Density Matrix Reconstructions in Ultrafast Transmission Electron Microscopy: Uniqueness, Stability, and Convergence Rates

In the recent paper Priebe et al (2017 Nat. Photon. 11 793–7) the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The purpose of this paper is to complement the experimental and algorithmic results in the work mentioned above by a mathematical analysis of the inverse problem concerning uniqueness, stability, and rates of convergence under different types of a priori information.