Current approaches to reconstruction in atom probe tomography produce results that exhibit substantial distortions throughout the analysis depth. This is largely because of the need to apply a multitude of assumptions when estimating the evolution of the tip shape, and other pseudo-empirical reconstruction factors, which vary both across the face of the tip and throughout the analysis depth. We introduce a new crystallography-mediated reconstruction to improve the spatial accuracy and dramatically reduce these in-depth variations. To achieve this, we developed a barycentric transform to directly relate atomic positions in detector space to real space. This is mediated by novel crystallographic analysis techniques, including: (1) calculating the orientation of a crystal directly from the field evaporation map, (2) tracking pole locations throughout the evaporation sequence, and (3) accounting for the evolving tip radius in a manner that removes the dependence on the geometric field factor. By improving the in-depth spatial accuracy of the atom probe reconstruction, a greater accuracy of the atomic neighborhood relationships is available. This is critical in modern materials science and engineering, where an understanding of the solid solution architecture, precipitate dispersions, and descriptions of the interfaces between phases or grains are key inputs to microstructure–property relationships.