Phase-space foundations of electron holography

We present a unified formalism for describing various forms of electron holography in quantum mechanical phase space including their extensions to quantum-state reconstructions. The phase-space perspective allows for taking into account partial coherence as well as the quantum mechanical detection process typically hampering the unique reconstruction of a wave function. We elaborate on the limitations imposed by the electron optical elements of the transmission electron microscope as well as the scattering at the target. The results provide the basis for vastly extending the scope of electron holographic techniques towards analyzing partially coherent signals such as inelastically scattered electrons or electron pulses used in ultrafast transmission electron microscopy.