3D Reconstruction of the Magnetic Vector Potential of Magnetic Nanoparticles Using Model Based Vector Field Electron Tomography

Lorentz TEM observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials of the sample. These potentials can be extracted from the electron wave phase shift by separating electrostatic and magnetic phase shifts, followed by 3D tomographic reconstructions. In past, Vector Field Electron Tomography (VFET) was utilized to perform the reconstruction. However, VFET is based on a conventional tomography method called filtered back-projection (FBP). Consequently, the VFET approach tends to produce inconsistencies that are prominent along the edges of the sample. We propose a model-based iterative reconstruction (MBIR) approach to improve the reconstruction of magnetic vector potential, A(r). In the case of scalar tomography, the MBIR method is known to yield better reconstructions than the conventional FBP approach, due to the fact that MBIR can incorporate prior knowledge about the system to be reconstructed. For the same reason, we seek to use the MBIR approach to optimize vector field tomographic reconstructions via incorporation of prior knowledge. We combine a forward model for image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to deduce the vector potential. A detailed study of reconstructions from simulated as well as experimental data sets is provided to establish the superiority of the MBIR approach over the VFET approach.