We study scanning gate microscopy (SGM) in open quantum rings obtained from buried semiconductor InGaAs/InAlAs heterostructures. By performing a theoretical analysis based on the Keldysh-Green function approach we interpret the radial fringes observed in experiments as the effect of randomly distributed charged defects. We associate SGM conductance images with the local density of states (LDOS) of the system. We show that such an association cannot be made with the current density distribution. By varying an external magnetic field we are able to reproduce recursive quasi-classical orbits in LDOS and conductance images, which bear the same periodicity as the Aharonov-Bohm effect.