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Click on the colour button of your choice to draw a trajectory
from a fixed x value.
Here we see the effect of chromatic aberration for
electron lenses: electrons of lower velocity are brought to a focus
closer to the lens, whereas electrons of higher velocity are focused
farther from the lens. This means that the energy (velocity) spread
for the electrons in the beam will result in a spread in the focus lengths
for trajectories emanating from the same point. This is called chromatic
Since the electrons passing through each lens in the EM
are emitted from a compact source, the further the electrons incident
on the lens are from the optic axis, the component of their velocity
perpendicular to the axis is greater. This causes the lens to deflect
them more than those with a lesser angle of incidence. Note that the
angles in the real microscope are very much smaller than the exaggerated
angles in the diagrams...
Left click the mouse with the cursor at F and N to construct
As the trajectories farther from the axis are bent
more strongly, they come into focus at a shorter distance from the lens.
The exact focus position depends on the angle the trajectory makes to
the optic axis (beta) and on the quality of the lens.
Click to draw at least 5 trajectories near X.
As we can see, there is a plane in which the spread
in the trajectories is minimum. This is called �plane of least confusion�,
or "disc of least confusion". The diameter of the beam at the disc of
least confusion depends on the maximum angle beta and the spherical
aberration coefficient of the lens. Any point in the plane of the specimen
is smeared by the presence of spherical aberrations to a disc of this
size, thus limiting the resolution of the microscope.
An aperture is placed above (or below) the lens to block
off-axis trajectories and shrink the disc of least confusion
Click to draw trajectories
through the aperture
We can limit the effect of spherical aberration by using
apertures to constrain the angles the electron trajectories make to
the optic axis. In TEM this is done by using the objective aperture.
In STEM this is done by using the condenser aperture.
Draw about 4 trajectories and note that the lens separated
the colours red, green and blue.
Of course, both chromatic and spherical aberrations
occur at the same time. A spread in the wavelengths of the incident
electrons increases the size of the disc of least confusion, and lowers
the resolution of the lens.