From Springer Nature via Jisc Publications RouterHistory: received 2021-03-05, registration 2021-11-04, accepted 2021-11-04, pub-electronic 2021-11-18, online 2021-11-18, collection 2021-12Publication status: PublishedFunder: RCUK | Engineering and Physical Sciences Research Council (EPSRC); doi: https://doi.org/10.13039/501100000266; Grant(s): EP/L015110/1, EP/R031924/1Funder: EC | Horizon 2020 Framework Programme (EU Framework Programme for Research and Innovation H2020); doi: https://doi.org/10.13039/100010661; Grant(s): 730872, ERC-714193-QUESTDO, 730872Abstract: Quasiparticle interference (QPI) imaging is well established to study the low-energy electronic structure in strongly correlated electron materials with unrivalled energy resolution. Yet, being a surface-sensitive technique, the interpretation of QPI only works well for anisotropic materials, where the dispersion in the direction perpendicular to the surface can be neglected and the quasiparticle interference is dominated by a quasi-2D electronic structure. Here, we explore QPI imaging of galena, a material with an electronic structure that does not exhibit pronounced anisotropy. We find that the quasiparticle interference signal is dominated by scattering vectors which are parallel to the surface plane however originate from bias-dependent cuts of the 3D electronic structure. We develop a formalism for the theoretical description of the QPI signal and demonstrate how this quasiparticle tomography can be used to obtain information about the 3D electronic structure and orbital character of the bands