The blue secondary and purple-to-green tail feathers of magpies are structurally coloured owing to stacks of hollow, air-containing melanosomes embedded in the keratin matrix of the barbules. We investigated the spectral and spatial reflection characteristics of the feathers by applying (micro)spectrophotometry and imaging scatterometry. To interpret the spectral data, we performed optical modelling, applying the finite-difference time domain (FDTD) method as well as an effective media approach, treating the melanosome stacks as multi-layers with effective refractive indices dependent on the component media. The differently coloured magpie feathers are realised by adjusting the melanosome size, with the diameter of the melanosomes as well as their hollowness being the most sensitive parameters that influence the appearance of the feathers.

Many bird species feature brightly coloured plumage owing to pigments and/or structural effects. The most common pigments of bird feathers are the carotenoids and melanins. Carotenoids strongly absorb in the blue to green wavelength range, thus causing yellow, orange or red feathers (McGraw, 2006a; Shawkey et al., 2009). The melanins are deposited in small organelles, so-called melanosomes (McGraw, 2006b; Prum, 2006; Shawkey et al., 2009), which are usually irregularly organised and thus cause matte colours: eumelanin creates grey to black, and phaeomelanin causes rather brown and rufous colours (Hill, 2010). In the absence of pigments, the feathers are generally white, owing to random scattering of incident light on the inhomogeneities of the feathers (Prum, 2006; Leertouwer et al., 2011). However, feather barbs containing a quasi-regularly organised, spongy medullary keratin matrix display a distinct blue structural colour, which is turned into green when filtered by short-wavelength absorbing pigments (Prum, 2006; Shawkey et al., 2009; Stavenga et al., 2011; D'Alba et al., 2012; Tinbergen et al., 2013).

Some bird species feature shiny, structurally coloured feathers owing to cuticular thin film effects, as is the case in pigeons (Yoshioka et al., 2007), grackles (Shawkey et al., 2006) and crows (Lee et al., 2012). Strikingly, many bird species have structurally coloured feathers due to layers of orderly arranged melanin. The high density of melanin pigment in the melanosomes creates a high absorption coefficient throughout the visible wavelength range, resulting in a higher refractive index (RI) than that of the surrounding keratin. By arranging melanosomes in the feather barbules in more or less regular patterns with nanosized dimensions, vivid iridescent colours are created due to constructive interference in a restricted wavelength range (Durrer, 1977; Prum, 2006).

The melanosomes come in many different shapes and forms, and their spatial arrangement is similarly diverse (Prum, 2006). This has been shown in impressive detail by Durrer (1977), who performed extensive transmission electron microscopy of the feather barbules of numerous bird species. He interpreted the observed structural colours to be created by regularly ordered melanosome stacks acting as optical multi-layers. This view was fully confirmed for the male bird of paradise Parotia lawesii, which has bright silvery occipital feathers because of widely spaced layers of melanin rodlets in the barbules. From measurements of the barbules' reflectance and transmittance spectra, while using the previously determined RI of keratin, the wavelength-dependent complex RI of melanin could be derived (Leertouwer et al., 2011; Stavenga et al., 2015).

The breast feathers of male P. lawesii have barbules that reflect strongly golden-orange, green or blue, depending on the angle of illumination and observation. The boomerang-shaped barbules contain densely packed stacks of solid melanosomes (Stavenga et al., 2010; Wilts et al., 2014). Using the measured melanin and keratin RI spectra, the various reflection phenomena could be explained by applying the finite-difference time domain (FDTD) method, which is the method of choice for modelling the reflection and absorption properties of intricate, complex-shaped photonic structures (Wilts et al., 2014). Another exemplary case is that of the feather barbules of the male common bronzewing, Phaps chalcoptera, which have neatly arranged layers of solid melanin rodlets interleaved and separated by keratin. This spatial arrangement acts as an optical multi-layer reflecting maximally blue, green or red light, depending on the size and distance of the melanosomes. The measured reflectance spectra could be explained by treating the melanosome stacks as optical multi-layers and implementing the effective RI profiles of the barbules (Xiao et al., 2014). Instead of well-separated melanosome layers, the structural coloured feather barbules of mallards contain stacks of close-packed, solid melanin rodlets (Eliason and Shawkey, 2012; Khudiyev et al., 2014). Calculations with the FDTD method and multi-layer modelling yielded virtually identical reflectance spectra, corresponding well to measured spectra (Stavenga et al., 2017).

Solid melanin rodlets embedded in a surrounding keratin matrix realise a RI contrast that is distinct but not impressive, with wavelength-dependent RI contrasts between 1.13 and 1.18. A much larger RI contrast of ∼1.7 to 1.8 is realised in hollow melanosomes with an air core. In bird feathers, hollow melanosomes, structured as hollow cylinders or flattened balloons, cause the striking structural colours of the feather barbules of numerous bird species, including trogonids (Durrer and Villiger, 1966), starlings and turkeys (Durrer and Villiger, 1967, 1970; Maia et al., 2013; Eliason et al., 2013). Notably, the brightly coloured hummingbirds have excessively large stacks of hollowed melanosomes in their feather barbules (Greenewalt et al., 1960; Durrer, 1977; Osorio and Ham, 2002; Parra, 2010; Meadows et al., 2011).

Hollow melanosomes are also found in the barbules of the blue secondary and the variably coloured tail feathers of the Eurasian or common magpie, Pica pica (Linnaeus 1758). The melanosomes are cylindrical rodlets, close-packed and pressed against the barbule's epicuticle in a few layers, causing a distinct, iridescent colouration. To explain the reflectance spectra of magpie feathers, the lattice of air holes that form the core of the melanosomes has been presumed to act as a colour-creating grating (Vigneron et al., 2006). In a related study on the black-billed magpie, Pica hudsonia, the stack of hexagonally packed, hollow melanosomes was treated as a two-dimensional photonic crystal, using photonic bandgap theory, taking into account the rodlet dimensions as well as the RIs of the material components of the barbules, keratin, melanin and air (Han et al., 2017). Close examination of the cross-sectional microstructures of the magpie feather barbules revealed, however, that the lateral arrangement was of minor importance and that the vertically layered structure of melanin rodlets along the barbule surface is responsible for the iridescence (Han et al., 2017).

Here we revisit the colouration of common magpie feathers by comparing FDTD simulations with effective-medium multi-layer (EMM) modelling. Treating the melanosome stacks as gradient multi-layers, we find that multi-layer optics allows ready understanding of the colouration of magpie feathers, thus expanding our insight into the intricacies of bird feather colouration.

Specimens

Common magpie feathers were collected in a local park in Groningen (The Netherlands), and purchased from a commercial supplier (Etsy, UK). Light microscopic images of the feather barbules were taken with a Zeiss Universal Microscope (Zeiss, Oberkochen, Germany).

Electron microscopy

The barbule anatomy was investigated by transmission electron microscopy (TEM) using standard methods. Briefly, a feather piece was (after a dehydration series) embedded in resin, and sections were stained using 2% aqueous uranyl-acetate solution and examined with a Hitachi 7100 TEM. In addition, for scanning electron microscopy, barbules were sputtered with a 3 nm thick layer of gold and observed with a MIRA3 LMH field-emission electron microscope (Tescan, Brno, Czech Republic).

Spectroscopy

Reflectance spectra of different feather areas were measured with an integrating sphere (AvaSphere-50), using an AvaSpec 2048-2 CCD detector array spectrometer (Avantes, Apeldoorn, The Netherlands). The light source was a deuterium-halogen lamp [AvaLight-D(H)-S], and the reference was a white diffuse reflectance tile (Avantes WS-2). The angle- and polarisation-dependence of the reflectance spectra of the feathers were measured using two optical fibres. One end of the first optical fibre was connected to a xenon lamp, and its other end was mounted at a goniometer together with a small lens, which focused the fibre tip at the goniometer's rotation axis. At a second goniometer one end of the second fibre was mounted with a focusing lens and a rotatable polarisation filter, and the other end of the fibre was connected to the CCD detector array spectrometer. The rotation axes of the two goniometers coincided and the two fibres rotated in about the same plane. The area to be measured was positioned in that plane, at the axis of rotation of the goniometers. The aperture of the fibres was 5 deg (full width at half-maximum, FWHM) and the distance of the tips to the centre of the illuminated spot was 6 and 12 cm, respectively. The receiving fibre thus sampled a larger area than the illuminated spot but captured only a small part of the reflected light. The white diffuse reflectance tile (Avantes WS-2) served as reference. Reflectance spectra 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 the detector array spectrometer, with a xenon arc lamp as the light source. Transmittance spectra of isolated barbules, immersed in immersion oil (RI 1.515), were also measured with the MSP; the measured area was a square with edge length 5–10 µm. The microscope objective was an Olympus 20× NA 0.46 (Olympus, Tokyo, Japan). Because of the glass optics, the MSP spectra were limited to wavelengths >350 nm.

Imaging scatterometry

For investigating the spatial reflection characteristics of the barbules, we performed imaging scatterometry (Stavenga et al., 2009; Vukusic and Stavenga, 2009; Wilts et al., 2009). A small feather piece attached to a glass micropipette was positioned at the first focal point of the ellipsoidal mirror of the imaging scatterometer. The scatterograms were obtained by focusing a white light beam with a narrow aperture (<5 deg) onto a small circular area, and the spatial distribution of the far-field scattered light was then monitored. A flake of magnesium oxide served as a white diffuse reference object.

Modelling

Using parameter values inspired by anatomy, we calculated the reflectance, transmittance and absorptance of model magpie barbules using Lumerical FDTD Solutions 8.16, a commercial-grade Maxwell equation solver. Being based on fundamental Maxwell theory, the FDTD method enables the detailed simulation of the light flux in any complex-structured material with arbitrary RI and spatial arrangement. Simulations were performed in a volume of ∼3×3×5 µm3. The model barbules contained two stacks of melanosomes, each near the two opposite sides of the barbule, embedded in a keratin matrix. As the RI of a material is generally complex (ñ=nik), the real parts of the wavelength-dependent RIs of keratin and melanin, nk and nm, were calculated with the Cauchy formula n=A+Bλ−2 (where λ is the light wavelength), using for keratin Ak=1.532 and Bk=5890 nm−2 and for melanin Am=1.648 and Bm=23,700 nm−2; the imaginary component of the RI of keratin was assumed to be negligible in the wavelength of interest, but that of melanin was taken to be km=amexp(−λ/bm), with am=0.56 and bm=270 nm (Leertouwer et al., 2011; Stavenga et al., 2015; the RI of the air core was na=1). We compared the FDTD results with EMM performed with a transfer-matrix program based on classical optical multi-layer theory, written in MATLAB (Stavenga, 2014). We therefore sliced the melanosome stacks into 10 nm thin layers and calculated the volume fractions of the components keratin, melanin and air (fk, fm and fa, respectively) of each layer, with fk+fm+fa=1. The effective RI of each 10 nm layer was then calculated with the volume fractions of the components:
formula
1
For light incident on a layer of parallel rods, effective medium theory predicts for light polarised perpendicular to the rods a weighting factor (w) of −2, and for light polarised parallel to the rods, w=2 (Bräuer and Bryngdahl, 1994; Lucarini et al., 2005; Halir et al., 2015). We also investigated the cases with w=−1 and 1.

Colours and anatomy of magpie feathers

The common magpie, P. pica, has blue secondary feathers and tail feathers with a distinct colour gradient, shifting from green (proximal) via purple to blue (distal; Fig. 1). Reflectance spectra measured from different areas of a secondary feather show slightly varying, broad reflectance bands in the blue wavelength range (Fig. 1B), and the reflectance spectra measured along the length of a tail feather gradually shift along the wavelength scale (Fig. 1C).

Fig. 1.

The common magpie, Pica pica, and its variously coloured plumage. (A) Drawing by Wilhelm von Wright (1810–1887; from the public domain). (B) Reflectance spectra of different areas of a secondary feather measured with an integrating sphere. Inset: a blue secondary feather; scale bar, 1 cm. (C) Reflectance spectra of different areas of a tail feather. Inset: the tail feather with the measured areas, indicated by coloured dots corresponding to the colours of the reflectance spectra. Distance between the coloured dots is 1 cm.

Fig. 1.

The common magpie, Pica pica, and its variously coloured plumage. (A) Drawing by Wilhelm von Wright (1810–1887; from the public domain). (B) Reflectance spectra of different areas of a secondary feather measured with an integrating sphere. Inset: a blue secondary feather; scale bar, 1 cm. (C) Reflectance spectra of different areas of a tail feather. Inset: the tail feather with the measured areas, indicated by coloured dots corresponding to the colours of the reflectance spectra. Distance between the coloured dots is 1 cm.

The reflectance spectra confirmed the structural basis of the feather colours. We therefore also investigated the spatial reflection properties of the barbules. Microscopic inspection of isolated feather barbs (with barbules) showed that most parts of the barbules are black, clearly owing to the abundant presence of irregularly distributed melanin; these parts are overlapped by the exposed coloured parts of adjacent barbules in situ (Fig. 2A–C). Studying the coloured barbules with an imaging scatterometer showed that illumination of a small feather with a small aperture, white-light beam resulted in light reflected into a narrow spatial wedge, oriented approximately perpendicular to the barbule's long axis (Fig. 2D,E). Closer inspection showed that the barbules are rows of elongated cells. The colour of the cells strongly depends on the location in the feather; it can slightly differ between neighbouring cells, and even can distinctly vary within each cell (Fig. 2G–I).

Fig. 2.

Scatterometry of differently coloured barbules of a magpie tail feather. (A–C) Differently coloured feather areas, locally illuminated at a spot marked by the dashed circle. (D–F) Scatterograms created by the spot illuminations of A–C. The red circles indicate angular directions of 5, 30, 60 and 90 deg. (G–I) Epi-illumination light micrographs of a purple, blue and green feather area, respectively, showing the slightly varying colour of the barbule cells. Scale bars: A–C, 50 µm; G–I, 100 µm.

Fig. 2.

Scatterometry of differently coloured barbules of a magpie tail feather. (A–C) Differently coloured feather areas, locally illuminated at a spot marked by the dashed circle. (D–F) Scatterograms created by the spot illuminations of A–C. The red circles indicate angular directions of 5, 30, 60 and 90 deg. (G–I) Epi-illumination light micrographs of a purple, blue and green feather area, respectively, showing the slightly varying colour of the barbule cells. Scale bars: A–C, 50 µm; G–I, 100 µm.

To study the colouration in more detail, we performed high-magnification epi-illumination light microscopy as well as electron microscopy. This revealed that the barbule colouration emerges from tightly packed, sub-micrometre-sized particles: the melanosomes. Epi-illumination of a green area of a tail feather immersed in oil revealed that the barbules contain slightly disordered, blue-to-yellow coloured rod-like particles (Fig. 3A). Transmitted light microscopy showed a completely different, red-brown colour, the signature of melanin. An ellipsoid-shaped area in each cell indicated the remnant of the cell nucleus (Fig. 3B). Similar to the elongated particles observed by light microscopy, scanning electron microscopy of intact barbules showed tightly organised small rodlets, of length 1–2 µm and width ∼0.2 µm (Fig. 3C). Cross-sectioning the barbules demonstrated that the melanosomes are assembled into two stacks on both sides of the barbule, and that the rodlets are hollow, and pressed against the cell surface in two to four layers (Fig. 3D–F). Transmission electron microscopy showed that the melanosome diameter varied between 160 and 200 nm, and that the air core diameter varied between 90 and 110 nm (Fig. 3E).

Fig. 3.

Magpie tail feather barbule anatomy. (A) Epi-illumination light micrograph of a barbule in oil immersion, showing the somewhat irregular organization of the melanosomes. (B) Transmitted light micrograph of an immersed barbule, revealing a dense melanin pigmentation; arrowheads denote cell nuclei. (C) Scanning electron micrograph (SEM) showing the curved and corrugated surface of the barbule cells with tightly packed melanosomes. (D) SEM of a sectioned barbule, showing the hollow melanosomes stacked in two to three layers. (E) Transmission electron micrograph of a barbule with melanosome stacks on both the upper and under side. (F) SEM of sectioned feather barbules, showing the hollow melanosome layers on both the upper and lower sides of the barbules. Scale bars: A–C, 10 µm; D, 1 µm; E,F, 2 µm.

Fig. 3.

Magpie tail feather barbule anatomy. (A) Epi-illumination light micrograph of a barbule in oil immersion, showing the somewhat irregular organization of the melanosomes. (B) Transmitted light micrograph of an immersed barbule, revealing a dense melanin pigmentation; arrowheads denote cell nuclei. (C) Scanning electron micrograph (SEM) showing the curved and corrugated surface of the barbule cells with tightly packed melanosomes. (D) SEM of a sectioned barbule, showing the hollow melanosomes stacked in two to three layers. (E) Transmission electron micrograph of a barbule with melanosome stacks on both the upper and under side. (F) SEM of sectioned feather barbules, showing the hollow melanosome layers on both the upper and lower sides of the barbules. Scale bars: A–C, 10 µm; D, 1 µm; E,F, 2 µm.

Microspectrophotometry of magpie barbules

To ascertain that the coloured barbules contain melanin, we measured absorbance spectra of single barbules immersed in oil (RI 1.515) with a microspectrophotometer, which clearly demonstrated that the absorbance is dominated by melanin absorption (Fig. S1A). Reflectance spectra measured from small areas (diameter ∼4 µm) of barbules (in air) taken from various tail feather locations showed marked high-frequency oscillations in the long-wavelength range, clearly indicating thin-film-like light interference (Fig. S1B). Analysing the oscillations as established before (Stavenga, 2014) and by assuming an effective RI of the barbule of ∼1.6, yielded barbule thicknesses of 2.0–3.5 µm (Fig. S1C), in full accordance with the barbule thickness following from anatomy (Fig. 3E,F). When measuring reflectance spectra from areas exceeding a diameter of ∼20 µm, the oscillations vanished, evidently because integration of the reflectance of larger areas causes smoothing of the local variations (Fig. 1B,C).

Modelling magpie barbule optics

Based on the anatomical data, we performed optical modelling by considering a 3 µm thick barbule, with N=3 melanosome layers on both sides, surrounded by an epicuticle with thickness tc=50 nm. The close-packed, cylindrical melanosomes were assumed to have an air core with diameter da=100 nm, and a melanin cladding with diameter dm=180 nm (Fig. 4, middle inset). We calculated the reflectance spectra for normally incident light, polarised parallel (TE) and perpendicular (TM) to the melanosome axes (Fig. 4, upper inset), applying the FDTD method (Fig. 5A).

Fig. 4.

Refractive index profiles and diagram of a magpie barbule. Upper inset: melanin rodlets normally illuminated. With the plane of light incidence perpendicular to the melanosome stack, the electric vectors of TE- and TM-polarised light are parallel and perpendicular to the rodlets, respectively. Lower inset: cross-section of a barbule showing stacks with three layers of close-packed, air-filled melanosomes embedded in keratin near both sides of the barbule. The total barbule thickness (tb) is 3000 nm, with an epicuticle thickness (tc) of 50 nm, melanosome diameter (dm) of 180 nm, air hole diameter (da) of 100 nm, and thickness of the intermediate keratin layer (ti) 1916 nm. The profiles of the real and imaginary components of the effective RI (neff) for 500 nm light were calculated with Eqn 1 for w=−2, −1, 1 and 2.

Fig. 4.

Refractive index profiles and diagram of a magpie barbule. Upper inset: melanin rodlets normally illuminated. With the plane of light incidence perpendicular to the melanosome stack, the electric vectors of TE- and TM-polarised light are parallel and perpendicular to the rodlets, respectively. Lower inset: cross-section of a barbule showing stacks with three layers of close-packed, air-filled melanosomes embedded in keratin near both sides of the barbule. The total barbule thickness (tb) is 3000 nm, with an epicuticle thickness (tc) of 50 nm, melanosome diameter (dm) of 180 nm, air hole diameter (da) of 100 nm, and thickness of the intermediate keratin layer (ti) 1916 nm. The profiles of the real and imaginary components of the effective RI (neff) for 500 nm light were calculated with Eqn 1 for w=−2, −1, 1 and 2.

Fig. 5.

FDTD optical modelling of a magpie barbule. (A) Reflectance spectra of the full barbule from Fig. 4, as well of only half the barbule, for normally incident TE- and TM-polarised light. (B) The corresponding absorptance spectra.

Fig. 5.

FDTD optical modelling of a magpie barbule. (A) Reflectance spectra of the full barbule from Fig. 4, as well of only half the barbule, for normally incident TE- and TM-polarised light. (B) The corresponding absorptance spectra.

The reflectance spectra for TE- as well as TM-polarised light showed high-frequency oscillations (Fig. 5A, full), evidently due to thin-film interference of the total barbule thickness. To confirm this, we also calculated the reflectance spectra for half the barbule (bounded by the dashed vertical line in Fig. 4, middle inset). The resulting TE and TM spectra no longer featured the oscillations and only had a main, broad reflectance band, peaking at ∼500 nm. Interestingly, the latter spectra are almost identical to the smoothed spectra of the full model barbule. In other words, the reflectance is almost completely determined by the upper melanosome stack.

Simultaneous with the reflectance, we also calculated the transmittance of both the full and half-barbule for TE- and TM-polarised light, which yielded the absorptance (the absorptance is 1 minus the sum of the reflectance and transmittance). The absorptance spectra clearly show the strong wavelength-dependent absorption of melanin that monotonically decreases for long wavelengths (Fig. 5B). In addition, a reduced absorptance is visible at the position of the reflectance peak. The absorptances of the full and half-barbule only slightly differ, indicating that the upper melanosome stack absorbs the main part of the incident light, leaving only a small part of the light flux to be additionally absorbed by the lower stack.

Dependence of the reflectance on the number of melanosome layers and melanosome hollowness

We subsequently investigated the consequences of changes in the number of melanosome layers, N, while keeping the melanosome outer diameter dm=180 nm and the inner diameter da=100 nm fixed. The reflectance spectra, calculated with the FDTD method, exhibit two major effects: (i) with an increasing number of melanosome layers, the reflectance rapidly increases and the bandwidth narrows, saturating when N>5 (Fig. 6A,B); (ii) the reflectance spectra show oscillations that increase in frequency with the number of melanosome layers, or increase proportional to the thickness of the internal melanosome stack, which will also act as a thin film interference reflector.

Fig. 6.

Dependence of the reflectance of a half-barbule on the number of melanosome layers and air hole diameter calculated with the FDTD method. (A,B) Reflectance spectra for TE- and TM-polarised light for one to eight layers of melanosomes with outer diameter (dm) 180 nm and air hole diameter (da) 100 nm. (C,D) Reflectance spectra for normally incident TE- and TM-polarised light for N=3 layers of melanosomes with dm=180 nm and da varying from 0 to 180 nm.

Fig. 6.

Dependence of the reflectance of a half-barbule on the number of melanosome layers and air hole diameter calculated with the FDTD method. (A,B) Reflectance spectra for TE- and TM-polarised light for one to eight layers of melanosomes with outer diameter (dm) 180 nm and air hole diameter (da) 100 nm. (C,D) Reflectance spectra for normally incident TE- and TM-polarised light for N=3 layers of melanosomes with dm=180 nm and da varying from 0 to 180 nm.

Changing the hollowness of the melanosomes (h=dm/da) has quite different optical effects. Keeping the melanosome outer diameter dm=180 nm and the number of layers N=3 fixed, an increasing air core diameter da (larger hollowness) yields a gradually rising reflectance until da≈150 nm (Fig. 6C,D). The reflectance spectra have a clear, main band for 60<da<100 nm, but for da>100 nm the spectra become progressively bimodal. A prominent single reflectance band is realised when da≈90, or h≈0.5 (Fig. 6C,D).

The magpie feather barbule considered as a multilayer reflector

The prominent optical feature revealed by the FDTD calculations is a strong polarisation-dependency of the feathers as TE-polarised light has a significantly higher reflectance compared with TM-polarised light (Figs 5 and 6). This optical anisotropy must be intimately related to the shape anisotropy of the melanosome stacks, being assemblies of parallel cylindrical rodlets (Figs 3 and 4). We therefore considered the RI profile of the melanosome stack. We sliced the model barbule of Fig. 4 into 10 nm layers and calculated the fractions of air, keratin and melanin as a function of depth into the barbule for melanosomes of different hollowness (Fig. S2). The effective RI of each layer was then obtained using Eqn 1 (see Materials and methods). The weighting factors for TE- and TM-polarised light, w=−2 and 2, yielded a much larger RI contrast for TE- than for TM-polarised light (Fig. 4). Subsequently we performed EMM by applying a standard transfer-matrix formalism for optical multi-layers to calculate the reflectance, transmittance and absorptance for both the full and half-barbule. The resulting spectra are remarkably similar to those obtained with the FDTD simulations (compare Fig. S3 with Fig. 5). The reflectance of TE-polarised light is much larger than that of TM-polarised light, evidently due to the larger RI contrast of the layers for TE light.

We also performed transfer-matrix calculations for the same parameter set as used in the FDTD modelling of Fig. 6. The resulting reflectance spectra (Fig. S4) are again very similar to those obtained with the FDTD approach. Fig. 7 compares the peak reflectance, peak wavelength and bandwidth (FWHM) of the spectra obtained with the FDTD method and the EMM results for four cases, using as weighting factors for the effective RI of the layers w=−2, −1, 1 and 2. Fig. 7A–C presents the results for varying numbers of melanosome layers, and Fig. 7D–F shows the results for different melanosome hollowness with a fixed number of layers. The overall behaviour of the FDTD and EMM spectra are clearly very similar, but the differences demonstrate that the heuristic expression for the effective RI with the chosen values of the weighting factor w is not fully adequate. The FDTD and EMM approach give approximately the same results for TE- and TM-polarised light when choosing w values of ∼−0.5 (TE) and ∼2.5 (TM), respectively.

Fig. 7.

Comparison of reflectance spectra characteristics calculated with the FDTD and EMM methods for normally incident TE- and TM-polarised light. (A–C) Peak reflectance, peak wavelength and spectral bandwidth of a half-barbule with melanosome diameter (dm) 180 nm and air core diameter (da) 100 nm as a function of the number of melanosome layers. (D–F) Peak reflectance, peak wavelength and spectral bandwidth of a half-barbule with three layers of melanosomes with dm=180 nm as a function of the hollowness (h=dm/da).

Fig. 7.

Comparison of reflectance spectra characteristics calculated with the FDTD and EMM methods for normally incident TE- and TM-polarised light. (A–C) Peak reflectance, peak wavelength and spectral bandwidth of a half-barbule with melanosome diameter (dm) 180 nm and air core diameter (da) 100 nm as a function of the number of melanosome layers. (D–F) Peak reflectance, peak wavelength and spectral bandwidth of a half-barbule with three layers of melanosomes with dm=180 nm as a function of the hollowness (h=dm/da).

Because the multilayer modelling facilitates an intuitive interpretation of the optical properties of magpie barbules, we applied this approach in a study of the effect of melanosome size. We calculated the reflectance spectra of a half-barbule with three layers of melanosomes that are close packed for normally incident light. The melanosomes are assumed to have a constant hollowness h=0.5, but with a changing melanosome diameter, from 140 to 220 nm (Fig. 8A). Weighting factors w=−0.5 (TE) and w=2.5 (TM) for the effective RI of the layers yielded strongly different reflectance spectra for TE- and TM-polarised light. The increase in melanosome size causes a distinct shift in peak wavelength, from ∼400 to ∼600 nm, an increase of the peak reflectance, and a broadening bandwidth. Averaging the TE and TM spectra yielded the reflectance for unpolarised light (Fig. 8A, av).

Fig. 8.

Reflectance spectra for normally incident TE- and TM-polarised light. (A) Spectra calculated with the multi-layer method for (half) a barbule with three layers of melanosomes with different diameter of the melanosomes, assuming a constant hollowness of h=0.5; ‘av’ denotes average of the TE and TM spectra. (B) TE and TM spectra measured from the purple and green areas of the tail feather of Fig. 1C.

Fig. 8.

Reflectance spectra for normally incident TE- and TM-polarised light. (A) Spectra calculated with the multi-layer method for (half) a barbule with three layers of melanosomes with different diameter of the melanosomes, assuming a constant hollowness of h=0.5; ‘av’ denotes average of the TE and TM spectra. (B) TE and TM spectra measured from the purple and green areas of the tail feather of Fig. 1C.

The reflectance spectra calculated for normally incident TE- and TM-polarised light are substantially different in amplitude and also in peak wavelength. Measurements of the polarisation-dependent reflectance spectra from different locations on the tail feather of Fig. 1C confirm the severe dependence on polarisation and thus the distinct optical effects of the anisotropy of the melanosome stacks (Fig. 8B).

We finally studied the dependence of the reflectance spectra for TE- and TM-polarised light on the angle of incidence. The peak reflectance of the TE spectra increases monotonically with an increasing angle of incidence while the peak reflectance of the TM spectra decreases up to the Brewster angle, fully in accordance with the reflection behaviour of isotropic multi-layers (Fig. S5).

Optical properties of magpie feathers

Our study compares measured reflectance spectra of magpie barbules with the results of modelling with the FDTD method and classical multi-layer modelling using effective medium theory. In the magpie feathers, the coloured barbules approximate slightly bent thin plates, and thus in principle will act as optical thin films. In general practice, however, the varying barbule thickness will obscure the thin film interference effects due to spectral smoothing (Fig. 1; Fig. S1).

The barbules contain hollow melanosomes, which are closely packed into a few layers and organised into two stacks, each of which is located on the outer edges of the barbules. The feather brightness is proportional to the number of melanosome layers, and the colour crucially depends on the melanosome diameter and hollowness (Figs 6 and 7). Calculations of the reflectance as a function of the number of layers demonstrated that it is hardly useful to install more than three or four melanosome layers to achieve magnificent feather colours. Optical modelling further established that the first reflector stack is virtually exclusively responsible for the observed colouration. Why the barbules nevertheless have two stacks, located at the outer edges of the cells, may be the consequence of the cellular process of pulling the melanosomes together against the cell wall during the feather's development, before the barbule cell dies (e.g. as discussed in Shawkey et al., 2015).

Recent TEM studies on black-billed magpie feathers revealed that the number of melanosome layers vary locally, corresponding with the local colour (Han et al., 2017). Furthermore, both optical and anatomical data indicated that the size and arrangement of the melanosomes is too irregular to treat the melanosome stack as an ideal photonic crystal (Figs 2 and 3) (Han et al., 2017). In our modelling we nevertheless used a regular melanosome packing in order to derive the RI profile (Figs 4 and 5), applying an effective medium approach. The reflectance spectra thus obtained compared well with the spectra following from FDTD modelling. In real barbules, a much shallower RI profile than those used in the modelling can occur, indicating that the reflectance is strongly dependent on the degree of irregularity of the spatial arrangement of the melanosomes. This will not seriously affect the wavelength range of the reflectance spectra, however, but will reduce their magnitude (for a related analysis of the effect of melanosome disorder in mallard barbules, see Stavenga et al., 2017). The experimentally obtained reflectance spectra (Figs 1 and 8B) have a distinctly lower amplitude than the modelled ones (Figs 5, 6 and 8A), which is because of the spatial spread of the reflected light and hence mostly due to the experimental conditions. The measured spectra noticeably differ from the modelled spectra in the long-wavelength range. The latter will be the result of light scattering in the lower feather parts, because melanin absorption rapidly decreases with increasing wavelength, and thus long-wavelength scattered light will be progressively less absorbed by the melanin of the feathers, resulting in a rising reflectance with increasing wavelength (e.g. Fig. S3), which however occurs beyond the spectral range of the bird's vision.

Barbule anisotropy and dependence of the reflectance on polarisation

FDTD calculations, as well as multi-layer modelling, indicated that the shape of the melanosomes and their spatial arrangement causes a distinct shape anisotropy of the barbule and thus a clear polarisation dependence of the reflectance spectra, which was confirmed experimentally (Fig. 8). The polarised reflections of the feathers are presumably not functional, however, as birds are not known to possess polarisation vision. The feather colours as seen by a conspecific will hence be the result of averaged TE and TM reflectance. Only with very large angles of light incidence will this cause an iridescent signal. Whether magpies use iridescence in intraspecific recognition is doubtful, especially as the tail feathers have a rather varied colouration, although magpies are most likely to have acute colour vision (Lind et al., 2013). Whether the black feathers, having strongly absorbing melanin, and the white feathers, where melanin is absent, increase or decrease the risk of attack of magpies by goshawks has been studied (Götmark, 1997), but the general biological functions of the pigmentary and structural colouration of the magpie plumage has so far remained uncharted territory.

Colouration of other magpies and related corvids

The plumage of magpies (Corvidae) does not have a universal colouration mechanism. Whereas the feathers of the closely related Korean magpie, Pica sericea, have barbules with hollow melanosomes similar to the Eurasian magpie investigated here (Lee et al., 2010), the Formosan (or Taiwan) blue magpie (Urocissa caerulea) derives its blue colouration from light interference in the spongy medulla of the feather barbs (Liao et al., 2015). Similarly, the structural colouration of the common green magpie (Cissa chinensis) is also based in the barbs, but the observed green colour arises from a filtering action of frontally deposited carotenoids. Cissa chinensis is green when in forest areas, but becomes blue when in open country or when reared on a low carotenoid diet (Rothschild, 1975; Hudon, 2005). Remarkably, the same optical method is realised in the green feathers of budgerigars and parrots, but here the high-pass colour filters are psittacofulvins (McGraw and Nogare, 2004; D'Alba et al., 2012; Tinbergen et al., 2013).

Magpies thus apply a diversity of colouration methods, as is generally the case with other corvids (Lee et al., 2016). In addition to thin film reflections causing the shiny appearance of many crows, the two main ways of structural colouration are regularly ordered melanosomes in the barbules and a quasi-regular ordered spongy medulla in the barbs. The melanosomes can be solid or hollow (Durrer, 1977; Prum, 2006); intermediate states with a dense melanised cladding and a less dense core also exist, e.g. in the occipital feather melanosomes of Parotia lawesii (Stavenga et al., 2015). Another colourful corvid is the blue jay, which has blue and white feathers due to barbs with a spongy medulla ordered with different length scales, while rufous and black feathers are due to phaeomelanin and eumelanin (Parnell et al., 2015). Similar to the polarisation signals discussed above, the physicochemical basis of the feather colours of many corvids and its connection to vision remains largely uninvestigated, a gap that future studies might close.

We thank Dr Julian Thorpe (University of Sussex, UK) for performing transmission electron microscopy, and Dr Daniel Osorio for advice and reading the manuscript.

Author contributions

Conceptualization: D.G.S.; Methodology: B.D.W.; Investigation: D.G.S., B.D.W., H.L.L.; Writing - original draft: D.G.S.; Writing - review & editing: B.D.W.

Funding

This study was financially supported by the Air Force Office of Scientific Research/European Office of Aerospace Research and Development (AFOSR/EOARD) (grant FA9550-15-1-0068 to D.G.S.) and the National Centre of Competence in Research ‘Bio-Inspired Materials’, the Adolphe Merkle Foundation, and the Ambizione program of the Swiss National Science Foundation (Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung) (168223 to B.D.W.).

Bräuer
,
R.
and
Bryngdahl
,
O.
(
1994
).
Design of antireflection gratings with approximate and rigorous methods
.
Appl. Opt.
33
,
7875
-
7882
.
D'Alba
,
L.
,
Kieffer
,
L.
and
Shawkey
,
M. D.
(
2012
).
Relative contributions of pigments and biophotonic nanostructures to natural color production: a case study in budgerigar (Melopsittacus undulatus) feathers
.
J. Exp. Biol.
215
,
1272
-
1277
.
Durrer
,
H.
(
1977
).
Schillerfarben der Vogelfeder als Evolutionsproblem
.
Denkschr. Schweiz. Naturforsch. Ges.
91
,
1
-
126
.
Durrer
,
H.
and
Villiger
,
W.
(
1966
).
Schillerfarben der Trogoniden
.
J. Ornithol.
107
,
1
-
26
.
Durrer
,
H.
and
Villiger
,
W.
(
1967
).
Bildung der Schillerstruktur beim Glanzstar
.
Zeitschr. Zellforsch. Mikrosk. Anat.
81
,
445
-
456
.
Durrer
,
H.
and
Villiger
,
W.
(
1970
).
Schillerfarben der Stare (Sturnidae)
.
J. Ornithol.
111
,
133
-
153
.
Eliason
,
C. M.
and
Shawkey
,
M. D.
(
2012
).
A photonic heterostructure produces diverse iridescent colours in duck wing patches
.
J. R. Soc. Interface
9
,
2279
-
2289
.
Eliason
,
C. M.
,
Bitton
,
P.-P.
and
Shawkey
,
M. D.
(
2013
).
How hollow melanosomes affect iridescent colour production in birds
.
Proc. R. Soc. B
280
,
20131505
.
Götmark
,
F.
(
1997
).
Bright plumage in the magpie: does it increase or reduce the risk of predation?
Behav. Ecol. Sociobiol.
40
,
41
-
49
.
Greenewalt
,
C. H.
,
Brandt
,
W.
and
Friel
,
D. D.
(
1960
).
The iridescent colors of hummingbird feathers
.
Proc. Amer. Phil. Soc.
104
,
249
-
253
.
Halir
,
R.
,
Bock
,
P. J.
,
Cheben
,
P.
,
Ortega-Moñux
,
A.
,
Alonso-Ramos
,
C.
,
Schmid
,
J. H.
,
Lapointe
,
J.
,
Xu
,
D.
,
Wangüemert-Pérez
,
J. G.
and
Molina-Fernández
,
Í.
(
2015
).
Waveguide sub-wavelength structures: a review of principles and applications
.
Laser Phot. Rev.
9
,
25
-
49
.
Han
,
C.
,
Kim
,
H.
,
Jung
,
H.
,
Lee
,
S.
,
Jablonski
,
P. G.
and
Jeon
,
H.
(
2017
).
Origin and biomimicry of weak iridescence in black-billed magpie feathers
.
Optica
4
,
464
-
467
.
Hill
,
G. E.
(
2010
).
Bird Coloration
.
Washington
:
National Geographic
.
Hudon
,
J.
(
2005
).
Considerations in the conservation of feathers and hair, particularly their pigments
. In
Fur Trade Legacy. The Preservation of Organic Materials
(ed.
M.
Brunn
and
J. A.
Burns
), pp.
127
-
147
.
Ottawa, ON
:
Canadian Association for Conservation of Cultural Property
.
Khudiyev
,
T.
,
Dogan
,
T.
and
Bayindir
,
M.
(
2014
).
Biomimicry of multifunctional nanostructures in the neck feathers of mallard (Anas platyrhynchos L.) drakes
.
Sci. Rep.
4
,
4718
.
Lee
,
E.
,
Lee
,
H.
,
Kimura
,
J.
and
Sugita
,
S.
(
2010
).
Feather microstructure of the Black-billed Magpie (Pica pica sericea) and Jungle Crow (Corvus macrorhynchos)
.
J. Vet. Med. Sci.
72
,
1047
-
1050
.
Lee
,
E.
,
Miyazaki
,
J.
,
Yoshioka
,
S.
,
Lee
,
H.
and
Sugita
,
S.
(
2012
).
The weak iridescent feather color in the Jungle Crow Corvus macrorhynchos
.
Ornith. Sci.
11
,
59
-
64
.
Lee
,
S.
,
Kim
,
M.
,
Choe
,
J. C.
and
Jablonski
,
P. G.
(
2016
).
Evolution of plumage coloration in the crow family (Corvidae) with a focus on the color-producing microstructures in the feathers: a comparison of eight species
.
Anim. Cells Syst.
20
,
95
-
102
.
Leertouwer
,
H. L.
,
Wilts
,
B. D.
and
Stavenga
,
D. G.
(
2011
).
Refractive index and dispersion of butterfly chitin and bird keratin measured by polarizing interference microscopy
.
Opt. Exp.
19
,
24061
-
24066
.
Liao
,
S.-F.
,
Yao
,
C.-Y.
and
Lee
,
C.-C.
(
2015
).
Measuring and modeling the inconspicuous iridescence of Formosan blue magpie's feather (Urocissacaerulea)
.
Appl. Opt.
54
,
4979
-
4983
.
Lind
,
O.
,
Mitkus
,
M.
,
Olsson
,
P.
and
Kelber
,
A.
(
2013
).
Ultraviolet vision in birds: the importance of transparent eye media
.
Proc. R. Soc. B
281
,
20132209
.
Lucarini
,
V.
,
Saarinen
,
J. J.
,
Peiponen
,
K.
and
Vartiainen
,
E. M.
(
2005
).
Kramers-Kronig Relations in Optical Materials Research
.
Berlin
:
Springer
.
Maia
,
R.
,
Rubenstein
,
D. R.
and
Shawkey
,
M. D.
(
2013
).
Key ornamental innovations facilitate diversification in an avian radiation
.
Proc. Natl. Acad. Sci. USA
110
,
10687
-
10692
.
McGraw
,
K. J.
(
2006a
).
Mechanics of carotenoid-based coloration
. In
Bird Coloration, Vol. 1
(ed.
G. E.
Hill
and
K. J.
McGraw
), pp.
177
-
242
.
Cambridge, MA
:
Harvard University Press
.
McGraw
,
K. J.
(
2006b
).
Mechanics of melanin-based coloration
. In
Bird Coloration, Vol. 1
(ed.
G. E.
Hill
and
K. J.
McGraw
), pp.
243
-
294
.
Cambridge, MA
:
Harvard University Press
.
McGraw
,
K.
and
Nogare
,
M. C.
(
2004
).
Carotenoid pigments and the selectivity of psittacofulvin-based coloration systems in parrots
.
Comp. Biochem. Physiol. B
138
,
229
-
233
.
Meadows
,
M. G.
,
Morehouse
,
N. I.
,
Rutowski
,
R. L.
,
Douglas
,
J. M.
and
McGraw
,
K. J.
(
2011
).
Quantifying iridescent coloration in animals: a method for improving repeatability
.
Behav. Ecol. Sociobiol.
65
,
1317
-
1327
.
Osorio
,
D.
and
Ham
,
A. D.
(
2002
).
Spectral reflectance and directional properties of structural coloration in bird plumage
.
J. Exp. Biol.
205
,
2017
-
2027
.
Parnell
,
A. J.
,
Washington
,
A. L.
,
Mykhaylyk
,
O. O.
,
Hill
,
C. J.
,
Bianco
,
A.
,
Burg
,
S. L.
,
Dennison
,
A. J.
,
Snape
,
M.
,
Cadby
,
A. J.
,
Smith
,
A.
, et al. 
(
2015
).
Spatially modulated structural colour in bird feathers
.
Sci. Rep.
5
,
18317
.
Parra
,
J. L.
(
2010
).
Color evolution in the hummingbird genus Coeligena
.
Evolution
64
,
324
-
335
.
Prum
,
R. O.
(
2006
).
Anatomy, physics, and evolution of avian structural colors
. In
Bird Coloration, Vol. I, Mechanisms and Measurements
(ed.
G. E.
Hill
and
K. J.
McGraw
), pp.
295
-
353
.
Cambridge, MA
:
Harvard University Press
.
Rothschild
,
M.
(
1975
).
Remarks on carotenoids in the evolution of signals
. In
Coevolution of Animals and Plants
(ed.
L.E.
Gilbert
and
P. H.
Raven
), pp.
20
-
52
.
Austin
:
University of Texas Press
.
Shawkey
,
M. D.
,
D'Alba
,
L.
,
Xiao
,
M.
,
Schutte
,
M.
and
Buchholz
,
R.
(
2015
).
Ontogeny of an iridescent nanostructure composed of hollow melanosomes
.
J. Morphol.
276
,
378
-
384
.
Shawkey
,
M. D.
,
Hauber
,
M. E.
,
Estep
,
L. K.
and
Hill
,
G. E.
(
2006
).
Evolutionary transitions and mechanisms of matte and iridescent plumage coloration in grackles and allies (Icteridae)
.
J. R. Soc. Interface
3
,
777
-
786
.
Shawkey
,
M. D.
,
Morehouse
,
N. I.
and
Vukusic
,
P.
(
2009
).
A protean palette: colour materials and mixing in birds and butterflies
.
J. R. Soc. Interface
6
,
S221
-
S231
.
Stavenga
,
D. G.
(
2014
).
Thin film and multilayer optics cause structural colors of many insects and birds
.
Mat. Today Proc.
1
Suppl.
,
109
-
121
.
Stavenga
,
D. G.
,
Leertouwer
,
H. L.
,
Marshall
,
N. J.
and
Osorio
,
D.
(
2010
).
Dramatic colour changes in a bird of paradise caused by uniquely structured breast feather barbules
.
Proc. R. Soc. B
278
,
2098
-
2104
.
Stavenga
,
D. G.
,
Leertouwer
,
H. L.
,
Osorio
,
D. C.
and
Wilts
,
B. D.
(
2015
).
High refractive index of melanin in shiny occipital feathers of a bird of paradise
.
Light Sci. Appl.
4
,
e243
.
Stavenga
,
D. G.
,
Leertouwer
,
H. L.
,
Pirih
,
P.
and
Wehling
,
M. F.
(
2009
).
Imaging scatterometry of butterfly wing scales
.
Opt. Exp.
17
,
193
-
202
.
Stavenga
,
D. G.
,
Tinbergen
,
J.
,
Leertouwer
,
H. L.
and
Wilts
,
B. D.
(
2011
).
Kingfisher feathers – colouration by pigments, spongy nanostructures and thin films
.
J. Exp. Biol.
214
,
3960
-
3967
.
Stavenga
,
D. G.
,
van der Kooi
,
C. J.
and
Wilts
,
B. D.
(
2017
).
Structural coloured feathers of mallards act by simple multilayer photonics
.
J. R. Soc. Interface
14
,
20170407
.
Tinbergen
,
J.
,
Wilts
,
B. D.
and
Stavenga
,
D. G.
(
2013
).
Spectral tuning of Amazon parrot feather coloration by psittacofulvin pigments and spongy structures
.
J. Exp. Biol.
216
,
4358
-
4364
.
Vigneron
,
J. P.
,
Colomer
,
J.
,
Rassart
,
M.
,
Ingram
,
A. L.
and
Lousse
,
V.
(
2006
).
Structural origin of the colored reflections from the black-billed magpie feathers
.
Phys. Rev. E
73
,
021914
.
Vukusic
,
P.
and
Stavenga
,
D. G.
(
2009
).
Physical methods for investigating structural colours in biological systems
.
J. R. Soc. Interface
6
Suppl. 2
,
S133
-
S148
.
Wilts
,
B. D.
,
Leertouwer
,
H. L.
and
Stavenga
,
D. G.
(
2009
).
Imaging scatterometry and microspectrophotometry of lycaenid butterfly wing scales with perforated multilayers
.
J. R. Soc. Interface
6
,
S185
-
S192
.
Wilts
,
B. D.
,
Michielsen
,
K.
,
De Raedt
,
H.
and
Stavenga
,
D. G.
(
2014
).
Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling
.
Proc. Natl. Acad. Sci. USA
111
,
4363
-
4368
.
Xiao
,
M.
,
Dhinojwala
,
A.
and
Shawkey
,
M.
(
2014
).
Nanostructural basis of rainbow-like iridescence in common bronzewing Phaps chalcoptera feathers
.
Opt. Express
22
,
14625
-
14636
.
Yoshioka
,
S.
,
Nakamura
,
E.
and
Kinoshita
,
S.
(
2007
).
Origin of two-color iridescence in rock dove's feather
.
J. Phys. Soc. Jpn.
76
,
013801
.

Competing interests

The authors declare no competing or financial interests.

Supplementary information