Diffraction mode

So far, everything we have done has been in what is called 'imaging mode'. Modern electron microscopes have several different modes of operation: imaging mode, diffraction mode, spot mode, micro-diffraction mode, nano-diffraction mode, scanning mode, rocking-beam mode, and all sorts of other flavours and variations.

After imaging mode, the next most useful mode is diffraction mode - sometimes called 'selected area diffraction'. For the first 40 years of electron microscopy, these were the only two modes available. It is essential that you understand the relationship between imaging and diffraction. In fact, it is so essential that most people teach diffraction mode almost immediately after teaching you to look at the phosphor screen.

Ask the demonstrator: Please load a crystalline sample: something easy like single crystal gold test specimen, preferably with a few holes in it.

Experiment: Watch the demonstrator load the new sample. It's usually pretty easy to do, and we can learn to do it in the next chapter. Let the demonstrator supervise as you turn on the beam. Find a hole in the specimen. Check the condenser alignment, including the condenser aperture and gun shifts. Correct the eucentric height. Focus the objective. It's much harder to focus on a crystal - especially without an objective aperture which we haven't learnt about yet - you'll see all sorts of funny ghostly images going in and out. If necessary, ask the demonstrator for advice.

Check the pivot points. Check, very roughly, the current centre.

Now, before going into diffraction mode, insert a selected area aperture. The SAD aperture is the lowest one in the column. If necessary, ask the demonstrator to remind you how to change its size and position. If the screen goes blank when you put it in, go down in magnification. Move it into the centre of the screen, and go up in magnification, keeping it in the centre of the screen. Move the specimen so that a thin (i.e. a bright) part of it is inside the aperture. Over- focus the brightness knob (C2) so that the screen goes quite dark.

Ask the demonstrator: Show me how to go into diffraction mode.

You will probably have to press a button. Watch the screen. Everything changes and we can see a series of points or little discs.

In fact, despite the fact that new mode looks completely different and strange, only one thing has changed: the projector system has changed setting so that instead of focussing on the first image plane (and hence passing whatever is there onto to the phosphor screen), it is now focussed on the back focal plane of the objective. So, now we have to understand what the back focal plane of the objective is.

In this figure,

we draw some rays coming out from different points in the specimen, which were then focussed on the image plane. Looking at the diagram, the beams reach a focus - that is to say they meet up with one another - at the image plane. But some pairs of beams also cross-over one another much further up the diagram, near the back of the lens. The back focal plane is that place where beams that come out of the specimen parallel to one another cross- over one another.

Aside: Ray diagrams can be rather confusing. In the diagrams we have used, we sometimes draw rays from one point in the object that go through different parts of the lens, or sometimes rays from different parts of the object that all go through the centre of the lens. In the next diagram, we draw rays that come from many different parts of the object, but which are all at the same angle to each other.

Why are we allowed to choose the different types of rays we draw? In fact, every point in a particular optical plane has rays going through it (or, in the case of the specimen plane, being scattered from it), and each of these points has a distribution of angles of rays going through it. To characterise a particular ray, we need a position and an angle (two co- ordinates). In the real world, the positions and angles are two-dimensional, so we really need four co- ordinates. The mathematics of ray propagation (called optical transfer theory) is therefore sometimes formulated in terms of a series of four numbers - a four- element vector. Lenses and other optical components act on these vectors in the form of four-by-four matrices. In other words, ray diagrams really are quite complicated - we have just made them easy by concentrating on sub-sets of positions, destinations (position and angle) or angles. Many textbook diagrams on electron microscopy are exceedingly confusing, because people try to show all the rays for lots of lenses at once.

In the figure above we consider a number of different points in the specimen plane, each of which is scattering a ray at two different angles. Rays at a particular angle, from any point in the image, meet up at one point at the back of the lens. We see that this confluence of parallel rays occurs, by definition, at the focal length of the lens. All such points lie on a plane called the back-focal plane of the lens. (Super pedants will point out that for a perfect imaging lens - one that would form an unaberrated image on a flat image plane - the back focal plane is very slightly curved.) What we see in the back focal plane is the angular distribution of intensity we would have seen if the lens had not existed, but if the angular pattern of rays scattered from the specimen had been allowed to travel very far away: to the so- called Fraunhofer diffraction plane.

We see spots because the specimen is crystalline, and so it acts as a diffraction grating for the electrons, which really behave as waves. This is a crucially important relationship in electron microscopy, but let's just keep to the practicalities for now.

When we press the diffraction button, the strength of next electron lens below the objective is decreased, so that it is now focussed on the back focal plane of the objective lens, as shown below.

Because the objective lens has a large magnification factor, the back focal plane is very close to the lens itself. In fact, we can think of the back focal plane being co-incident with the lens: in practice is it about 1 mm below the specimen.

Mounted in the back-focal plane is the objective aperture: the middle aperture on the column.

Experiment: Go into diffraction mode. Put in an objective aperture. Can you see it? You might not be able to see it very easily because the diffraction pattern from a crystal is just made of spots - the spots will go on and off as the object aperture is moved about. It is quite easy to 'lose' the objective aperture; finding it again is just one of the fun parts of being an electron microscopist (!) Sometimes it is easier to see if you have an amorphous (non- crystalline) specimen, which scatters is all directions, instead of just into spots.

What does the selected area aperture play in all of this? It's sitting in the first image plane below the specimen, which is below both the objective lens and the objective aperture. When in diffraction mode, the objective and the lens below it (sometimes called the 'first intermediate lens' or 'diffraction lens) are arranged like this:

It is important to emphasise that the difference between diffraction mode and image mode only arises from which optical plane we choose to map onto the phosphor screen. By changing the excitation of the first lens below the objective, we can form either an image or a diffraction pattern (which is an 'image' of whatever is going on at the back focal plane). However, when we form a diffraction pattern, we are still 'looking through' the selected area aperture, so the diffraction pattern we see on the screen is not really what's at the back-focal plane, it's the diffraction pattern we would see from the part of the specimen which has been selected by the selected area aperture in the image plane.

Look at the figure above. We have only drawn three beams coming out of the specimen; two from a point on the optic axis; and one from a point off the optic axis. Of the first two beams, only one gets through the objective aperture - the other is coming out of the specimen at too high an angle. The beam from the second point makes an appearance in the back focal plane, but gets stopped by the selected area aperture, because it originated from a point which was too far away from the optic axis in the specimen plane.

Remember: The objective aperture filters out beams which come out of the specimen in a particular range of angles. The selected area aperture filters out beams which have come from a particular set of positions in the specimen. They do these jobs all the time, irrespective of whether we are in diffraction or image mode. Never record an image without knowing what's being filtered out by the objective aperture. Never record a diffraction without knowing which bit of specimen has been selected by the selected area diffraction aperture.

Experiment: Under the guidance of the demonstrator, practice flipping between image mode and diffraction mode. Move the specimen so that a hole appears. Position a selected area aperture over the hole, so none the specimen within its shadow. In diffraction mode, there is now only one central spot. Why?

When in diffraction mode, the demonstrator may read another 'riot act' about burning holes in the phosphor screen with a very bright spot.

Ask the demonstrator:

All these things - shift, astigmatism and focus - are what we have learnt about before for the condenser lenses and the objective lens. The diffraction lens, immediately below the objective lens, is the last important lens that we need to learn about.

Now we know just about everything about the electron microscope, we can try to understand various technical issues in more detail...

Copyright J M Rodenburg