The Ronchigram

Experiment: Load a test specimen of polystyrene spheres, shadow coated with gold particles on a carbon film. Line up the microscope as usual in normal TEM mode. Select the largest condenser aperture and centre it.

Ask the demonstrator: Show me how to put the microscope into STEM mode, with the scan switched off. Please align the condenser lens, aperture and stigmators, and objective rotation centre, so that I can see a reasonably well-aligned Ronchigram.

Lets start by not actually scanning the probe at all. Examine what we see on the phosphor screen at the bottom end of the electron microscope. The rays coming out of the sample have conical shape, formed by the condenser aperture, and this cone eventually hits the phosphor screen, where it forms a bright circle. The circle is called the 'Gabor hologram', the 'Ronchigram' or the 'central zero-order disc of the convergent beam electron diffraction pattern' depending on the context and whose talking about it. I'm going to call it the Ronchigram. It provides the best way of lining up a STEM, and it will also teach us a lot about electron lens aberrations.

Experiment: Look at the Ronchigram. Start by going through focus on both C2 and the objective lens. Move the specimen.

You will find that the Ronchigram looks pretty odd, a sort of fish-eye view of the specimen. Go through focus with either the objective or C2. If you want to increase the contrast, go up in spot size. Weird shapes move in and out. If the microscope is well aligned, the Ronchigram from an amorphous specimen should look something the next figure, which has been calculated in a computer:

Well, why does the Ronchigram look like this? As a first approximation, what we should see is a shadow image cast by the specimen which reverses as we change the cross-over of the beam near the specimen, as shown below:

When the beam is crossing over exactly at the specimen, there will be a burred mess over the whole disc (middle picture above). If the specimen has some feature, like the curly P above, then above and below focus we see a shadow of that feature cast onto the central disc, and magnified according to how far away the beam cross-over is above or below the specimen.

Experiment: Turn C2 from a zero setting, slowly increasing its strength. You should see the image reversal. All this occurs at a rather low setting of C2. At higher settings, the Ronchigram may get focussed into a bright spot and undergo a second reversal. However, this reversal is to do with the way we are using the lower part of the microscope (below the specimen plane) to image the cone of illumination coming out of the specimen. Concentrate on the low settings of C2.

In fact, the behaviour of image is much more complicated than the figure above suggests because of the effects of aberrations in the lens. All sorts of aberrations may be present in C2, but these tend to over-focussing high angle beams (ones that pass well off-centre), bringing them to an premature focus, i.e. a focus that is nearer the lens than it should be.

To understand this, first consider a perfect lens. A perfect lens, by definition, focuses all beams from the source to a single point, as shown below.

If we have aberration presents, high-angle beams tend to be over-focussed, so that they focus at a plane above the plane of perfect focus, like this:

How is this extra complication going to affect what we see in the Ronchigram? Start by thinking about just two sets of beams: two which are virtually 'paraxial' (which means that they are travelling very close the centre of the lens) and which therefore come to the correct focal point of the lens (a point which is called the Gaussian focus); and two which are at very high angle, or close to the very edge of the condenser aperture, as shown below.

Now, when the probe-forming lens is highly over-focussed (which in this experiment means that C2 is moderately excited), all the beams, including the paraxial and high- angle beams, cross-over before they reach the specimen. What we see is just a shadow-image Ronchigram as we would expect, although there will be a slight change in magnification between areas near the centre of the Ronchigram and its edge.

Similarly, when the lens is highly under-excited, we see a reversed shadow image, again slightly distorted in magnification. However, near focus there is a peculiar region which I have called the 'region of radial inversion' in the figure above. When the specimen is lying somewhere in this region (or the lens has been adjusted accordingly), paraxial beams are crossing below it, but high-angle beams are crossing above it. In the Ronchigram, the centre of the pattern has undergone a reversal, the edge of the pattern is still in the over-focussed orientation.

Experiment: On a well-aligned Ronchigram, focus C2 so that the magnification of the image is at maximum. Under-focus slightly and move the specimen. You should be able to find a condition where the centre of image moves in one direction, while the outer area moves in the opposite direction. If you do, then you are within the region of radial inversion. If all you can see are streaking effects and asymmetric stretching of areas of the Ronchigram, then the lenses have not been lined up properly, or the astigmatism in the condenser lens has not been corrected.

Look again carefully at the artificial Ronchigram:

There are two characteristic rings, which you should be able to see experimentally as well. When the focus is set within the region of radial inversion, there is a central circular area where we see just a normal shadow image at rather high magnification. There is then a ring where everything is streaked out in the radial direction: this is called the ring of infinite radial magnification. At a higher radius, there is a ring where everything is streaked out into a circular pattern: this is called the ring of infinite azimuthal magnification. We don't have to understand why this happens like it does - it is all to do with the mathematics of how much the rays miss Gaussian focus as a function of their angle through the lens.

What is important is that the Ronchigram must be circularly symmetric if you want to get a good STEM image.

Experiment: Put the C2 stigmators onto their coarsest setting, and change them by a large amount. Watch the Ronchigram as a function of C2 defocus, especially at or near Gaussian focus (i.e. when you can see a highly magnified blob at the centre of the Ronchigram). You should see streaking shapes, which are like ovals or figures of eight.

If you can't see any of the effects we've talked about, then the lenses are not properly aligned. Lets first discuss in more detail how the lenses are arranged...

Copyright J M Rodenburg