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.