Model-based reconstruction of magnetisation distributions in nanostructures from electron optical phase images
Year: 2018
Type: dissertation
Abstract: Off-axis electron holography is a powerful technique for recording the phase shift ofhigh-energy electron waves that pass through a thin specimen in the transmissionelectron microscope. Information about the electromagnetic field in and around thespecimen is encoded in the phase, according to the Aharonov-Bohm equations. Inthis thesis, a model-based iterative reconstruction (MBIR) algorithm was developed,which allows the retrieval of the projected in-plane magnetisation distribution fromindividual magnetic phase images or a complete tomographic reconstruction of thethree-dimensional magnetisation distribution from two ideally orthogonal tilt seriesof phase images. To guarantee efficient model-based reconstructions, an optimisedforward model implementation for fast and accurate simulations of magnetic phaseimages from a given magnetisation distribution was derived. This new approachutilises sparse matrix multiplications and fast convolutions in Fourier space withpre-calculated convolution kernels based on known analytic solutions for the phasecontribution of simple geometries. As the inverse problem of retrieving the magnetisationdistribution is ill-posed, regularisation techniques had to be applied, thatguarantee the existence of a solution and its uniqueness. Modelled after the minimisationof the exchange energy, Tikhonov regularisation of first order is used to applysmoothness constraints to the solution of the reconstruction. In addition, a prioriknowledge about the position and size of the magnetised regions is utilised in theform of a three-dimensional mask to significantly reduce the number of retrievaltargets. Optimal estimation diagnostic tools were adapted for the assessment of thequality of the reconstruction results. The MBIR algorithm was successfully appliedto simulated phase images for the reconstruction of two-and three-dimensional magnetisationdistributions. External sources of magnetisation outside the field of viewwere addressed by linear phase ramp and offset fits, as well as with buffer pixels thatincrease the number of degrees of freedom for the MBIR algorithm. A method toaccount for the perturbed reference wave of the electron hologram was provided andother artefacts in the magnetic phase images were tackled by excluding them fromthe reconstruction process. In three dimensions, studies about the influence of themaximum tilt angle and angular sampling were performed. The MBIR algorithmwas successfully used to reconstruct a projected in-plane magnetisation distributionfrom a magnetic phase image of a lithographically patterned cobalt structure. Finally,a three-dimensional magnetisation distribution was reconstructed from a set ofsimulated phase images with limited angular range under the influence of Gaussiannoise and random phase offsets and ramps, proving the feasibility of the algorithmfor future three-dimensional experimental studies.
Source: JuSER (Forschungszentrum Jülich)
Author: Jan Caron
Language: English
Subfield: Structural Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W2893594872