Inverse problems-based self-calibrated reconstruction for tomographic diffractive microscopy

In this work we propose an inverse problems based iterative reconstruction method for tomographic diffractive microscopy, involving measurements in off-axis configuration. More precisely, we propose a strategy that aims to eliminate reconstruction errors that can be caused by perturbations in the illumination wave of the reference arm. Our original contribution is to build the inverse problem considering as unknowns both the targeted 3D sample map and the perturbation map, that are jointly reconstructed and unmixed during the iterative process. This self-calibration process is rendered possible by the multiplicity of sample observations from multiple views, where the reference perturbed background remains invariant. We validate the feasibility of our approach on reconstructions from simulated data under different experimental conditions.