  We propose algorithms based on an optimisation method for inverse multislice
ptychography in, e.g. electron microscopy. The multislice method is widely used
to model the interaction between relativistic electrons and thick specimens.
Since only the intensity of diffraction patterns can be recorded, the challenge
in applying inverse multislice ptychography is to uniquely reconstruct the
electrostatic potential in each slice up to some ambiguities. In this
conceptual study, we show that a unique separation of atomic layers for
simulated data is possible when considering a low acceleration voltage. We also
introduce an adaptation for estimating the illuminating probe. For the sake of
practical application, we finally present slice reconstructions using
experimental 4D scanning transmission electron microscopy (STEM) data.
