  We compare classical versus quantum electron transport in recently
investigated magnetic focusing devices [S. Bhandari et al., Nano Lett. 16, 1690
(2016)] exposed to the perturbing potential of a scanning gate microscope
(SGM). Using the Landauer-B\"uttiker formalism for a multi-terminal device, we
calculate resistance maps that are obtained as the SGM tip is scanned over the
sample. There are three unique regimes in which the scanning tip can operate
(focusing, repelling, and mixed regime) which are investigated. Tip interacts
mostly with electrons with cyclotron trajectories passing directly underneath
it, leaving a trail of modified current density behind it. Other (indirect)
trajectories become relevant when the tip is placed near the edges of the
sample, and current is scattered between the tip and the edge. We also discuss
possible explanations for spatial asymmetry of experimentally measured
resistance maps, and connect it with specific configurations of the measuring
probes.
