Atomic-resolution imaging in an aberration-corrected scanning transmission electron microscope (STEM) can enable direct correlation between atomic structure and materials functionality. The fast and precise control of the STEM probe is, however, challenging because the true beam location deviates from the assigned location depending on the properties of the deflectors. To reduce these deviations, i.e. image distortions, we use spiral scanning paths, allowing precise control of a sub-Å sized electron probe within an aberration-corrected STEM. Although spiral scanning avoids the sudden changes in the beam location (fly-back distortion) present in conventional raster scans, it is not distortion-free. "Archimedean" spirals, with a constant angular frequency within each scan, are used to determine the characteristic response at different frequencies. We then show that such characteristic functions can be used to correct image distortions present in more complicated constant linear velocity spirals, where the frequency varies within each scan. Through the combined application of constant linear velocity scanning and beam path corrections, spiral scan images are shown to exhibit less scan distortion than conventional raster scan images. The methodology presented here will be useful for in situ STEM imaging at higher temporal resolution and for imaging beam sensitive materials.