Biomedical Engineering Reference
In-Depth Information
where
is wavelength in vacuum,
is the incident angle,
d
and
n
are the thickness
and refractive index of the thin film, respectively, and
r
is the reflection coefficient.
For
s
and
p
polarizations, the reflection coefficients
r
are different, given by
p
n
2
p
n
2
sin
2
sin
2
n
2
cos
cos
r
s
D
p
n
2
;
r
p
D
p
n
2
:
(8.8)
sin
2
sin
2
cos
C
n
2
cos
C
For unpolarized light, the reflectance of a thin film is the superposition of those from
both
s
and
p
polarizations, namely,
R
1
D .R
1s
C R
1p
/=2
,where
R
1s
and
R
1p
are
the reflectance for
s
and
p
polarizations, respectively.
For a keratin thin film with a refractive index of 1.54 and a thickness of 595
and 530 nm, mimicking respectively the green and purple barbules, the calculated
reflection spectra for unpolarized light at different incident angles, obtained from
the above equations, are in good agreement with the measured ones. The converted
RGB colors from the measured and calculated reflection spectra, shown in the insets
of Fig.
8.10
, can well reproduce the observed opposite iridescence: green feathers
change their coloration from green to purple with the viewing angle varying from
normal to oblique, while purple feathers alter their coloration in an opposite way,
i.e., from purple to green. This is rather meaningful for color vision since both green
and purple colors can be perceived no matter what the perspective angle is, or how
the green and purple feathers are arranged. This strategy of opposite iridescence
may provide an optimal way for signalling and communication. For multilayers,
however, it is difficult to achieve such opposite iridescence. It can thus be concluded
that the exploitation of a single thin film for iridescent coloration in neck feathers of
domestic pigeons might not be accidental.
Another interesting feature is the optical function of the poor mirror. Without the
poor mirror underneath, the peak reflectance of the keratin thin film is less than 17%,
and the reflection minimum is zero [
41
]. With the introduction of the poor mirror,
the peak reflectance increases to 20%, and the reflection minimum also increases to
about 5%. The poor mirror can thus raise the overall reflectance. Without this poor
mirror it is difficult to perceive the iridescent colors in a white background, similar
to the case for insect wings [
38
]. With the poor mirror the color visibility can be
largely enhanced since the poor mirror acts also as a black background.
8.5.2
Multilayer
Multilayers are those consisting of alternating layers of materials with different
refractive indices. For multilayers, the mechanism of structural coloration is basi-
cally similar to that for single thin films, namely, thin-film interference. In general,
structural colors produced by multilayers are much brighter than those by single
thin films. This is due to multiple interference from the successive interfaces.
Multilayers are the most common form of structural coloration in the biological
world, appearing, e.g., in insects, fishes, and even plants [
7
-
9
,
44
-
46
].