Biomedical Engineering Reference
In-Depth Information
a
b
Fig. 8.1
(
a
) Thin-film interference. A thin film with a thickness
d
and refractive index
n
is
sandwiched between an upper medium with a refractive index
n
1
and a lower medium with a
refractive index
n
2
. The refracted angle with respect to the surface normal in the thin film is denoted
by
.(
b
) Interference in a multilayer
Constructive interference occurs when the optical path difference is an integral
number of wavelength. On the other hand, destructive interference happens when
the optical path difference is a half integral number of wavelength. Considering
the possible phase change upon reflection at both the upper and lower surfaces, the
condition for constructive interference for
n
1
<n<n
2
or
n
1
>n>n
2
is given by
2nd
cos
D m;
(8.1)
where
is the wavelength in vacuum and
m
is an integer. For
n
1
<n>n
2
or
n
1
>
n<n
2
, e.g., a free-standing thin film, the condition for constructive interference
becomes
m
:
1
2
2nd
cos
D
(8.2)
For a thin film, its reflection reaches maxima at the wavelengths that satisfy the
constructive interference condition, giving rise to structural coloration. It is obvious
that the optical path difference increases with increasing incident angle. As a result,
reflection peaks undergo a blue shift in wavelength with increasing incident angle,
leading to iridescence. Similar to that in thin films, multiple interference occurs also
in multilayers, as shown schematically in Fig.
8.1
b, since successively reflected light
from each interface can interfere with each other.
8.3.2
Diffraction
When light interacts with a periodically structured surface such as a grating
shown in Fig.
8.2
, diffraction is expected [
23
]. This is because the scattered light
beams by neighboring corrugations possess a constant optical path difference
