Biomedical Engineering Reference
In-Depth Information
vibrating in perpendicular planes. Splitting plane polarized light into two
vector components is called double refraction or birefringence. The two
components follow two principal vibration directions within the material
having different RIs. This causes them to move through the material at
different rates and they emerge with one component retarded behind the
other by a defi nite amount which depends on the difference in the two RIs
(
n
2 −
n
1) and the thickness (
t
). The actual distance of one component behind
the other is called retardation.
If the material is oriented so that one of its principal RIs is parallel to the
vibration direction of the polarizer, the second vector component becomes
zero. All light emerging from the material has the same vibration direction
as the polarizer and is absorbed by the analyzer (vibration direction perpen-
dicular to the polarizer). The material and the entire observed fi eld appear
dark. The material is known to be at extinction. If the material is oriented so
that one of its principal RIs is not parallel to the vibration direction of the
polarizer, the emerging vector components will recombine in the vibration
plane of the analyzer. Since one of the components is retarded, interfer-
ence on recombination of the two components by the analyzer will cause
the image to appear colored. The colored appearance is caused by optical
interference which destroys some wavelengths and reinforces others. The
reinforced wavelengths constitute the interference colors for the material.
Substances that exhibit these interference colors are termed birefringent,
anisotropic or doubly refractive.
The actual interference colors observed depend upon the retardation (
r
),
material thickness and birefringence. If the material thickness varies, sev-
eral colors may be observed. The colors are brightest when the material
is rotated farthest from an extinction position, usually 45° away from this
position. The interference colors produced are determined by the following
equation:
r
= 1000 ×
t
(
n
2 −
n
1)
[1.7]
where
n
1 and
n
2 = RIs of material; (
n
2 −
n
1) = birefringence;
t
= thickness,
1000 = conversion factor.
If a wedge of regularly increasing thickness of any anisotropic material
(i.e. quartz) is turned to the 45° position while being observed between
crossed polars, a defi nite sequence of interference colors or Newton's
series is seen. This series is divided into 'orders' by the red bands which
occur periodically as the material thickness increases. The fi rst-order col-
ors are black, gray, white, yellow, orange and red as thickness increases.
The higher orders include blues and greens in place of gray and white. The
colors also become paler until they approach 'high-order' white at about
the tenth order. The color series observed in the quartz wedge becomes a
