Page 145 - Fundamentals of Light Microscopy and Electronic Imaging

128 PROPERTIES OF POLARIZED LIGHT

• Flow birefringence refers to the induced alignment of asymmetric plate- or rod-
shaped molecules in the presence of fluid flow or agitation. Examples: stirred solu-
tions of detergents (shampoo), DNA, or flagella.
• Strain birefringence describes the forced alignment of molecules in a transparent
solid deformed by an externally applied force. Example: stretched films of
polyvinyl alcohol.
• Stress birefringence is descriptive when electronic deformation occurs in response
to an external mechanical force without there being significant gross deformation.
Example: a stressed lens caused by compression during mounting in a retaining
ring or lens barrel.

PROPAGATION OF O AND E WAVEFRONTS
IN A BIREFRINGENT CRYSTAL

In Chapter 3 we employed the concept of Huygens’ wavelets to describe the location of
a secondary wavefront generated by spherical wavelets and originating from a point
source of light in a homogeneous medium. In a transparent birefringent material, the
ordinary or O ray behaves in the same way, generating a spherical wavefront. However,
the extraordinary or E waves behave differently. As described by Huygens in 1690, the
expanding wavefront of the E ray at a time t can be described as the surface of an ellip-
soid (Fig. 8-8). An ellipsoid is the figure generated by rotating an ellipse about its major
or minor axis. The ellipsoidal form indicates the presence of different velocities for the
E ray along different trajectories in the crystal, where the upper- and lower-limit veloc-
ities define the long and short axes of the wavefront ellipsoid. The long axis corresponds
to the direction along which the wavefront reaches its greatest possible velocity through
the crystal, and is termed the fast axis, while the short axis corresponds to the direction
giving the smallest velocity, and is called the slow axis. The velocities of waves travel-
ing in all other directions have intermediate values. Since the velocity of light in a
medium is described as v c/n, where c is the speed of light in a vacuum and n is the
refractive index, we may infer that n is not constant in a birefringent crystal, but varies,
depending on the path taken by a ray through the crystal. Several additional points about
the propagation of wavefronts in a crystal are worth noting:

• For uniaxial crystals, the O and E wavefronts coincide at either the slow or the fast
axis of the ellipsoid, and the difference in surface wavefronts along the propagation
axis is termed the optical path difference or relative retardation.
• If the O and E wavefronts coincide at the major axis of the ellipsoid, n n in
e
o
directions other than along the optic axis, and the specimen is said to be positively
birefringent (Fig. 8-9). This is the case for crystals such as quartz and most ordered
biological materials. For materials such as calcite, whose O and E wavefronts meet
at the minor axis of the ellipsoid, n n in directions other than along the optic
o
e
axis. Such materials are said to exhibit negative birefringence.
• For the unique case that the incident illuminating beam is parallel or perpendicular
to the optic axis of the crystal, the paths of O and E rays follow the same trajectory
and exit the crystal at the same location. If the incident ray is parallel to the optic
axis, the E ray behaves as an O ray; if the incident ray is perpendicular to the optic
axis, the O and E ray components experience different optical paths.