It is a fundamental problem in photon science that at X-ray energies, the oscillation frequency of the electromagnetic field is so high that a detector cannot measure the phase of an interacting object. This ‘phase problem’ also occurs in measurements of an object’s atomic-level properties using recoilless nuclear resonant scattering (NRS) of pulsed synchrotron radiation, which is based on the Mössbauer effect. In this thesis, we demonstrate how to use a ptychographic scanning technique to perform computational phase retrieval for an object in the energy domain via overlapping NRS measurements in the time domain. The technique enables hyperfine spectroscopy of objects at a synchrotron, without the need for a dedicated synchrotron Mössbauer source.
