Removal of phase residues in electron holography

Electron holography provides quantitative phase information regarding the electromagnetic fields and the morphology of micro- to nano-scale samples. A phase image reconstructed numerically from an electron hologram sometimes includes phase residues, i.e. origins of unremovable phase discontinuities, which make it much more difficult to quantitatively analyze local phase values. We developed a method to remove the residues in a phase image by a combination of patching local areas of a hologram and denoising based on machine learning. The small patches for a hologram, which were generated using the spatial frequency information of the own fringe patterns, were pasted at each residue point by an algorithm based on sparse modeling. After successive phase reconstruction, the phase components with no dependency on the vicinity were filtered out by Gaussian process regression. We determined that the phase discontinuities that appeared around phase residues were removed and the phase distributions of an atomic resolution phase image of a Pt nanoparticle were sufficiently restored.