SeriesInformation ; Physical review / B covering condensed matter and materials physics 93(13), 134116(2016). doi:10.1103/PhysRevB.93.134116 ; Abstract ; We introduce an algorithm for the reconstruction of the complex transmission function of a specimen using segmented detectors in scanning transmission electron microscopy geometry. The phase of the transmission function can be related to magnetic and electric fields within the specimen and is sensitive to lighter elements. The technique is demonstrated for simulated data and also using experimental datasets taken from a MoS$_2$ monolayer and a SrTiO$_3$ crystal. We present an extension to the algorithm to account for uncertainties in the illuminating probe. The algorithm can be implemented using fast Fourier transforms, and this provides the possibility of reconstructing specimen transmission functions in real time. ; Other ; Published by APS, Woodbury, NY