OK, so let's go...

Here, instructions are given for both the person being taught and the teacher. I'll call the teacher a ‘ demonstrator’: in a research environment, this person is likely to be post-doc or a more experienced research student.

9.00am

Ask the demonstrator:  To remove any specimen, switch on the microscope and the electron beam, preferably with the filament slightly under saturated.  Align the condensers and gun.  Form an image of the source at about 4000x magnification.  Align a large condenser aperture.  Let me see the screen and tell me which knob controls the second condenser lens (C2).

It will probably take a bit of time for the demonstrator to get the microscope up and running. While you are waiting you may as well spend the time doing the simplest imaginable optical experiment. If you know about ray optics, you can skip to the first electron experiment. If you are unfamiliar with ray diagrams, then...

Experiment: Pick up an ordinary optical lens and hold it parallel to a white piece of paper. In any well-equipped electron microscopy laboratory there should be an optical lens for examining the specimen before you put it into the electron microscope. If there is a light-bulb nearby - the room light will do - position the lens below the light with the piece of paper underneath it. Move the lens up and down relative to the piece of paper and try to form a sharp image on the piece of paper. You should be able to form an image of the light bulb, or whatever the top of the lens is pointing towards. This experiment is analogous to the first experiment we will do in the electron microscope.

The picture is meant to represent a cross-section through the lens. Imagine cutting an optical lens in half, right through its centre. Some demonstrators and textbooks draw a lens as a line with two points at the end, like this

because it is much quicker than drawing two curved lines.

Demonstrators and textbooks draw lines going through the lens to represent rays of light, or rays of electrons. Rays of electrons are often called 'beams'. There are some very important differences between optical lenses and electron lenses, but to begin with we can treat them as roughly the same.

The first important rule is that any ray or beam that passes through the very middle of a lens continues in a straight line, no matter what angle it goes through the lens. (In fact, like almost everything we say in the first lesson or two, that last statement is not perfectly true, but to begin with it is a very good approximation.)

Using the first rule, we could draw a diagram of our first experiment like this.

All the rays or beams we have drawn are straight lines through the middle of the lens. We have drawn the source (light-bulb or filament) at the top of the diagram, in what is called the 'object plane' because that's where the object we are looking at is actually positioned in reality. The image appears on the piece of paper or, (in the electron microscope) the phosphor screen, at the bottom of the diagram, which called the 'image plane'. Note that the image is upside down relative to the object, because the rays have crossed over in the middle of the lens.

This diagram is a good start, but it not very informative because it does not explain why the image goes in and out of focus when you move the lens up and down. If we move the lens up, like this

all that happens is that the image gets bigger.

To understand focus, we must consider rays or beams which do not go through the middle of the lens. Lets draw one beam that goes through the middle of the lens, and one other beam that comes from the same bit of the object, but goes through the side of the lens, like this:

Now we see that there is only one distance away from the lens where both beams coming from the same point of the object meet up in the image: that is the place where the two beams cross. In fact, this is really the definition of a lens. In a perfect lens, all rays from one point in the image, and which do not go straight through the centre of the lens, are bent by exactly the right amount to go through one point in the image plane.

Think of the optical experiment. When we arrange the piece of paper and the lens so that the image is in sharp focus, we can draw lots of rays or beams, which go through different parts of the lens, like this:

When the lens is focussed (as above) all the rays from any point in the object come to one point in the image. Now lets draw lots of rays or beams when the lens is moved up, away from the focus position:

Why does the image appear blurred? The easiest way to understand this is to just concentrate on two rays or beams, which come from a single point in the object. Redrawing the last diagram, but with only two beams, we have

The place where the two beams cross is called, not surprisingly, a beam cross-over. If we are trying to make a sharp image of some object, it is essential that all the beams that come out at different angles from the object meet up at a single cross-over in the image plane. If they don't, that single point in the object will appear blurred or spread out by the amount that the rays have missed each other.

Now we come to first important difference between optical lenses and electron lenses. The knob that controls C2 (the 'brightness' knob) does not change the distance between the lens and the phosphor screen, it actually changes the strength of the electron lens. Here are two lenses, one thin and one thick.

A thin lens is called a weak lens, a thick lens is called a strong lens. When we draw the rays or beams through the two lenses, they appear like this:

The source (or object) is in the same position relative to both lenses, but note that the strong lens focusses the beams into a cross-over at a point much closer to the lens. The 'focal length' of a lens is a measure of its strength, and it is defined as the distance between the lens and the beam cross-over (which is also known as the focal point) when all the beams coming into the lens are parallel to one another, as shown below. A strong lens has a short focal length.

The best way to make the beams going into a lens parallel is to point at it at something a very long distance away. An easy way to measure the focal length of the lens you used in the optical experiment is to use it and the piece of paper to form an image of a scene through a window of some distant buildings. When the buildings are in focus (which are effectively so far away that all the beams from any point on them are travelling parallel to one another through the width of the lens), then the paper is lying at the focal length of the lens.

OK, so lets get back to the electron microscope

Remember, we had asked the demonstrator: To remove any specimen, switch on the microscope and the electron beam, preferably with the filament slightly under saturated. Align the condensers and gun. Form an image of the source at about 4000x magnification. Align a large condenser aperture. Let me see the screen and tell me which knob controls the second condenser lens (C2).

The demonstrator will probably then read the riot act

Don’t worry that you don’t know what ‘C2’ means.  C2 is just the name of one of the lenses in the electron microscope, and we will use it to perform our first experiment, which is equivalent to the one we did above with the optical lens.

The knob that controls C2 will probably be labelled ‘intensity’ or ‘brightness’ (depending on the make of the microscope), because when you are actually using the electron microscope, it affects how bright the image appears on the screen. 

The demonstrator says:  “Well, despite everything I just said in the ‘riot act’, you can turn the brightness knob (C2) whenever you want.  In fact, you have to turn it all the time when are using the electron microscope.  I give you full permission to turn the brightness knob (C2) as much as you like, whenever you like: there is nothing you can do by turning this knob that will ever damage the electron microscope or inconvenience other users.”

Experiment:  Turn the brightness knob (C2) fully in both directions and see what happens on the phosphor screen, which is at the bottom of the electron microscope.  When the electrons hit the screen, they give off light, so you can see what’s going on.  When you bring the brightness knob to a focus - i.e. when the beam becomes a bright tiny spot - you are seeing an image of the source of electrons, which is equivalent to the light bulb in the optical experiment .  Look closely at the focussed spot.  What you can see is an image of the filament (which is another name for the electron source).

The ray diagram for the condenser looks like this:

When C2 is weak, which happens when the brightness knob which controls C2 is turned fully anti-clockwise, the rays from the source spread all over the phosphor screen.  As we turn up C2, which we do by turning the brightness knob clockwise, the rays get more and more concentrated on the screen, so what we see gets brighter and brighter.  Then we reach the focal position: electrons coming from any particular point on the source all arrive at the same place, and so we can see a sharp image of the source. 

As we turn C2 yet higher, the beams spread out again into a circle shape, which eventually spills off the phosphor screen.  As we turn it even higher, the screen gets darker and darker as the electrons get spread ever more thinly.

When an electron lens is turned up (knob turned clockwise) above the focal position, it is said to be ‘over-focussed’; when it is turned down it is said to be ‘under-focussed’.  Focus is an essential experimental variable in electron microscopy, especially in high resolution imaging.When you are doing normal imaging, you should always run C2 (the brightness or intensity) over-focussed: in other words like in the right-hand diagram above.  The reason for this is explained elsewhere.

Copyright J M Rodenburg