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@PHDTHESIS{Caron:851773,
      author       = {Caron, Jan},
      title        = {{M}odel-based reconstruction of magnetisation distributions
                      in nanostructures from electron optical phase images},
      volume       = {177},
      school       = {RWTH Aachen},
      type         = {Dr},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {FZJ-2018-05288},
      isbn         = {978-3-95806-346-4},
      series       = {Schriften des Forschungszentrums Jülich. Reihe
                      Schlüsseltechnologien / Key Technologies},
      pages        = {XXI, 183 S.},
      year         = {2018},
      note         = {RWTH Aachen, Diss., 2017},
      abstract     = {Off-axis electron holography is a powerful technique for
                      recording the phase shift of high-energy electron waves that
                      pass through a thin specimen in the transmission electron
                      microscope. Information about the electromagnetic field in
                      and around the specimen is encoded in the phase, according
                      to the Aharonov-Bohm equations. In this thesis, a
                      model-based iterative reconstruction (MBIR) algorithm was
                      developed, which allows the retrieval of the projected
                      in-plane magnetisation distribution from individual magnetic
                      phase images or a complete tomographic reconstruction of the
                      three-dimensional magnetisation distribution from two
                      ideally orthogonal tilt series of phase images. To guarantee
                      efficient model-based reconstructions, an optimised forward
                      model implementation for fast and accurate simulations of
                      magnetic phase images from a given magnetisation
                      distribution was derived. This new approach utilises sparse
                      matrix multiplications and fast convolutions in Fourier
                      space with pre-calculated convolution kernels based on known
                      analytic solutions for the phase contribution of simple
                      geometries. As the inverse problem of retrieving the
                      magnetisation distribution is ill-posed, regularisation
                      techniques had to be applied, that guarantee the existence
                      of a solution and its uniqueness. Modelled after the
                      minimisation of the exchange energy, Tikhonov regularisation
                      of first order is used to apply smoothness constraints to
                      the solution of the reconstruction. In addition, $\textit{a
                      priori}$ knowledge about the position and size of the
                      magnetised regions is utilised in the form of a
                      three-dimensional mask to significantly reduce the number of
                      retrieval targets. Optimal estimation diagnostic tools were
                      adapted for the assessment of the quality of the
                      reconstruction results. The MBIR algorithm was successfully
                      applied to simulated phase images for the reconstruction of
                      two-and three-dimensional magnetisation distributions.
                      External sources of magnetisation outside the field of view
                      were addressed by linear phase ramp and offset fits, as well
                      as with buffer pixels that increase the number of degrees of
                      freedom for the MBIR algorithm. A method to account for the
                      perturbed reference wave of the electron hologram was
                      provided and other artefacts in the magnetic phase images
                      were tackled by excluding them from the reconstruction
                      process. In three dimensions, studies about the influence of
                      the maximum tilt angle and angular sampling were performed.
                      The MBIR algorithm was successfully used to reconstruct a
                      projected in-plane magnetisation distribution from a
                      magnetic phase image of a lithographically patterned cobalt
                      structure. Finally, a three-dimensional magnetisation
                      distribution was reconstructed from a set of simulated phase
                      images with limited angular range under the influence of
                      Gaussian noise and random phase offsets and ramps, proving
                      the feasibility of the algorithm for future
                      three-dimensional experimental studies.},
      cin          = {ER-C-2},
      cid          = {I:(DE-Juel1)ER-C-2-20170209},
      pnm          = {899 - ohne Topic (POF3-899)},
      pid          = {G:(DE-HGF)POF3-899},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      url          = {https://juser.fz-juelich.de/record/851773},
}