Lensless fourier transform electron holography applied to vortex beam analysis.

Lensless Fourier transform holography has been developed. By treating Bragg diffraction waves as object waves and a transmitted spherical wave as a reference wave, these two waves are interfered and recorded as holograms away from the reciprocal plane. In this method, reconstruction of holograms requires only one Fourier transform. Application of this method to analyze vortex beams worked well and their amplitude and phase distributions were obtained on the reciprocal plane. By combining the conventional holography with the developed lensless Fourier transform holography, we can reconstruct and analyze electron waves from the real to reciprocal space continuously.

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.

Illumination semiangle of 10-9 rad achieved in a 1.2-MV atomic resolution holography transmission electron microscope.

The coherency of a 1.2-MV transmission electron microscope was evaluated through illumination semiangles calculated from lengths over which Fresnel fringes can be observed. These lengths were determined from the diameters of circular holes fully filled with Fresnel fringes, i.e. this method allows lengths to be accurately measured even if micrographs are subjected to distortions. The smallest illumination semiangle of 4.0 × 10-9 rad was obtained for a circular hole with a diameter of 191 µm. In addition, electron beam brightness was estimated to be approximately 3 × 1014 A/m2·sr from the obtained illumination semiangle values and current densities. The results provide us with essential information that can be referred to in future electron holography studies aimed at detecting weak electromagnetic fields in materials.

Interference experiment with asymmetric double slit by using 1.2-MV field emission transmission electron microscope.

Advanced electron microscopy technologies have made it possible to perform precise double-slit interference experiments. We used a 1.2-MV field emission electron microscope providing coherent electron waves and a direct detection camera system enabling single-electron detections at a sub-second exposure time. We developed a method to perform the interference experiment by using an asymmetric double-slit fabricated by a focused ion beam instrument and by operating the microscope under a "pre-Fraunhofer" condition, different from the Fraunhofer condition of conventional double-slit experiments. Here, pre-Fraunhofer condition means that each single-slit observation was performed under the Fraunhofer condition, while the double-slit observations were performed under the Fresnel condition. The interference experiments with each single slit and with the asymmetric double slit were carried out under two different electron dose conditions: high-dose for calculation of electron probability distribution and low-dose for each single electron distribution. Finally, we exemplified the distribution of single electrons by color-coding according to the above three types of experiments as a composite image.