ions will be greatly magnified. This magnification is sufficient to observe field variations due to individual atoms, thus allowing in field ion and field evaporation modes for the imaging of single atoms. The standard projection model for the atom probe is an emitter geometry that is based upon a revolution of a conic section, such as a sphere, hyperboloid or paraboloid. For these tip models, solutions to the field may be approximated or obtained analytically. The magnification for a spherical emitter is inversely proportional to the radius of the tip, given a projection directly onto a spherical screen, the following equation can be obtained geometrically. Where rscreen is the radius of the detection screen from the tip centre, and rtip the tip radius. A practical tip to screen distances may range from several centimeters to several meters, with increased detector area required at larger to subtend the same field of view. Practically speaking, the usable magnification will be limited by several effects, such as lateral vibration of the atoms prior to evaporation. Whilst the magnification of both the field ion and atom probe microscopes is extremely high, the exact magnification is dependent upon conditions specific to the examined specimen, so unlike for conventional electron microscopes, there is often little direct control on magnification, and furthermore, obtained images may have strongly variable magnifications due to fluctuations in the shape of the electric field at the surface. Reconstruction 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. Typically the sweep takes the simple form of advancement of the surface, such that the surface is expanded in a symmetric manner about its advancement axis, with the advancement rate set by a volume attributed to each ion detected and identified. This causes the final reconstructed volume to assume a rounded-conical shape, similar to a badminton shuttlecock. The detected