Specimens

Five bird species with profoundly black plumage and two species with normal black plumage were identified by visual observation of museum study skins from the Yale Peabody Museum (YPM), Harvard Museum of Comparative Zoology (MCZ), American Museum of Natural History (AMNH), and the University of Kansas Biodiversity Institute (KU). Details of the specimens and plumage patches studied are summarized in Supplementary Table 1. To the human observer, super black plumage had a strongly matte appearance with so little specular reflectance that it was difficult to focus on the surface of the plumage and distinguish individual feathers. The species with normal black plumage lacked any conspicuous glossy specular highlights. Individual contour feathers were sampled from museum skins for scanning electron microscopy (SEM) and synchrotron-radiation X-ray microtomograhy (nano-CT). We could not obtain SEM of Lophorina superba back feathers or CT scans for Lophorina superba back and display cape feathers due to availability of material. Visual inspection of the Lophorina back plumage using a light microscope confirmed that the barbules have normal morphology, without the modified barbule arrays present in super black feathers.

Spectrophotometry

Light reflectance and absorbance by the plumage can be influenced by the specific orientation of the feathers in the plumage and also by the interaction of light scattered by multiple feathers. The optical properties of the intact plumage cannot be reconstructed reliably by plucking feathers and then laying them (singly or together) on a different surface. Therefore, reflectance spectra of super black and normal black plumage patches were recorded directly from the plumage of prepared museum skins.

Total integrated (diffuse and specular) reflectance spectra were measured with an Ocean Optics USB2000 spectrophotometer and ISP-REF integrating sphere using a Spectralon white standard (Ocean Optics, Dunedin, FL). The light source provided diffuse light from all directions and the gloss trap was closed to collect both specular and diffuse reflectance. To ensure repeatable measures of reflectance from these profoundly black samples, we averaged 10 scans for each output file, and used an integration time of 40 μs. For each patch, we measured three spectra from three different positions within the patch and averaged them to produce a single spectrum for the patch. Two specimens per species were measured for all species except for Astrapia stephaniae and Parotia wahnesi, for which only one specimen was measured due to availability of material.

Directional reflectance spectra were measured with an Ocean Optics USB2000 spectrophotometer and Ocean Optics DH-2000Bal deuterium–halogen light source (Ocean Optics, Dunedin, FL, USA). The geometry of the directional reflectance measurements placed the detector at 0° normal to the plumage, which would be the specular direction for typically flat materials. A bifurcated illumination/detection optical fiber was held in an anodized aluminum block ~6 mm above and perpendicular to the plumage. A ~3-mm-diameter circle of light illuminated the plumage. Reflectance between 300 and 700 nm was recorded to obtain the species spectra for the patch. Measures of super black plumage reflectance were quite low and noisy, and signal processing was required. Negative values were converted to 0, and five spectra from each individual were averaged to produce an average spectrum for the patch. Loess smoothing was applied to produce a reflectance spectrum curve (Supplementary Fig. 2).

The light source in our integrating sphere lacked near-ultraviolet light (300–400 nm), but the directional reflectance measures confirmed that none of these patches produced UV reflectance features. Reflectance, %R, was calculated as the area under the measured reflectance spectrum between 400 and 700 nm using Riemann sums and was normalized by the number of wavelength bins measured and 100% reflectance of the white standard.

SEM

For SEM, feathers were mounted on stubs using carbon-adhesive tabs, coated with ~15 nm of gold, and viewed and micrographed using an ISI SS40 SEM operating at 10 kV. For Parotia wahnesi, Ptiloris paradiseus (Fig. 3d), and Melampitta lugubris (Fig. 3c) feathers were coated with 5 nm of gold, and then viewed and photographed using a SEM-4 FESEM Ultra55 operating at 5 kV.

Nano-CT

For nano-CT, one black contour feather from each species was washed and then soaked in an aqueous solution of Lugol’s solution—1% (wt/v) iodine metal (I 2 ) + 2% potassium iodide (KI) in water—for 2–3 weeks to improve X-ray contrast30. Feathers were scanned at beamline 2-BM at the Advanced Photon Source facility at U.S. Department of Energy’s Argonne National Laboratory, Argonne, Il. Feathers were mounted to a post using modeling clay and surrounded by a Kapton tube to reduce sample motion. Feathers were aligned in the beam to scan a portion of the distal tip that is exposed in the plumage. Scans were made with an exposure time of 30 ms at 24.9 keV to acquire 1500 projections as the sample rotated 180° at 3° s−1. Data sets were reconstructed as TIFF image stacks using the TomoPy Python package (https://tomopy.readthedocs.io) in Linux on a Dell Precision T7610 workstation with two Intel Xeon processors yielding 16 cores, 192-GB RAM, and NVIDIA Quadro K6000 with 12-GB VRAM. The isotropic voxel dimensions of the image stacks were 0.65 µm and the field of view of each data set was ~1.5 mm3.

3D polygon models

The external surface of each feather was segmented in VGStudioMAX 2.0 (Volume Graphics) and a 3D polygonal mesh comprising a geometric model of the external surface was extracted using the QuickMesh setting and exported as an OBJ file. To optimize the ray-tracing simulations, each polygonal model was cropped to a 500-µm by 500-µm swatch of the feather vane and then the triangle count was further reduced using the decimate feature (tolerance set to 325 nm) in Geomagic Wrap (3D Systems). Finally, we used the Mesh Doctor feature in Geomagic Wrap to make the surface model manifold, i.e., “water tight.” This last step was necessary to repair any defects in the polygonal mesh through which simulated rays could artifactually enter and become trapped inside the feather during ray-tracing simulations.

Ray-tracing simulations

The directional reflectance, transmittance, and absorbance of super black and normal black plumage patches were analyzed by numerical ray trace simulations using the software package FRED31 (Photon Engineering LLC). Simulations employing two types of illumination were conducted for each feather: (1) omni-directional and (2) directional.

The “omni-directional” setup was configured with a hemispherical light source, a hemispherical reflectance detector, and a hemispherical transmittance detector. Into this setup, we imported a 3D polygonal mesh of each feather. Feathers were placed at the center of all three hemispheres and oriented with their vanes in plane with the base of the hemispheres and perpendicular to their poles. The upper or obverse feather surface was oriented toward the light source and reflectance hemisphere; the lower or reverse feather surface was oriented toward the transmittance hemisphere. One million rays of random wavelength between 300 and 700 nm were emitted from random positions on the hemispherical source and propagated in random directions constrained by a square plane with a side length of 330 µm centered on the feather (corresponding to 66% of the width of the feather swatch).

The “directional” setup was configured as a scale model of the directional reflectance spectrophotometry setup. Directional reflectance simulations were conducted for each feather sample under three different light source orientations: (i) tilted +45° toward the proximal end of the feather, (ii) 0° normal to the feather, and (iii) tilted −45° toward the distal end of the feather. While the plumage was illuminated by a 3-mm-diameter spot in the spectrophotometry experiments, the illumination spot in the simulations was scaled from 11% to 330 µm (corresponding to 66% of the 500-µm width of the feather swatch). The width of the light source representing the bare optical fiber bundle and its distance above the feather swatch were also scaled at 11% to ensure that the size of the solid angle illuminating the plumage patch in the simulations matched that in the spectrophotometry measurements. One million rays of random wavelength between 300 and 700 nm were positioned on a grid spanning the light source. A circular aperture was used to cull rays from the square source, thereby shaping the source to match that of the spectrophotometer probe. Ultimately, 785,398 rays were emitted by the circular source in random directions within an angular range of 28˚, thereby illuminating the 330-µm-diameter spot centered on the feather.

In both “omni-directional” and “directional” simulations, each ray had one of three possible fates. (1) No interaction, where the ray passes through gaps in the feather vane without ever striking the surface of the feather and ultimately terminates when it intersects the transmittance hemisphere. (2) “Transmitted,” where the ray strikes the surface of the feather one or more times until it ultimately exits the underside or reverse surface of the feather vane and terminates on the transmittance hemisphere. (3) “Reflected,” where the ray strikes the surface of the feather one or more times until it ultimately exits the topside or obverse surface of the feather vane and terminates on the reflectance hemisphere. For the scope of this study, we only consider the subset of incident rays that are “reflected” (fate 3). Rays that terminate on the transmittance hemisphere (fates 1 and 2), represent more complex interactions between multiple overlapping feathers in the plumage and/or the skin that we do not consider here.

We simplified the ray-tracing simulations of the feather surface and controlled for potential differences in surface roughness between the real feathers by excluding surface scattering caused by surface roughness (reflections in nonspecular directions) from the simulation. We traced rays using the surface normals of the bare polygon mesh of the feather, treating each polygon in the mesh as a smooth surface. Since no BRDF model was applied to the surface, all radiant power was directed in the specular direction. Thus, each time a ray struck the surface of the feather (a simplified “scattering” event), it bifurcated into one and only one component ray that reflected from the surface of the feather, and one and only one component ray that transmitted into the feather. The direction of the reflected ray was computed based on the law of reflection (θ i = θ r ), and Fresnel equations yielded the fraction of the incident radiant power reflected as a function of the incident angle and the ratio of the index of refraction of air (1.0) and feather keratin (1.56). To investigate the effects of surface microstructure independent of any potential differences in melanin or internal nanostructure between the real feathers, we assumed that rays transmitted into the feather were entirely absorbed before exiting the feather. Thus, any difference in calculated absorption between simulated feathers is caused by variations in the orientation of the feather surface and differences in the number of multiple scattering events.

The ray-tracing simulation proceeded as follows: first, rays with equal amounts of radiant power were emitted from the light source and propagated in the direction of the feather. Then, rays repeatedly intersected the surfaces of the feather vane and reflected from those surfaces in the specular direction until they exited the volume of space occupied by the feather vane and terminated on a hemisphere. For each ray, the simulation recorded the number of light ray-surface intersections, the hemisphere of and spherical coordinates of the termination point, and the ending radiant power. For each ray, absorbance was calculated from the difference between the starting and ending radiant power. For comparison with the directional reflectance spectrophotometry measurements, total absorbance under 0° normal directional illumination was calculated as the sum of reflected light rays that terminated within an angular range of 27°. Percent multiple scattering was calculated as the percentage of this set of rays that scattered two or more times off of the surface of the feather.

To determine how reflectance varies based on the angle incident light and viewing directions, we calculated the locally averaged reflectance at different viewing directions with a nonparametric kernel regression fit using the kreg function with default settings from the R package gplm. The kernel density estimate and regression fits were evaluated at 400 points, representing different viewing directions that were uniformly distributed over the reflectance hemisphere, and the results were plotted as a log-scale color gradient on orthogonal projections of the hemisphere using the persp3d function from the R package rgl.

We used linear regression to estimate correlation between the proportion of rays that scattered at least twice and the actual measured reflectance for the 0° normal directional light ray-tracing setup; we report R 2, slope, standard error of the slope, and P value.

Data availability

The data that support the findings of this study are available from the corresponding author on request.