Electron holography on Fraunhofer diffraction

Interference and interferometry in electron holography

This paper reviews the basics of electron holography as an introduction of the holography part of this special issue in Microscopy. We discuss the general principle of holography and interferometry regarding measurements and analyses of phase distributions, first using the optical holography. Next, we discuss physical phenomena peculiar to electron waves that cannot be realized by light waves and principles of electromagnetic field detection and observation methods. Furthermore, we discuss the interference optical systems of the electron waves and their features, and methods of reconstruction of the phase information from electron holograms, which are essential for realization of practical electron holography. We note that following this review application of electron holography will be discussed in detail in the papers of this special issue.

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.