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Images generated by a transmission electron microscope (TEM) are blurred byaberrations from the objective lens and can be difficult to interpretcorrectly. One possible solution to this problem is to reconstruct theso-called exit wave, i.e. the electron wave in the microscope right before itpasses the objective lens, from a series of TEM images acquired with varyingfocus. While the forward model of simulating a TEM image from a given exit waveis known and easy to evaluate, it is in general not possible to reconstruct theexit wave from a series of images analytically. The corresponding inverseproblem can be formulated as a minimization problem, which is done in the wellknown MAL and MIMAP methods. We propose a generalization of these methods byperforming the exit wave reconstruction and the registration of the imageseries simultaneously. We show that our objective functional is not convex withrespect to the exit wave, which also carries over to the MAL and MIMAPfunctionals. The main result is the existence of minimizers of our objectivefunctional. These results are based on the properties of a generalization ofthe cross-correlation. Finally, the applicability of our method is verifiedwith a numerical experiment on simulated input data.

A least-squares functional for joint exit wave reconstruction and image registration