$fraunhofer single slit diffraction$ $fraunhofer single slit diffraction$

In this paper, we propose electron holography on Fraunhofer diffraction utilizing an asymmetric double slit created by a biprism from a symmetric double slit placed at the specimen position. In light optics, on the other hand, several experimental and theoretical studies have been performed using microwaves on the wave fields in the reciprocal space, i.e. Few trials using electron microscopes have been reported except for electron holography approach for vortex beams. In particular, the phase distribution in the reciprocal space is difficult to detect directly even by using holography technique because intensity of the object wave in diffraction patterns is a few orders of magnitudes larger than that of the diffracted waves and also because no appropriate reference waves exist in the reciprocal space. In electron microscopy, the amplitude and phase distributions of wave fields in the reciprocal space, such as diffraction planes, have been extensively discussed in phase microscopy and vortex beam microscopy.

$fraunhofer single slit diffraction$

In wave optics, this has already been performed theoretically as well as experimentally. Precise investigation of amplitude and phase distributions of wave fields in the reciprocal space is necessary for these purposes. Understanding of wave propagation between the real space and the reciprocal space is very important from the optical point of view, especially in image reconstructions in the real space from data in the reciprocal space, and in phase retrieval for data in the real and reciprocal spaces. These developments are due to advancement of the following technologies: highly sensitive imaging technologies based on direct electron detection cameras, image-processing technologies for multiple and large-scale image data, and iteration algorisms for image data analysis. Recently several electron imaging methods have been developed by utilizing not only the real space but also the reciprocal space, such as diffractive imaging and ptychography. We hope that the developed Fraunhofer electron holography can be extended to a direct phase detection method in the reciprocal space. 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. Amplitude and phase distributions of the Fraunhofer diffraction wave were reconstructed from the hologram by the Fourier transform reconstruction method. 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. 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. Electron holography in Fraunhofer region was realized by using an asymmetric double slit.

$fraunhofer single slit diffraction$

Fraunhofer single slit diffraction