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electron holography
Electron holography is holography with electron waves. Dennis Gabor invented holography in 1948〔D. Gabor, A new microscopic principle, Nature 4098, 777 (1948).〕 when he tried to improve resolution in electron microscope. The first attempts to perform holography with electron waves were made by Haine and Mulvey in 1952;〔M. E. Haine, T. Mulvey, The formation of the diffraction image with electrons in the Gabor diffraction microscope, J. Opt. Soc. Am. 42, 763 (1952).〕 they recorded holograms of zinc oxide crystals with 60keV electrons, demonstrating reconstructions with approximately 1 nm resolution. In 1955 G. Möllenstedt and H. Düker〔G. Möllenstedt and H. Düker, Beobachtungen und Messungen an Biprisma-Interferenzen mit Elektronenwellen, Zeitschrift für Physik, 145, 377 (1956).〕 invented an electron biprism. thus enabling the recording of electron holograms in off-axis scheme. There are many different possible configurations for electron holography, with more than 20 documented in 1992 by Cowley. 〔J. M. Cowley, Twenty forms of electron holography, Ultramicroscopy 41, 335–348 (1992).〕 Usually, high spatial and temporal coherence (i.e. a low energy spread) of the electron beam are required to perform holographic measurements.
==High-energy electron holography in off-axis scheme==
Electron holography with high-energy electrons (80-200keV) can be realized in a transmission electron microscope (TEM) in an off-axis scheme. Electron beam is split into two parts by very thin positively charged wire. Positive voltage deflects the electron waves so that they overlap and produce an interference pattern of equidistantly spaced fringes.
Reconstruction of off-axis holograms is done numerically and it consists of two mathematical transformations.〔M. Lehmann, H. Lichte, Tutorial on off-axis electron holography, Microsc. Microanal. 8(6), 447–466 (2002).〕 First, a Fourier transform of the hologram is performed. The resulting complex image consists of the autocorrelation (center band) and two mutually conjugated sidebands. Only one side band is selected by applying a low-pass filter (round mask) centered on the chosen side-band. The central band and the twin side-band are both set to zero. Next, the selected side-band is re-positioned to the center of the complex image and the backward Fourier-transform is applied. The resulting image in the object domain is complex-valued, and thus, the amplitude and phase distributions of the object function are reconstructed.
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