A sample inspection system (100) includes an X-ray emitter, a collimator (170) and a first energy resolving detector (180) arranged along a symmetry axis (105). The X-ray emitter generates at least one focused conical shell beam (150) of X-ray radiation comprised of X-ray photons that propagate through a focal point on the symmetry axis downstream of the X-ray emitter. The collimator (170) has one or more channels, each channel being adapted to receive diffracted or scattered radiation propagating either along the symmetry axis, or parallel with the symmetry axis, or both along and parallel with the symmetry axis (105). Upon incidence of the conical shell beam (150) onto a sample (106) the first energy resolving detector (180) detects radiation diffracted or scattered by the sample (106) via the collimator (170).