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## The specimen height and eucentric height

What defines the position of specimen? Well, pretty obviously, the specimen. But if we think about it, there's nothing to stop us running the microscope with the specimen moved up or down relative to the objective and condenser lenses.

Suppose we moved the specimen up, as in the next Figure:

We can still focus on the specimen and make the microscope work by slightly de-exciting (defocusing) the objective lens and, if necessary, slightly increasing the excitation of the condenser lens. In the picture we haven't worried deeply about the exact arrangement of the illuminating coming out of the condenser system because its not important in the present discussion. All that's important is that we can simply de-excite the objective and still form an image on the first image plane, which then gets imaged onto the phosphor screen. We have drawn four rays in both diagrams, a pair from a point in the specimen on the optic axis, and a pair from another point which off-axis. Note that the magnification has changed slightly.

On most microscopes, we can also change the physical height of the specimen. The height adjustment of the specimen is sometimes called the 'eucentric height' adjustment or 'the z- shift' or 'z-adjustment'. 'Eucentric' is a complicated word for an easy idea described shortly. Z is 'z' because when we move the specimen laterally we call it x-y shift, and so 'z' is as in 'coordinates x,y and z', meaning that z is a vertical movement.

Ask the demonstrator: How do I mechanically adjust the eucentric height or, in other words, the specimen z shift?

You will be shown a mechanical adjustment on the specimen holder, although many modern machines have an electrical servo drive for this adjustment.

Experiment: In image mode, form an in-focus image of the specimen. Make sure the step size of the objective lens is at a high setting. Adjust the z-shift. See what happens to the image. Refocus the image using the objective lens (ie the focus knob). By noting which way you have to turn the focus knob, work out whether the specimen has moved up or down. Repeat the experiment until you have a feeling for how a movement in z corresponds to a change in focus of the objective lens. Can you notice any change in magnification as you change the objective focus?

Ask the demonstrator: How do I tilt the specimen?

You may be shown a mechanical knob on the specimen holder, an electrical device, or possibly one or two foot pedals. These all have the effect, either directly, or via a motor, of rotating the specimen holder so that the specimen tilts over, away from the horizontal.

Experiment: Try tilting the specimen back forth. Watch the image to see if it moves. Change the z shift as before and repeat the experiment. Can you work out what's happening?

You should be able to find an adjustment of the z-shift where tilting the specimen leads to a minimal movement of the image. This is called the eucentric height, which means 'the height of the specimen at which its image does not moved laterally as a function of specimen tilt'.

What happens is this. Unless you are using an unusual type of microscope which has a 'top entry stage', then the specimen is supported on a thin rod which comes in horizontally from the outside of the objective lens (a 'side entry stage'). The rod can rotate around a fixed axis, tilting the specimen. The z-shift adjustment effectively lifts or lowers the specimen without affecting the rotation axis of the rod. (Exactly how it does this varies according to the design of the specimen holder).

It is common practice to adjust the z-shift so that the middle of the specimen lies on the rotation axis of the specimen loading arm. This has the convenience of meaning that when the specimen is tilted, the point you are observing remains stationary: i.e. we adjust the specimen to the eucentric height.

All sorts of aspects of the performance of the microscope depend upon the exact height of the specimen. The height of the specimen defines the excitation of the objective lens, which affects the magnification of the whole machine. There is a further complication that we will learn about in more detail later: the magnetic field of the objective lens actually spills over the top of the specimen. This means the objective setting also affects the illumination beam, in a way which is determined by the specimen height, and which is very important when we come on to STEM imaging. The resolution of the microscope is wholly determined by the performance of the objective, and hence also by the specimen height.

For this reason, the manufacturer will often recommend that the microscope should always be run with the specimen at the eucentric height. In fact, you may find you can improve the performance of the microscope for certain applications by operating at a different specimen heights. Many microscopists determine the very best setting of the objective lens for a particular application (say, high-resolution imaging) and then adjust the specimen height to get the microscope in focus, even if this means the specimen is non-eucentric.