Phase retrieval using through-focus images in Lorentz transmission electron microscopy

Electron holography for observing magnetic bubbles and stripe-shaped domains in magnetic fields

An electron holography optical system was developed for relatively high magnetic fields up to 500 mT. The objective lens worked as a magnetic field generator for the specimen and the first intermediate lens worked for imaging as one of the pair lens composed of the objective lens. Specimen images were first formed on the object plane of the second intermediate lens. Electron biprism for conventional holography was installed under the second intermediate lens. Reconstruction of phase distributions was performed by the Fourier transform method and the vector maps were used to clarify small phase modulations. By using the developed system, magnetic characteristics of hexaferrite magnets (BaFe_12-x-δSc_xMg_δO₁₉), such as magnetic bubbles and stripe-shaped magnetic domains, were observed at smaller than 200 mT. Their magnetization structures and their interactions are demonstrated with the experimental results.

Transport of intensity equation method and its applications

A phase retrieval technique based on a transport of intensity equation (TIE) is one of the defocus series reconstruction techniques in microscopy. Since it does not require any dedicated devices like a biprism, and only three defocus images are enough to retrieve phase information, it has been applied to observe magnetic fields, magnetic domains, electrostatic potentials and strains. It is also used to improve image resolution by correcting spherical aberration. This technique is simple and easy to use, but some artifacts often appear in the retrieved phase map. One should pay careful attention to the experimental conditions and the algorithms and boundary conditions used to solve the TIE. This paper reviews the principle of the TIE method, the algorithms used to solve it and application results in materials science.

Electron holography on Fraunhofer diffraction

Electron holography in Fraunhofer region was realized by using an asymmetric double slit. A Fraunhofer diffraction wave from a wider slit worked as an objective wave interfered with a plane wave from a narrower slit as a reference wave under the pre-Fraunhofer condition and recorded as a hologram. Here, the pre-Fraunhofer condition means that the following conditions are simultaneously satisfied: single-slit observations are performed under the Fraunhofer condition and the double-slit observations are performed under the Fresnel condition. Amplitude and phase distributions of the Fraunhofer diffraction wave were reconstructed from the hologram by the Fourier transform reconstruction method. The reconstructed amplitude and phase images corresponded to Fraunhofer diffraction patterns; in particular, the phase steps of π at each band pattern in the phase image were confirmed. We hope that the developed Fraunhofer electron holography can be extended to a direct phase detection method in the reciprocal space.