  Subsampling and fast scanning in the scanning transmission electron
microscope is problematic due to scan coil hysteresis - the mismatch between
the actual and assumed location of the electron probe beam as a function of the
history of the scan. Hysteresis limits the resolution of the microscope and can
induce artefacts in our images, particularly during flyback. In this work, we
aim to provide insights on the effects of hysteresis during image formation. To
accomplish this, a simulation has been developed to model a scanning system as
a damped double-harmonic oscillator, with the simulation being capable of
managing many microscope dependant parameters to study the effect on the
resultant scan trajectories. The model developed shows that the trajectory of
the electron beam probe is not obvious and the relationship between scanning
pattern and probe trajectory is complex.
