Page 144 - Fundamentals of Light Microscopy and Electronic Imaging

KINDS OF BIREFRINGENCE 127

Depending on the values of n and n , the sign of birefringence may be positive or
e
o
negative, and specimens are therefore said to be either positively or negatively birefrin-
gent. Note also that birefringence is not a fixed value, but varies, depending on the ori-
entation of the birefringent object relative to the illuminating beam of polarized light.
We return to this important point in later sections.
Birefringence is related to another term, the optical path difference
(or in the field
of polarized light, the relative retardation ), and both are defined as the relative phase
shift expressed in nanometers between the O and E waves emergent from a birefringent
object. As described in Chapters 5 and 7, the optical path length is given as nt,
where n is the refractive index of a homogeneous medium between points A and B and
t is the object thickness. Notice that the optical path length is a distance given in units of
parameter t and that this term is equal to the geometric distance only when n 1. The
optical path difference
for two objects spanning the same distance is

(n n )t.
2
1
Relative retardation and birefringence are related by the analogous expression

(n n )t,
o
e
where t is the thickness, the physical distance traversed through the specimen. Accord-
ingly, small and large objects may give the same retardation depending on the magni-
tude of their birefringence and physical size. Retardation can also be expressed as the
mutual phase shift δ between the two wavelengths, and is given (in radians) by

2
/ .

Double refraction or birefringence is a property of polarizers used in a polarizing
microscope and of microscope specimens that are active in polarized light. Its presence
in a specimen allows us to measure the pattern and extent of molecular alignments,
refractive index differences, and specimen thickness.

KINDS OF BIREFRINGENCE

Birefringence can be an inherent physical property of specimens such as the calcite
crystal, or can be generated through cell biosynthetic activities (cellulose fibrils and
starch granules in plant cells), or can arise from outside physical forces (cytoplasmic
flow, cell movements) acting on components of an otherwise disorganized system. Var-
ious kinds of birefringence have been defined:

• Intrinsic birefringence is based on the asymmetry of polarizability of chemical
bonds within naturally occurring materials such as crystals. Examples: crystals of
calcite and quartz.
• Form birefringence or structural birefringence is associated with extensive ordered
arrangements of macromolecular assemblies having dimensions and spacings com-
parable to the wavelength of light. Form birefringence is sensitive to the refractive
index of the surrounding medium. Examples: parallel arrangements of actin and
myosin filaments in muscle myofibrils, microtubule bundles in mitotic spindle
fibers of dividing cells.