The computational conversion of the ion sequence data, as obtained from a position sensitive detector, to a three-dimensional visualisation of atomic types, is termed "reconstruction". Reconstruction algorithms are typically geometrically based, and have several literature formulations. Most models for reconstruction assume that the tip is a spherical object, and use empirical corrections to stereographic projection to convert detector positions back to a 2D surface embedded in 3D space, R3. By sweeping this surface through R3 as a function of the ion sequence input data, such as via ion-ordering, a volume is generated onto which positions the 2D detector positions can be computed and placed three-dimensional space.