A three-dimensional grid (10) is used as a phantom for mapping geometric distortion in magnetic resonance imaging (MRI) apparatus. This phantom provides an array of densely distributed control points in three-dimensional space. These points are each defined by three orthogonal planes. In the phantom image, the planes are determined by detecting boundary surfaces between portions of the phantom and its surrounding medium, enabling the positions of the control points to be measured to sub-voxel accuracy. The mapped distortion can then be used to automatically correct images produced by the MRI apparatus.