Astigmatism

Ask the demonstrator: Show me how to control the condenser stigmators. Show me how to change the step size (in other words, the sensitivity) of the condenser stigmators: put the step size on the coarsest setting.

Once again, actually obtaining control of the stigmators may involve pressing buttons on the console and the computer screen, but eventually you should be able to turn two knobs – quite possibly the ‘multifunction knobs’ – which control the condenser stigmators. It’s easiest to understand stigmation by doing an experiment.

Experiment: Go back to our old favourite of imaging the filament using C2. It doesn’t matter if there is a specimen loaded, as long as you can find a hole. Turn the spot size up, i.e. demagnify the filament and focus it into a sharp point. Turn the magnification up so you can see it clearly. Now play around with the condenser stigmator and watch what happens. Change the defocus of the filament – i.e. change C2 (the brightness knob) – while you play with stigmators. What’s happening?

We are seeing the third important difference between optical lenses and electron lenses.

Remember: The differences so far: it is easy to change the strength of an electron lens, which we call defocus. Electron lenses are also highly aberrated, which in practice means we should avoid putting large-angle beams through them.

We now discover that electron lenses are routinely ‘astigmatic.’ In fact, purists would argue that defocus and astigmatism are themselves aberrations or simply errors in the lens. That’s true. But its worth thinking of these things separately in order to understand all the shenanigans we have to go through in order to get the microscope to work at its best. Focus is the most important adjustment. High- angle aberrations make lining up the different lenses essential. Astigmatism is something that we have to adjust if we want good images.

Astigmatism occurs when a magnetic lens is not perfectly round. Every time you switch on or adjust an electron lens, the magnetisation of the metal in the lens changes. Because of hysteresis, the lens never quite goes back to where it was, even though you return the knob that controls it to the same setting. The lens will have non-round features due to pockets of different magnetisation around the pole-piece, which is the focussing part of the electron lens. Also, apertures tend to charge up if they have dirt on them, leading to another source of asymmetry.

We can control the astigmatism in the condenser, the objective, and the diffraction lenses. (We haven’t actually discussed the diffraction lens yet – it’s the first lens (i.e. the topmost lens) in the projector system.)

Imagine an oval optical lens. A cross-section through the longest axis of the oval will look like a weak round lens. A cross-section through the shortest axis will look like a stronger round lens. Astigmatism means that the strength of the lens is different in two different directions. That means there are now two focus points.

Experiment: Repeat the previous experiment, but check out the different foci. When the filament appears as a thin line, it is focussed in the direction at right angles to the line. As you change C2, you can get to another focus where the thin line appears at right angles to the first line. Between the foci, it is possible to get a small circle, but not a sharp image of the filament. A long way above and below focus, the thin lines open up into ovals and then, approximately, circles.

Can you understand what’s going on? The figure below might help. [Note that in this diagram, the oval is not a cross-section of the lens as in previous diagrams, but is meant to represent a perspective view of the top of the lens - sorry, I will make a better picture one day if I have time...]

The next question is how to correct the astigmatism.

Stigmators work by adding a small quadrupole distortion to the lens. A quadrupole is an arrangement around the electron beam of four magnetic poles: two south poles opposite one another, and two north poles opposite one another. These have the effect of focussing the electron beam in one direction, and defocussing it in the direction at right angles; just exactly what we want in order to correct astigmatism. In fact, if you think about it, in order to cope with every possible orientation of astigmatism, we need two sets of quadrupoles mounted at 45 degrees to one another. When we adjust the two condenser stigmator knobs, the relative excitation of these two quadrupoles are being changed.

Anyway, luckily you don’t need to understand quadrupoles in order to correct astigmatism: just turn the knobs until you minimise the distortion.

Experiment: Practice introducing astigmatism and getting rid of it by turning the condenser stigmators together with the C2 focus. A good method is to correct all three knobs in a series; for example, correct focus, correct first stigmator, correct focus, correct second stigmator, correct focus, correct first stigmator, and so on.

A quicker way, which needs a little more thought, is to set the focus exactly half-way between the two 'maximally streaked' settings. In other words, focus the lens until you have a sharp streak in one direction. Turn the focus knob, counting the number of clicks, until there is a sharp streak in the perpendicular direction (make sure you turn the focus in the correct direction). Now reverse the direction of focus and move half the number of clicks back again. The spot should appear as a disc. Now correct both stigmators until the disc is as small as possible.

If you are having difficulties, ask the demonstrator for more help.

Astigmatism occurs in all electron lenses. There are usually three obvious set of stigmators on a conventional microscope - the condenser stigmators (which are now playing with), the objective lens stigmators (truly essential for good high resolution images) and the diffraction lens stigmators.

Copyright J M Rodenburg