Focusing Diffraction Patterns and Correct Camera Length Calibration

Tips & Tricks for Beginners in Electron Microscopy

  • Fig. 1: Creation and imaging of a diffraction pattern for a) a parallel, b) convergent and c) divergent primary beam. See text for details.Fig. 1: Creation and imaging of a diffraction pattern for a) a parallel, b) convergent and c) divergent primary beam. See text for details.

If, using a transmission electron microscope, one presses the “diffraction” button, usually one sees immediately a diffraction pattern. However, in most cases, this diffraction pattern will not be focused, i.e. instead of fine spots (in the case of a single-crystalline material) or sharp Debye-Scherrer rings (for poly-crystalline specimens) one usually gets disks instead of spots or a broadened ring system instead of sharp and clearly distinguishable rings. Obviously, a focusing is needed. Beginners in electron microscopy often try different lenses to find out which one does the focusing and are surprised to see that one can get a sharp diffraction pattern by varying two different lens settings, the diffraction lens and the condenser lens (usually condenser lens no. 2).

We want to address the question, which lenses have to be used in which order to achieve both i) a focused diffraction pattern and ii) a well-defined camera length which allows the determination of lattice spacings after proper calibration. To do so, we have to understand the optics involved, as shown in figure 1.

In figure 1a we see the ideal case, a parallel beam of electrons hits the specimen, the diffracted beams are focused exactly in the objective aperture plane, and the intensity distribution is then imaged by the diffraction lens to the image plane (i.e. the fluorescent screen or a camera). The general problem is now that it is difficult to know when the beam is exactly parallel. A change in condenser lens current can cause the primary beam to be convergent or divergent, as illustrated in figures 1b and 1c. Note that for these latter cases the diffraction pattern is focused in front of or behind the objective aperture. To bring the image in focus in the image plane, one has now to modify the diffraction lens setting accordingly.

However, while the diffraction pattern is now perfectly in focus, its size has changed considerably. Obviously, it is not possible to use the distances between the zero order and some higher order diffraction spot for a lattice constant determination, as the displayed camera length on the microscope does not vary at all.

A standard solution to the problem is (after you brought the specimen to the eucentric height and pressed the “diffraction” button on your microscope) to insert the objective aperture and center it coarsely.

You should now see an unsharp aperture with an unsharp diffraction pattern in its opening.

Next, use the diffraction lens control (this may be the “focus” knob or other, depending on your microscope) to focus precisely the rim of the aperture. Sometimes, you may have difficulties to focus the rim which is much darker than the diffraction spots. In this case, slightly shift the aperture to exclude the brightest spots - usually you have enough diffuse intensity left to see the rim much clearer now. By this way you assure that any intensity distribution positioned at the exact height of the aperture will be imaged in focus in the image plane. Now use the condenser lens (sometimes labelled as “intensity” knob) to focus the diffraction pattern. Once you did this, you can be sure that the magnification of the diffraction pattern from the aperture plane to the image plane is set to a fixed value which is responsible for the camera length. This camera length, however, does not necessarily have to be exactly the one which is displayed on your microscope’s screen, although it should be within 5% of the correct value already. If you need a very precise calibration, use a specimen with a known lattice constant, perform exactly the steps described above, and calculate the true camera length for the known structure.

Further Tips and Pitfalls:

  • For very precise measurements, recalibrate the camera length after you mechanically changed the aperture’s height as e.g. after an aperture exchange.
  • To avoid hysteresis effects of the lenses, you should approach the two focusing points always from the same direction, i.e. monotonuously increasing or decreasing the lens currents from aconsiderably lower (increasing) or higher (decreasing) values.
  • Once you found the perfect setting, you may simply use the same lens current reading alternatively, but be aware of the hysteresis problem.
  • If you are not sure, which knob on your microscope controls which lens (they are sometimes used “multi-functionally”, depending on the current mode) you can always check which lens current changes, when a certain knob is turned, to find out.
  • Once you have a sharp diffraction pattern, your beam is nearly parallel, i.e. it is rather broad and thus the image may be very dark. Be aware of the fact that, if you now increase the beam brightness again in order to see better, you will make your diffraction pattern unsharp again. In a worst case, parts of the broadened outer diffraction spots may be cut from the aperture which will cause image distortions
  • As the fluorescent screen, film plate (where still in use) and camera(s) are usually mounted in different distances from the imaging lenses, the camera lengths differ also. Calibrate the camera length for the method of registration you use.

 

Contact
Prof. Dr. Josef Zweck
Physics Faculty
University of Regensburg, FRG
Germany
 

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