  We investigated the mechanism of structural coloration by quasi-ordered
nanostructures in bird feather barbs. Small-angle X-ray scattering (SAXS) data
reveal the structures are isotropic and have short-range order on length scales
comparable to optical wavelengths. We performed angle-resolved reflection and
scattering spectrometry to fully characterize the colors under directional and
omni-directional illumination of white light. Under directional lighting, the
colors change with the angle between the directions of illumination and
observation. The angular dispersion of the primary peaks in the
scattering/reflection spectra can be well explained by constructive
interference of light that is scattered only once in the quasi-ordered
structures. Using the Fourier power spectra of structure from the SAXS data we
calculated optical scattering spectra and explained why light scattering peak
is the highest in the backscattering direction. Under omni-directional
lighting, colors from the quasi-ordered structures are invariant with the
viewing angle. The non-iridescent coloration results from isotropic nature of
structures instead of strong backscattering. By comparing the data to those of
an periodic structure, we demonstrated the difference in structural coloration
between the quasi-ordered structures and ordered structures.
