  The achievable instrumental performance of a scanning transmission electron
microscope (STEM) is determined by the size and shape of the incident electron
probe. The most important optical factor in achieving the optimum probe profile
is the radius of the probe-forming aperture, which determines the convergence
semi-angle of the illumination. What is often overlooked however is that small
deviations from this optimum can degrade both the resolution and
interpretability of image contrast. A 30% error in aperture radius can lead to
a factor of 2 contrast reduction in typical lattice spacings, and a 5 {\AA}
error in the thickness measurement of thin layers (such as gate oxides).
Theoretical calculations of the optimum convergence angles, from a wave-optical
consideration of the probe forming conditions, are explained and their
consequences discussed. An experimental approach to the measurement and tuning
of the convergence angle is then introduced.
  This is intended for uncorrected electron microscopes. For corrected
instruments, Cs=0, and Cc usually determines the choice of aperture - see e.g.
ULTRAMICROSCOPY 108, (2008) 1454-1466
