Reflections on iridescent neck and breast feathers of the peacock, Pavo cristatus

Abstract

The blue neck and breast feathers of the peacock are structurally coloured due to an intricate photonic crystal structure in the barbules consisting of a two-dimensionally ordered rectangular lattice of melanosomes (melanin rodlets) and air channels embedded in a keratin matrix. We here investigate the feather coloration by performing microspectrophotometry, imaging scatterometry and angle-dependent reflectance measurements. Using previously determined wavelength-dependent refractive indices of melanin and keratin, we interpret the spectral and spatial reflection characteristics by comparing the measured spectra to calculated spectra by effective-medium multilayer and full three-dimensional finite-difference time-domain modelling. Both modelling methods yield similar reflectance spectra indicating that simple multilayer modelling is adequate for a direct understanding of the brilliant coloration of peacock feathers.

1. Introduction

An iconic example of structural coloration in birds is the male peafowl. While the neck and breast feathers display a striking blue colour, the tail feathers have brilliant multi-coloured eye-like patterns. Durrer [1] demonstrated in his fundamental anatomical study on the peacock, Pavo cristatus, that the structural colours of the feather barbules are created by complex photonic structures that consist of a two-dimensionally ordered rectangular lattice of melanosomes (melanin rodlets) and air channels embedded in a keratin matrix [2,3]. Treating the different melanosome lattices in the barbules as periodic one-dimensionally ordered multilayers, Durrer calculated reflectance peak wavelengths that agreed well with the observed colours [1,4].

More recently, Yoshioka & Kinoshita [5] measured reflectance spectra of the blue neck feathers as well as the yellow tail covert feathers and modelled the angle dependence of the spectra with a scalar field approximation. Furthermore, Zi and co-workers studied various coloured barbules in the eye pattern of the tail feathers of a male green peafowl (Pavo muticus). Using a plane-wave expansion method, they calculated the photonic band structure of the two-dimensional photonic crystal and also applied a transfer matrix method to compute reflectance spectra, thus demonstrating that the reflectance characteristics depend on the architecture of the melanosome and air channel stack [6].

Structural coloration of bird feathers is widespread and is caused by a variety of optical mechanisms [7]. For instance, simple thin films create green and purple colours in pigeon neck feathers [8,9]; multilayer stacks consisting of planar arranged melanosomes in a keratin matrix create the brilliant-reflecting neck and breast feathers of the bird of paradise, Lawes parotia [10,11], as well as the shiny feathers of the common bronzewing, Phaps cholcoptera [12]; layers of hollow cylindrical melanosomes colour the feathers of starling [13,14], turkey [15] and magpie [16]; and stacks of air-filled melanosome platelets cause the extremely iridescent colours of the feathers of several hummingbird species [17,18]. Compared to other iridescent bird feathers, the stacked structure of interlaced solid melanin rodlets and air channels in a rectangular lattice appears to be a unique feature of peacocks, and it is arguably one of the most sophisticated biophotonic crystal structures that have ever evolved in birds.

Although important progress has been made in the understanding of peacock coloration, how and to what extent the different parameters contribute to the resulting reflectance spectrum has hardly been explored. Here we focus on the peacock's blue neck and breast feathers as they are particularly prominent in the peacock's structural coloration display and show a characteristic colour gradient that has often been treated as separated blue and green colours [3,6]. To understand the origin of these colours, we performed microspectrophotometry, polarization- and angle-dependent reflectance measurements and imaging scatterometry (ISM). We compare the obtained experimental data with spectra calculated by effective-medium multilayer (EMM) and finite-difference time-domain (FDTD) modelling, thus enhancing our understanding of how the nanostructure causes the feathers' optical properties.

2. Material and methods

2.1. Peacock feathers

Blue feathers of the neck and breast of the male peacock, Pavo cristatus, were collected at a children's farm in Groningen (The Netherlands) and were additionally purchased from a commercial supplier (moonlightfeather.com).

2.2. Photography

Photomacrographs of the feathers were made with a Canon EOS 30D camera. Micrographs were made with an Olympus SZX16 stereomicroscope (Olympus, Tokyo, Japan), equipped with a Kappa DX-40 digital camera (Kappa Optronics, Gleichen, Germany), and we also used a Zeiss Universal microscope (Zeiss AG, Oberkochen, Germany) fitted with an Olympus SC30 camera.

2.3. Spectrophotometry

Reflectance spectra were measured with a microspectrophotometer (MSP) consisting of an ultraviolet–visible CCD detector array spectrometer (AvaSpec-2048; Avantes, Apeldoorn, The Netherlands) attached to a Leitz Ortholux microscope with an Olympus 20×, NA 0.46 objective and a xenon illuminator. The barbules appeared to be about specular-reflecting, and because the reference was a diffuse white reflectance tile (Avantes WS-2), the MSP reflectance signals were scaled to the modelled peak intensity. The angle- and polarization-dependence of the feather reflectance spectra was measured with an angle-dependent reflectance measurement set-up, consisting of two optical fibres, equipped with a focusing lens, mounted on two coaxial goniometers. The two fibre tips rotated in the same plane and the sample was located at the goniometer's rotation axis. The first fibre focused the light from a xenon lamp onto the sample. Part of the light reflected from the object entered the second fibre through a rotation-adjustable polarization filter. The second fibre then guided the light to the CCD detector array spectrometer.

2.4. Imaging scatterometry

For investigating the spatial reflection characteristics of the scales, we performed ISM [19–21]. An isolated barbule was attached to a glass micropipette and then positioned at the first focal point of the ellipsoidal mirror of the imaging scatterometer. Small-aperture scatterograms were obtained by focusing a white-light beam with an aperture less than 5° onto a small circular area (diameter approx. 13 µm) and monitoring the spatial distribution of the far-field scattered light. Hemispherical, white light illumination (aperture 90°) was applied to visualize the angle dependence of the barbule reflections. The polarization dependence was studied by inserting a linear polarizer into the light source. The exposure times of the scatterograms were appropriately adjusted so as to obtain a contrastful image without overexposure.

2.5. Anatomy

Durrer was the first to show that the photonic structures that are responsible for the distinct blue coloration consist of a stack of parallel melanin rodlets (melanosomes) and air channels, which are embedded in a keratin matrix [1,4,18]. We used anatomical data from the transmission electron micrographs of breast feathers that were studied by Yoshioka & Kinoshita [5]. The derived parameters (and also those used by Zi et al. in their study on Pavo muticus [6]) fall into the statistical variation given by Jiang et al. [3] and Durrer [4]. The cortex thickness (parameter c in figure 3) has not been treated explicitly in the literature; we have chosen the value c = 110 nm based on the mean cortex thickness found in the blue-violet barbules of Afropavo congensis [22].

Figure 3.

Anatomy of peacock feather barbules. (a) Cross-sectional transmission electron microscopy image of a blue-green barbule cell of a peacock tail feather (from [4]); scale bar: 0.5 µm. (b) Diagram of the barbule's structure (from [4]). (c) Idealized schematic of the lattice of melanosomes and air channels, with a and b the transversal and lateral distance of the melanosomes, c the thickness of the keratin cortex and D_m and D_a the diameter of the melanosomes and air channels.

2.6. Effective-medium multilayer and finite-difference time-domain modelling

We calculated the reflectance, transmittance and absorbance of model barbules using parameter values derived from published data [3–5] together with previously determined complex refractive indices ñ = n – ik [23,24]. The real part of the wavelength-dependent refractive indices of keratin and melanin, n_k and n_m, was 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 nm² and for melanin A_m = 1.648 and B_m = 23 700 nm²; 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 [23,24]; the refractive index of the air channels was taken to be n_a = 1. We implemented these values in a transfer matrix program based on classical optical multilayer theory, written in Matlab [25]. We sliced the melanosome and air channel stack into 1 nm thin layers and calculated the volume fractions of the components keratin, melanin and air, f_k, f_m and f_a, of each layer, with f_k + f_m + f_a = 1. The effective refractive index of each 1 nm layer was then calculated with the volume fractions of the components:

$${\tilde{n}}_{\mathrm{eff}}={(f_{\mathrm{k}}{n}_{\mathrm{k}}^w+f_{\mathrm{m}}{\tilde{n}}_{\mathrm{m}}^w+f_{\mathrm{a}}{n}_{\mathrm{a}}^w)}^{1/w},$$ 2.1

where the weighting factor w depends on whether the incident light was polarized parallel (TE: transverse electric) or perpendicular (TM: transverse magnetic) to the melanin rodlets and air channels (see inset figure 4c). Effective-medium theory predicts for TE- and TM-polarized light weighting factors w_TE = 2 and w_TM = −2 [26–28]. This EMM model considerably simplifies the complex photonic structure of the peacock barbules, and therefore we compared the spectral results with those following from more rigorous FDTD modelling, which enables the detailed simulation of the light flux in any complex-structured material with arbitrary refractive index and spatial arrangement. We used Lumerical FDTD solutions 8.18, a commercial-grade Maxwell equation solver. Simulations were performed in a simulation volume of approximately 3 × 3×5 µm³. In a previous study on magpie feathers [16] that are structural coloured by photonic stacks of hollow melanosomes, we found that EMM calculations corresponded well with results from FDTD modelling when using slightly modified weighting factors. In the present study, we similarly found that the spectra obtained with EMM and FDTD modelling agreed well with adjusted weighting factors: w_TE = 2.5 and w_TM = −1.5.

Figure 4.

Modelling the reflectance spectra of the blue barbules for normally incident light. (a) Real and imaginary effective refractive index profiles (at 500 nm) of the model barbule (inset). (b) Reflectance spectra for TE-polarized light calculated for half the model barbule using the EMM and FDTD methods. (c) Reflectance spectra for TM-polarized light calculated for the same model barbule. Inset: TE-light is polarized parallel and TM-light perpendicular to the melanosome longitudinal axis.

3. Results

3.1. The blue-coloured feathers of the peacock

The neck and breast of the male peafowl are covered with brilliant-blue-coloured feathers (figure 1a). The feathers are not uniformly blue, however. Isolating a single feather revealed that the barbules have a prominent blue colour at the distal side of the barbs (figure 1b, arrow). Towards the middle of the barbs, which in situ is covered by overlapping feathers, the colour turns gradually to green, and at the in situ fully hidden proximal side, the barbules are brown (figure 1b, arrow head).

Figure 1.

Brilliant coloration of peacock feathers. (a) The prominent blue neck and breast. (b) An isolated feather displays distally an iridescent blue colour, turning green towards the proximal pigment-based brown colour. (c) Close-up of a distal barb showing that the blue colour resides in the barbules. (d) Epi-illumination photograph of a distal barbule (arrow in (b)) showing the linear array of single, blue reflecting cells. (e) The same barbule photographed in transmitted light. (f) Epi-illumination photograph of a proximal barbule (arrow head in (b)) with light-brown reflecting/scattering cells. (g) The same barbule photographed in transmitted light, showing distinguishable cell nuclei. Scale bars: (b) 1 cm, (c) 200 µm, (d–g) 50 µm.

The barbules consist of a single row of cells that are saddle-shaped (cell length 10–30 µm, width 30–50 µm; figure 1c–g). Epi-illumination of the distal barbules shows that the colour of the cells is a rather uniform blue, but locally slight variations occur (figure 1d). Very differently, in transmitted light, the barbules appear red-brown (figure 1e), characteristic for the presence of a high concentration of melanin pigment. This immediately demonstrates that the blue colour of the reflected and back-scattered light must have a structural origin. Quite differently, the proximal barbules appear faint brown under epi-illumination as well as in transmitted light, which indicates a very low melanin content and the absence of an ordered structure (figure 1f,g).

3.2. Iridescence of the blue feather: angle-dependent reflectance spectra

We investigated the spatial reflection properties of the blue barbules by performing ISM. A small-aperture illumination produced a locally restricted, bright blue spot (figure 2a), characteristic for approximately specular objects [11,19]. Because the angle-dependent reflection properties of specular objects can be directly visualized by ISM [29], we applied a hemispherical, linear-polarized, white-light beam. This created a scatterogram with colours changing from cyan-blue to violet with increasing angle of incidence (figure 2b). With light polarized parallel to the plane of incidence, the reflectance was minimal for an angle of incidence and reflection of 60–70° (black areas at 12 and 6 o'clock in figure 2b).

Figure 2.

Imaging scatterometry and angle-resolved reflectance spectra of a distal part of a peacock neck feather. (a) Scatterogram of a single barbule cell illuminated by a narrow-aperture, unpolarized light beam (indicated by the white dot). (b) Scatterogram of a few barbule cells illuminated with a hemispherical, wide-aperture beam. The beam was vertically polarized (indicated by the up–down arrow), parallel to the barbule; the black bar at 9 o'clock is due to the shadow of the glass micropipette holding the barb. (c) Reflectance spectra for TE-polarized light as a function of the angle of light incidence (varying from 0° to 70°). (d) Reflectance spectra for TM-polarized light as a function of the angle of light incidence. The plane of incidence was parallel to the feather's rachis.

To analyse the spatial and spectral characteristics of the reflected light in more detail, we performed angle-dependent reflectance measurements (figure 2c,d). For TE-polarized light, the peak amplitude of the reflectance spectra increased with increasing angle of light incidence; for TM-polarized light the reflectance peak amplitude decreased up to an angle of incidence of approximately 60°, and it increased again for larger incidence and reflection angles (figure 2c,d), similar to the reflection properties of optical multilayers [30,31].

3.3. Origin of the blue colour: barbule anatomy and spectral modelling

To quantitatively understand the reflection properties of the blue peacock feathers, we performed optical modelling using published anatomical data [3–5]. The black dots in the transmission electron micrograph of figure 3a represent melanosomes, rodlets with a high melanin content, with a diameter approximately 120 nm and length approximately 1 µm, which are arranged in a rectangular lattice. Air channels, diameter approximately 75 nm, are interspersed within this lattice (figure 3a,b). The melanin rodlets and air channels are aligned along the barbule's longitudinal axis and are embedded in a keratin matrix, thus effectively forming an approximately 2 µm thick photonic stack of 5–12 layers parallel to the cell surface. The barbule cells (total thickness approximately 10 µm) contain two roughly identical photonic stacks pressed against the upper and lower surface, respectively. In the barbule core of approximately 6 µm thickness, the melanosomes and air cavities are randomly arranged.

Figure 3c is an idealized diagram of the photonic stack, and the inset of figure 4a shows a diagram of the full anatomy of the barbule, which we used in modelling the barbule reflectance spectra. We assumed a model barbule, thickness 10 µm, with on both sides the same photonic structure, where a keratin cortex layer, thickness c = 110 nm, covered a stack of N_m = 12 layers of melanosomes interspersed with N_a = 11 air channel layers. For the melanosomes, diameter D_m = 120 nm, we considered a few different values of the transversal lattice parameter a (see below); the lateral lattice parameter was taken to be b = 150 nm, and the diameter of the air channels was D_a = 75 nm (figure 3c). The space between the two melanosome stacks was filled with keratin only (figure 4a). The anatomical parameters together with the previously determined refractive indices of keratin and melanin yielded the real and imaginary parts of the effective refractive index profile as a function of the distance from the barbule cell surface and as a function of wavelength (see Material and methods). We used weighting factors 2.5 and −1.5 for TE- and TM-polarized light, with TE-light polarized parallel and TM-light polarized perpendicular to the melanosome longitudinal axis (figure 4c, inset). Figure 4a shows the effective refractive index profiles resulting for TE- and TM-polarized light at 500 nm.

We implemented the effective refractive index profiles in a transfer matrix program for optical multilayers [25] to calculate the reflectance spectra for normally incident light (figure 4b,c). Electronic supplementary material, figure S1a,b, shows the dependence of the reflectance on cortex thickness (c) and number of layers (N_m). We first calculated reflectance spectra for the complete barbule, which has two photonic stacks. The reflectance spectra calculated for the intact barbule are marked by short period oscillations with small amplitude, caused by interference effects of the whole barbule acting as a thin film (electronic supplementary material, figure S2, full). These effects are not observed experimentally, which must be attributed to the randomness of the melanosomes and air channels in the core as well as the irregularities in the thickness of real barbules as we will discuss below.

We also calculated the reflectance spectra for half a barbule with a single stack (electronic supplementary material, figure S2, half). This demonstrated that the reflectance is essentially determined by a single stack of melanosome–air channels, for which the spectra are shown in figure 4b,c (EMM). We thus performed further modelling of reflectance spectra only with a single, upper photonic stack, neglecting the reflections on the lower stack and the lower barbule surface. As a control, we performed FDTD modelling for the two-dimensional photonic crystal structure, using the same model parameters. The resulting spectra (figure 4b,c, FDTD) correspond closely to the EMM spectra, indicating the validity of the EMM approach. Because the latter approach is considerably simpler than FDTD modelling, we interpreted our subsequent experimental studies with EMM modelling.

3.4. Comparing experiments and modelling

To further validate the modelling results, we measured the reflectance and absorbance spectra of barbule cells with a MSP applying unpolarized light. The reflectance spectra of the different colour regions indicated in figure 1b are marked by a prominent band with peak wavelength ranging between approximately 420 nm distally (blue; figure 5a, dist exp) and approximately 540 nm medially (green; figure 5a, med exp). The light-brown proximal barbules have a low broad-band reflectance spectrum without a prominent peak (not shown).

Figure 5.

Reflectance and absorbance spectra of peacock neck feather barbules measured with a microspectrophotometer and calculated by EMM modelling. (a) Reflectance spectra measured at the distal (blue and green) regions, scaled by set-up-specific factor and modelled spectra. (b) Absorbance spectra measured at the distal region in air and immersed in water, and modelled spectra for a barbule in air and water, where (1) the water was assumed to be only present outside the barbule, and (2) the air channels were also assumed to be filled with water. (c) Reflectance spectra of the three model cases of (b).

The measured spectra could be well understood with EMM modelling by adjusting the transversal lattice parameter, a. The dotted model spectra of figure 5a were obtained by choosing for the blue distal barbules a = 142 nm and for the green medial barbules a = 182 nm; to account for unpolarized light, the spectra calculated for TE- and TM-polarized light were averaged.

The absorbance spectrum of a barbule in air showed a decreasing absorbance with increasing wavelength, characteristic for melanin, but also had a shallow hump in the blue wavelength range (figure 5b, air exp). The absorbance spectrum calculated for a complete barbule, with the two photonic stacks, using a = 170 nm, had a much larger hump (figure 5b, air model). As the difference between the measured and calculated spectra might be due to scattering created by structural irregularities, we performed measurements on barbules immersed in water. This yielded absorbance spectra with a bathochromic-shifted hump (figure 5b, water exp). To understand the spectral shift, we modelled two cases, namely (1) where only the air medium outside the barbule was changed into water (figure 5b, water model 1), and (2) where also the air channels were filled with water (figure 5b, water model 2). The absorbance spectra for an intact barbule with as the outside medium either air or water are hardly distinguishable, but the absorbance spectrum for a barbule with air channels filled by water has a reduced hump, shifted to longer wavelengths (figure 5b). As a similar shift was observed experimentally, this indicates that upon water immersion the air channels take up water. We also calculated the reflectance spectra for the three cases, which similarly showed a very slight spectral change when changing the outside air medium with water and a much more severe spectral shift when filling the air channels with water (figure 5c, air versus water model 1 and 2).

The measured angle-dependent reflectance spectra for TE- and TM-polarized light had a characteristic spectral trend (figure 2c,d). We investigated this further by EMM modelling, using the same barbule parameters as in figure 4. In agreement with figure 2c,d, the peak wavelength of the calculated reflectance spectra for TE- and TM-polarized light shifted to shorter wavelengths with increasing angle of incidence, while the amplitude of the reflectance spectra increased for TE- and decreased for TM-polarized light (figure 6a,b). With identical model parameters, FDTD modelling (electronic supplementary material, figure S3) produced reflectance spectra with only slightly different peak wavelengths and peak reflectances (figure 6c,d).

Figure 6.

Modelled angle-dependent reflection characteristics of a melanosome–air channel stack. (a) Reflectance spectra of the photonic structure of figure 4 for TE-polarized light calculated with the EMM method. (b) The same as in (a), but for TM-polarized light. (c) Peak wavelength of the reflectance spectra for TE- and TM-polarized light as a function of the angle of light incidence calculated with the EMM as well as the FDTD method. (d) Peak reflectance of the calculated spectra.

3.5. Effects of size disorder

In the above FDTD modelling, we assumed a perfectly ordered square lattice of identically sized elements, neglecting the clearly present disorder in the melanosome–air channel stack. We therefore studied the effect of size disorder in the melanosome rodlets and the air channels by varying the rodlet diameter (D_m) and the air channel diameter (D_a). For this, we added a random maximal displacement to the diameter of each element (i.e. σ_mΛ for melanosomes and σ_aΛ for air channels, with Λ being a randomly negative or positive number ∈ (−1, 1)). The resulting reflectance spectra (normal angle illumination) were all very similar (figure 7a,b). Even a significant disorder with a maximal variation of 30% in the melanin rodlets and air channels resulted in a peak reflectance change less than 10% (figure 7c). Clearly, the photonic structure of the peacock feather is very robust to size disorder.

Figure 7.

Reflectance spectra of the two-dimensional photonic structures of peacock barbules dependent on size disorder calculated with the FDTD method. (a) The size of the melanosomes was varied randomly with a different amount of maximal change (σ_m), keeping the air channel size constant. (b) The size of the air channels was varied randomly with a different amount of maximal change (σ_a), keeping the melanosome size constant. (c) The effect of disorder when varying both diameters randomly up to a maximum variation of 30%.

4. Discussion

The blue peacock feathers contain regular layers of melanosomes and air channels with dimensions and interdistances of the melanosomes and air channels much smaller than the wavelength of visible light. Anatomy shows that the arrays of melanosomes and air channels distinctly deviate from ideal, crystalline structures [3,4], and the somewhat different colours within each barbule cell (figure 1c) demonstrate that the photonic structures vary locally. The measured reflectance spectra are therefore local averages, even when obtained with the MSP from areas with a diameter as small as 5–10 µm (see also [30,31]).

The measured reflectance spectra appear to be fully determined by the photonic melanosome–air channel stack at the side of light incidence. However, the absorbance spectra are due to both stacks and will be affected more strongly by the irregular arranged melanosomes in the barbule centre. As the peak values of the measured absorbance spectra in the blue-green wavelength range are often greater than 2, even small background signals of the order of 1% or less will gravely distort the experimental transmittance measurements and thus the resulting absorbance spectra. Therefore, background scattering will readily cause discrepancies between experimental and modelled absorbance spectra (figure 5b).

To explain the measured spectra, we used an EMM model to calculate the reflectance and absorbance spectra of the barbules for both TE- and TM-polarized light. As a control, we performed spectral calculations for the same structure using the FDTD method, which takes full account of the detailed spatial organization of the photonic structure [11,31]. When using proper weighting factors in the effective refractive index approximation, the two approaches yielded closely corresponding results (figure 6c,d) [31].

However, it is important to realize that several anatomical and geometrical factors affect the macroscopic reflectance measurements. The structural coloration of the feather is essentially caused by the nanoscopic arrangement of the barbule components, i.e. the melanosomes, the air channels and the keratin cortex layer. Especially the latter has so far not been described, although it has the ability to substantially change the shape of the primary reflectance band (electronic supplementary material, figure S1a). Reducing the number of melanosome and air layers, on the other hand, causes peak-broadening and reduction of the peak reflectance (electronic supplementary material, figure S1b). Disorder in the components of the photonic crystal will cause a decoherence (phase randomization) of the reflected light and thus reduced peak intensities (figure 7).

Several other important factors at the more macroscopic level will contribute to the actual feather colour as well. The barbule surface is not flat but rather saddle-shaped and the barbule thickness is not uniform. Accordingly, the layers of melanosomes and air channels are not parallel everywhere so that incident light is reflected into a slightly distributed angle (figure 2a). The intensity of the reflected light also depends on the macroscopic arrangement of the feathers and their barbules. Although the barbs and barbules of the peacock breast and neck feathers are closely spaced, they do not fully cover the feather surface (figure 1b,c). Furthermore, the barbule cell colour can vary along one and the same barb (figure 1b).

Since the one-dimensionally ordered EMM model yielded nearly the same results as the two-dimensionally ordered FDTD model, even at large angles of incidence, we conclude that the reflection characteristics of the blue feathers of the peacock can be understood to be essentially generated by a multilayer with a varying refractive index profile. The same conclusion was reached in related studies on structural coloured feathers with barbules containing stacks of melanosomes [12,16,24,31].

Whereas the neck and breast feathers of the peacock body are about uniformly blue, the tail feathers have richly coloured eye-like patterns, where the various colours are caused by subtle modifications in the anatomical composition of the barbules' photonic structures. The tail feather colours can indeed also be well understood with EMM modelling (in preparation).

Data accessibility

This article has no additional data.

Authors' contributions

All authors performed and analysed the measurements, performed modelling, wrote the manuscript and gave final approval for publication.

Competing interests

The authors declare no competing or financial interests.

Funding

This study was financially supported by the Air Force Office of Scientific Research/European Office of Aerospace Research and Development AFOSR/EOARD (grant no. FA9550-15-1-0068, to D.G.S.) and the National Centre of Competence in Research ‘Bio-Inspired Materials’ and the Ambizione programme of the Swiss National Science Foundation (168223, to B.D.W.).