis.

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3.2. Spectrometry and imaging scatterometry reveal multilayer characteristics

Interference of incident light with the lattice of melanosomes must cause the barbule's colours, and we therefore performed spectrometry as well as imaging scatterometry. Reflectance spectra measured by MSP from the upper and undersides of single barbule cells of speculum and head feathers yielded narrow-band spectra (FWHM 70–90 nm) with peak wavelengths at approximately 470 nm (figure 4a) and approximately 540 nm (figure 4b). Depending on the location, the spectra slightly varied in magnitude and spectral position (see the varying colours in figure 2e,f). Interestingly, the rising long-wavelength tail showed small but characteristic oscillations. These can be readily explained from the thickness of the barbule cells, 4–5 µm (figure 3a,b), when assuming an effective refractive index of approximately 1.6 [28]; for examples with more prominent oscillations, see the electronic supplementary material, figure S1.

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To quantitatively investigate the iridescence, we measured the reflectance of a speculum feather (figure 1d) as a function of polarization and angle of light incidence (figure 5a,b). In the measurements of figure 5a,b, the detection angle was changed mirror-wise; that is, the angle between the detector and the normal to the feather plane was equal but opposite the angle between the illumination and the normal. The reflectance peak wavelengths, derived from the spectra of figure 5a,b, decreased monotonically with increasing angle of light incidence for both TE- and TM-polarized light (figure 5c). Although the value of the peak reflectance of the TE-reflectance increased with increasing incidence angle, the TM-reflectance decreased up to an angle of incidence of approximately 60° and increased above that value (figure 5d).

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The angle dependence of the reflectance spectra of the TE- and TM-polarizations is characteristic for a multilayer structure [28,29]. The assembly of barbules in the mallard feathers may, however, not function as an ideal, classical optical multilayer, because that acts as a mirror, i.e. it reflects light from a point source into the mirror angle. To see to which extent the individual barbule cells approximate an ideal multilayer, we tested the spatial reflection properties of barbules of both speculum and head feathers using an imaging scatterometer (figure 6). In both cases, focusing a white light beam with aperture approximately 5° at a barbule cell with spot size approximately 13 µm caused a reflected beam with a slightly widened aperture of approximately 20° (figure 6a,b). The minor spread of the barbule reflection can be easily understood from the non-planar, inhomogeneous arrangement of the melanosomes when considering areas larger than a few micrometres (figure 3a). Applying light with a 90° aperture beam shows clear radial-symmetric iridescence (figure 6c,d), reinforcing the view that the reflection properties of single barbules can be locally interpreted with multilayer theory.

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3.3. Multilayer and finite-difference time-domain modelling of mallard barbules

We computationally investigated the reflection characteristics of the melanosome stacks in the barbules with a multilayer model (figure 7a, inset). In the model, a keratin layer, thickness t_b, contains two stacks of m layers of melanosomes, with melanosome axial interdistance a, layer period b, melanosome diameter d_m. The two stacks are separated by an interdistance t_i and enveloped by a cortex with thickness c. Based on the anatomy, we chose as initial model values m = 6, a = 145 nm, b = 160 nm, c = 270 nm, d_m = 130 nm, t_i = 2000 nm, yielding t_b = 4400 nm; subsequently, in more detailed modelling, we varied these values.

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As described in the Material and methods, we sliced the model of figure 7a in 1 nm thin layers and calculated for each layer the fraction of keratin and melanin, yielding with equation (2.1) the complex refractive index as a function of wavelength. With the obtained wavelength-dependent refractive index profile, we calculated the reflectance spectrum of the model barbule for normally incident light using a transfer-matrix method. To ascertain the validity of the multilayer approach, we also used the FDTD method to calculate the reflectance spectrum of a full three-dimensional model for normally incident light, which for TE- and TM-polarized light yielded only slightly different spectra (figure 7b). Satisfactorily, the FDTD spectra were almost identical to those resulting from the multilayer calculations.

The calculated reflectance spectra showed high-frequency oscillations, especially in the longer wavelength range and also in the main reflectance band near 500 nm, presumably due to interference of light reflected at both surfaces of the model barbule that acts as a thin film. We therefore calculated the reflectance spectra for varying thicknesses t_i of the intermediate keratin layer of the model barbule, which yielded spectra with shifted oscillations (electronic supplementary material, figure S2a). Real barbules deviate from the model in that the upper and under surfaces are not at all perfectly parallel (figure 3a,b). We therefore performed model calculations keeping the cortex and melanosome stacks constant, but assuming a Gaussian distribution of the intermediate keratin layer thickness, with standard deviation σ and average t_i = 2000 nm. With increasing σ the high-frequency oscillations rapidly decreased, vanishing at σ = 250 nm (electronic supplementary material, figure S2b). A prominent blue-green reflectance band with only some lower frequency waves then remained (shown in figure 7b,c, σ = 250 nm).

To investigate the relative importance of the two stacks of melanosomes, we calculated the reflectance and transmittance spectra for only the distal half of the barbule, i.e. with only the distal cortex, one melanosome stack and a keratin medium ending at a distance t_b/2 from the surface (indicated by the dashed vertical line in figure 7a). The spectra obtained with the transfer-matrix and FDTD calculations were again virtually identical; of course, the spectrum of the half barbule showed no high-frequency oscillations because the last layer was keratin and not air (figure 7c). The main green bands in the reflectance spectra of the Gaussian-varied full barbule (σ = 250 nm) and the half barbule appeared to be almost identical. The spectra slightly deviate at the longer wavelengths, where the full barbule's reflectance is somewhat higher than that of the half barbule (figure 7c). This is understandable from the decreasing absorption, or increasing transparency, of the melanosome stacks with increasing wavelength as illustrated by the transmittance spectra of figure 7d. The transmittance calculated for only one melanosome stack is greater than 0.5 at wavelengths above 600 nm (figure 7d, half), so that in the full barbule the second melanosome stack contributes to the total reflectance in the long-wavelength range (figure 7c).

The transmittance spectra calculated for the full barbule with the transfer-matrix and FDTD methods are similar (figure 7d), but they are still substantially higher than the spectrum measured from an immersed barbule by MSP (figure 7d). The latter can be understood from the fact that in the calculations the keratin layer between the melanosome stacks was assumed to be fully made up of keratin, i.e. to be transparent. The considerable number of randomly arranged melanosomes in the inner medium, between the two melanosome stacks (figure 3), will add substantially to absorption, and hence reduce the transmittance.

Varying the thickness of the intermediate keratin layer while keeping the other parameters fixed caused smoothing of the fine-structured reflectance spectrum of the model barbule (figure 7b and electronic supplementary material, figure S2). Similar effects can be expected in barbules where the other parameters vary. We investigated this by calculating the reflectance spectra of the half barbule of figure 7c for different parameter values. First, we calculated reflectance spectra for various values of the number of melanosome layers, m. An increase in m causes an obvious increase in peak reflectance, and furthermore the bandwidth slightly narrows and a small bathochromic (towards longer wavelengths) peak shift occurs (figure 8a). The latter results from the combined cortex and melanosome stack, as may be concluded from the increase in the frequency of the waves in the greater than 600 nm spectral range with increasing layer number. Anatomy shows that the layer number varies (figure 3), and the shift in the spectral waves of figure 8a hence explains that the reflectance spectra will be smoothed and that as a consequence the experimental spectra of figure 4 do not feature the waviness in the higher spectral range.

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Increasing the value of the spacing of the melanosomes in the layers, a, causes both a decrease in peak reflectance and a slight hypsochromic (towards shorter wavelengths) shift of the reflectance spectra, due to the decrease in the effective refractive index of the melanosome layers (figure 8b). An increase in the multilayer period, b, results in a bathochromic shift of the reflectance peak (figure 8c). This behaviour can be interpreted with the rule for a multilayer built up of two components with refractive indices n₁ and n₂ and thicknesses d₁ and d₂. As an example, taking n₁ = 1.55 and n₂ = 1.65 and b/2 = d₁ = d₂ = 80 nm, yields λ_max = 512 nm. Higher (lower) values will result with an increasing (decreasing) multilayer period. We must emphasize, however, that light interference in the combined structure consisting of the upper thin-film cortex and the multilayer stack ultimately determines the reflectance spectrum. The importance of the cortex is shown by figure 8d, where an increasing cortex thickness, c, causes an increase in both the peak reflectance and peak wavelength.

The measurements yielded a reflectance peak wavelength for the blue speculum of approximately 470 nm and for the green head of approximately 540 nm. The treated model yielded a peak wavelength of 510 nm for a multilayer period 160 nm and cortex thickness 270 nm. We found that the peak wavelength is most sensitive for changes in the multilayer period and cortex thickness, and therefore presumably the speculum feather barbule's period and cortex thickness are smaller than the model values, approximately 140 and approximately 250 nm (figure 8e), and the values of the green head barbules are larger, approximately 170 nm and approximately 280 nm (figure 8f). Figure 8e shows reflectance spectra obtained for a half barbule with the initial parameter values except that b = 140 nm and c = 250 nm while the number of melanosome layers was m = 5, 6 and 7, respectively. The averaged spectrum has a peak wavelength at λ_max = 468 nm, approximately that of a speculum barbule; note that averaging removes the waviness of the spectrum in the longer wavelength range (figure 8e, av). Similarly, figure 8f shows reflectance spectra for b = 170 nm and c = 280 nm for m = 5, 6 and 7. The peak wavelength of the averaged spectrum is λ_max = 538 nm, approximately that of a head feather barbule. (For a direct comparison of the reflectance spectra of figure 8e,f and the experimental spectra of figure 4, see the electronic supplementary material, figure S3.) Minor changes in the parameter values hence result in substantial colour changes. The light micrographs and anatomy of figures 2 and 3 indeed show that the parameter values are not constant. This means that light interference in melanosome stacks of barbules with varying parameters will yield smoothed reflectance spectra. We have investigated this further below.

3.4. Consequences of disorder in the melanosome arrangement

In the above modelling, we assumed a perfectly ordered arrangement of identically sized melanosomes inside the barbules, but our anatomical results showed that the melanosomes are only roughly orderly arranged and also vary somewhat in size. We studied the effect of melanosome disorder in two ways. We first smoothed the refractive index profile of figure 7a to various degrees, resulting in a more or less sinusoidal depth dependence, well corresponding to the density profiles following from transmission electron micrographs (figure 9a). The reflectance spectra calculated with the transfer-matrix method show that an increase in the smoothing window, resulting in a decreasing refractive index contrast, causes a decrease in the peak amplitude (figure 9b).

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We also performed FDTD calculations for half barbules with disordered melanosome stacks (figure 9c). The melanosome position was varied randomly with a maximal displacement of 10–50 nm, resulting in spectra with gradually decreasing amplitude (figure 9d), very similar as found with the smoothed refractive index profile and the transfer-matrix approach (figure 9b). The spectra calculated for the smoothed multilayer profiles have all the same peak wavelength, because the multilayer period stays constant with smoothing, but the FDTD spectra of figure 9d show a slight variation in peak wavelength, which is due to disorder-induced change in the multilayer period. In summary, the close correspondence of the multilayer and FDTD calculations for disordered melanosomes corroborates the findings above that the barbule photonics is well approximated by multilayer optics.

This conclusion was further confirmed by calculating the reflectance spectra as a function of the angle of incidence, for both TE- and TM-polarized light, for (half) the model barbule of figure 7. Transfer-matrix as well as FDTD calculations yielded again virtually identical results (electronic supplementary material, figure S4). Furthermore, the angle dependence of the peak wavelength and peak reflectance corresponded closely with those of the experimental spectra of figure 5.

3.5. Tuning of feather reflectance spectra to photoreceptor sensitivity spectra

The colours of the speculum and head feathers as seen by human eyes are very different. That the barbule's reflectance spectra are indeed well separated (figure 4) indicates a distinct difference in the spacing of the melanosome layers, the principal parameter that determines the spectral location of the reflectance band (figure 8c). Presumably, the feather colours are also quite different for the mallard visual system, and we therefore compared the reflectance spectra with the spectral sensitivities of the photoreceptors of mallards (figure 10). We calculated the photoreceptor spectral sensitivities as described in the Material and methods (figure 10, dashed curves), yielding as peak wavelengths of the four photoreceptor types (VS, SWS, MWS and LWS) 418, 475, 536 and 604 nm, respectively. The reflectance spectra of the mallard speculum and head feathers measured with a bifurcated probe, with peak wavelengths 472 and 545 nm, closely correspond to the sensitivity spectra of the SWS and MWS cone photoreceptors (figure 10). The close correspondence of the feather reflectance spectra with the photoreceptor spectral sensitivities suggests spectral tuning of the duck feathers to the characteristics of the visual system.

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