  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
and can be interpreted ignoring the dispersion in the direction normal to the
surface. 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.
