Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Illumination: Condenser System

The shape of the beam of electrons emitted by the source can be approximated to a cone. Manipulation of the electron beam is the key to getting information from the sample. This is achieved using electromagnetic lenses. Here we shall see how the paths of electrons in the microscope can be modified by the lenses to focus the beam as required.

The action of electron lenses can be described in the same way as light-optical lenses. The way of describing the function of a lens in an optical system is by means of a ray diagram, which is a slight abstraction based on the thin lens approximation. This geometric construction allows us to see the behaviour of different rays incident on a lens.

Electromagnetic lenses in a TEM By using a small number of lenses in series we can achieve very high magnifications/demagnification very quickly, since these multiply. For example, three lenses each giving a magnification of 50× give a 503 = 125000× magnification when placed in series. Any magnification may be achieved in theory. However, beyond a limit any increase in magnification becomes meaningless, as the amount of information available is limited by resolution.

A typical TEM uses a system of two condenser lenses to control the beam incident on the sample. The first lens demagnetises the source, either to increase the brightness or decrease the area of the specimen that is illuminate. A second lens with an aperture above it controls the convergence angle, $$\alpha$$, of the beam at the specimen.

It is possible to reduce the effects of spherical aberration dramatically through the use of a large number (as many as 50) of finely adjustable lenses acting in series, much like the lenses in a camera lens are arranged to reduce chromatic aberration. With the computing power available today it is possible to adjust the lenses simultaneously to find the optimum combination of strengths. This has made it possible to construct aberration-corrected microscopes with a resolution better than 0.1 nm (1 Å).