Physical Principles of Electron Microscopy: An Introduction to TEM ...

80 Chapter 3
contrast (for a given objective-aperture diameter), which is usually of prime
concern because the contrast in tissue-sample images can be very low.
Objective aperture
An objective diaphragm can be inserted located at the back-focal plane
(BFP) of the post-field of the objective lens, the plane at which a diffraction
pattern of the specimen is first produced. In this plane, distance from the
optic axis represents the direction of travel (angle relative to the optic axis)
of an electron that has just left the specimen.
Although in practice the objective behaves as a thick lens, we will discuss
its properties using a thin-lens ray diagram in which the focusing deflection
is considered to occur at a single plane: the principal plane of the lens.
Accordingly, an electron that leaves the specimen parallel to the optic axis is
deflected at the principal plane and crosses the axis at the BFP, a distance f
below the principal plane, as illustrated by the solid ray in Fig. 3-12c.
Assuming parallel illumination and correctly-adjusted tilt controls, such an
electron will have arrived at the specimen parallel to the axis and must have
remained undeflected (unscattered) during its passage through the specimen.
The dashed ray in Fig. 3.12c represents an electron that arrives along the
optic axis and is scattered (diffracted) through an angle � by interaction with
one or more atoms in the specimen. It therefore leaves the specimen on the
optic axis but at angle � relative to it, arriving at the principal plane at a
radial distance from the axis equal to R = u tan ��f tan �. After deflection
by the objective, this electron crosses the optic axis at the first image plane, a
relatively large distance (v � 10 cm) from the lens. Below the principal
plane, the dashed ray is therefore almost parallel to the optic axis, and its
displacement from the axis at the back-focal plane is approximately R . By
inserting an aperture of diameter D (centered around the optic axis) at the
BFP, we can therefore ensure that the electrons that pass through the rest of
the imaging system are those with scattering angles between zero and �,
where
�� tan� � R/f = D/(2f ) (3.9)
Electrons scattered through larger angles are absorbed by the diaphragm
surrounding the aperture and do not contribute to the final image. By making
� small, we can ensure that almost all scattered electrons are absorbed by the
diaphragm. As a result, regions of specimen that scatter electrons strongly
will appear as dark areas (due to fewer electrons) in the corresponding final
image, which is said to display scattering contrast or diffraction contrast.