Small circular beams of synchrotron radiation (0.1 mm and 0.4 mm in diameter) were used to irradiate ionization chambers of the types commonly used in radiotherapy. By scanning the chamber through the beam and measuring the ionization current, a spatial map of the dosimetric response of the chamber was recorded. The technique is able to distinguish contributions to the large-field ionization current from the chamber walls, central electrode and chamber stem. Scans were recorded for the NE 2571 Farmer chamber, the PTW 30013, IBA FC65-G Farmer-type chambers, the NE 2611A and IBA CC13 thimble chambers, the PTW 31006 and 31014 pinpoint chambers, the PTW Roos and Advanced Markus plane-parallel chambers, and the PTW 23342 thin-window soft x-ray chamber. In all cases, large contributions to the response arise from areas where the incident beam grazes the cavity surfaces. Quantitative as well as qualitative information about the relative chamber response was extracted from the maps, including the relative contribution of the central electrode. Line scans using monochromatic beams show the effect of the photon energy on the chamber response. For Farmer-type chambers, a simple Monte Carlo model was in good agreement with the measured response.