Biomedical Engineering Reference
In-Depth Information
Fig. 8.34
(
a
) 2D Fourier power spectrum of the spongy keratin matrix in a blue feather barb of
Cotinga maynana
.(
b
) Observed reflection spectrum of a blue feather barb (
black squares
, right
axis) and predicted reflection spectrum (
bars
, left axis) based on the 2D Fourier power spectrum
in (
a
) (Reproduced from [
143
])
In late 1990s Prum and coworkers demonstrated ambiguously by structural
analyses in the reciprocal space that the blue coloration of feather barbs is indeed
produced by coherent light scattering [
143
,
144
]. They performed 2D Fourier
analyses for cross-sectional TEM images of the spongy keratin layer in the blue
feather barbs of some birds, and revealed a nearly circular ring around the origin
in 2D Fourier power spectra, as shown in Fig.
8.34
. The existence of a ring in 2D
Fourier power spectra indicates that the spongy keratin has only short-range order,
which will lead to coherent light scattering and hence cause the non-iridescent blue
coloration. Recently, they employed small-angel X-ray scattering to characterize
the nanostructures of the blue feather barbs of some birds [
145
,
146
], as shown
in Fig.
8.35
. Clearly, the scattering spectra exhibit rings, implying again that these
nanostructures possess only short-range order, resulting in non-iridescent coloration
via coherent light scattering.
To compare with measurements quantitatively, a simply theory has been fre-
quently used [
6
,
143
-
146
], namely, simply translating 2D Fourier power spectra or
small-angle X-ray scattering spectra into reflection spectra by imposing a Bragg-like
condition
2
n D
k
max
2
;
(8.9)
where
n
is the averaged refractive index of a nanostructure and
k
max
is the peak value
of the spatial frequencies. It should be mentioned that this simply theory is valid only
for very weak scattering. The application to amorphous photonic structures seems
problematic.
