Sources and effects of errors in vector field electron tomography

Abstract

Vector field electron tomography is a relatively new technique for quantitative three-dimensional imaging, combining phase retrieval with vector tomography to reconstruct electromagnetic fields, potentials, and sources, from transmission electron micrographs. Vector field electron tomography reconstructs electromagnetic vector fields (i.e., the vector potential, magnetic induction field, and current density) associated with magnetic nanomaterials, such as magnetic recording media, spintronics devices, grain boundaries in hard magnets, and magnetic particles for biomedical applications. Although there is a range of techniques for characterising magnetic nanomaterials, such as Kerr microscopy, magnetic force microscopy, and Lorentz microscopy, these techniques only provide projections or surface components of the vector field. Vector field electron tomography takes projections of the potential obtained using electron holography, acquired over two or more tilt series, and reconstructs complete vector fields associated with the particle. In the present work, we consider the reconstruction of the vector potential of magnetite nanoparticles, a material of significant interest in the study of nanomagnetism. This work addresses errors, both in the recorded micrographs and those incurred during the reconstruction process, and examines the effect that these errors have on the accuracy of the reconstructed vector field. We use simulated micrographs in order to have complete control over the nature of the errors, and to be able to precisely quantify the accuracy of the reconstruction. In this thesis, we use a phase retrieval algorithm based on the transport-of-intensity equation, and reconstruct the vector potential of the simulated magnetite specimen using two tilt series and a filtered backprojection algorithm. We use three different root-mean-square error metrics to determine the accuracy of the reconstruction in terms of the total vector difference, the difference in magnitude, and the difference in direction. We then compare these results with analytical predictions. We derive expressions to predict the error in a vector field electron tomography reconstruction as functions of image noise and initial specimen orientation, and test the applicability of these expressions under a range of conditions. There is strong, quantitative agreement between our analytical and numerical results regarding the effects of image noise. Our work on orientation-dependent errors provides a semi-quantitative analysis of the total root-mean-square error as a function of magnetic moment orientation. We also present a method for reducing orientation-dependent errors by averaging reconstructions from multiple pairs of tilt series. We find that the reconstruction of the magnetic vector potential of uniformly magnetised specimens can be significantly improved by distributing the acquired images over additional tilt series.