Pivot points

When we tilt the beam, we change the angle of that the incident illumination coming from the condenser hits the specimen. By now, you may have noticed that the words ‘tilt’ and ‘shift’ are used in many different contexts in electron microscopy. We can tilt or shift the specimen, tilt or shift the gun, tilt or shift lenses or tilt or shift the illumination. However, in general, when used in conjunction with the word ‘beam’, then altering ‘beam tilt’ and ‘beam shift’ usually means tilting or shifting the illumination: in other words, we are adjusting the double deflection coils below C2 and above the specimen - the lower set of coils in the picture below, which is all above the specimen plane.

Now lets think in a bit more detail about how the beam tilt and shift works. As we described before, we have two pairs of coils for each of two Cartesian co-ordinates. When the coils are used to either shift or tilt the beam, the two pairs of coils work in opposite senses, but the ratio of the individual coil excitations is different for these operations.

Consider a single ray that starts off travelling down the centre or the condenser system. If this beam is shifted, it is laterally displaced but ends up travelling parallel with the optic axis. If the beam is tilted, it is first bent off axis, and then bent towards the specimen in such a way that it goes through the same point on the specimen as it would have done, but now at an angle.

Now think what happens if we were to change the height of the specimen. The beam shift is not really affected (it is in fact slightly affected at off-axis points by the objective pre-field – but just don’t worry about this). However, the beam tilt is seriously affected because the lower coil will no longer bend the beam back by the right amount so that it goes through the same point in the specimen plane, as shown below.

In a perfect world, beam tilt should just rotate the beam through a point in the specimen, like a lever pivoting about a point. This process is sometimes called rocking the beam about a ‘pivot point’ or ‘rocking point’. Anyway, because it depends on specimen height, then whenever you change the specimen height, you must re-adjust the pivot points (also known as rocking points – the term rocking point is more often applied to situations where the beam is scanned through all tilt-angles, as in certain specialised forms of electron diffraction).

Most modern electron microscopes have a very easy way of doing this. There is usually a button for ‘pivot points’ which makes the beam jump between two tilt settings. If the pivot points are wrong, you see two beams separated laterally: just two blobs of intensity on the phosphor screen. It is then a simple matter to adjust the two correction knobs (which may well be the multi-function knobs again) until the two beams are coincident. The correction knobs adjust the ratio of excitation of the two sets of deflection coils. There are two ratios, because sometimes the x- and y- coils have cross-talk between them as a result of residual misalignment and the rotation effects of the objective pre-field. Don’t worry about details: just get the beams coincident. You have to do this twice – for both x- and y- tilts.

Ask the demonstrator: Show me how to adjust the pivot points.

Experiment: Repeat the previous experiment, changing the specimen height and the objective focus. Check the pivot points. Change specimen height again and focus, and recheck the pivot points. Try changing the objective excitation (focus) with the pivot point adjustment still on, preferable through a hole in the specimen. You should find that the separation of the two blobs of intensity varies as a function of objective defocus. Of course, as far as the correction of the pivot points is concerned, the actual specimen height is not important compared to the objective excitation. Why? Can you draw a ray diagram?

Some manufacturers’ manuals advise you to adjust the focus of the objective lens so that the double images of the specimen during the pivoting process merge into one image. If you have some spare time, you could try to work out why this works. (Think of the illumination on the specimen casting a shadow below it: as the beam tilts, the shadow is cast at different angles, which affects where it appears in the first image plane.)

All the double-deflection coils in the TEM have their own pivot points for both 'shift' and 'tilt' - indeed, the only difference between tilt and shift is the ratio of the excitation of the two sets of coils. As an ordinary user, the only pivot point you commonly adjust is the illumination tilt (or simply 'beam tilt'), as above. The pivot points of the gun and image alignment coils are adjusted by the site engineer (or simply even just set in the factory). A full alignment of the column involves adjusting the image pivot points, but this process is normally disguised as part of a lengthy alignment sequence. As an ordinary user, only the illumination tilt is important.

However, if you want to do something clever, like good quality STEM imaging, you may have to worry about pivot points in more detail. By the way, the terms tilt purity and shift purity are just ways of saying that pivot points have been correctly set to introduce a pure tilt or a pure shift. The tilt point for pure shift is at infinity (parallel lines never meet).

Copyright J M Rodenburg