Electron holography is

holography Holography is a technique that enables a wavefront to be recorded and later re-constructed. Holography is best known as a method of generating real three-dimensional images, but it also has a wide range of other applications. In principle, i ...

with electron waves.

Dennis Gabor Dennis Gabor ( ; hu, Gábor Dénes, ; 5 June 1900 – 9 February 1979) was a Hungarian-British electrical engineer and physicist, most notable for inventing holography, for which he later received the 1971 Nobel Prize in Physics. He obtained ...

invented holography in 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; they recorded holograms of zinc oxide crystals with 60 keV electrons, demonstrating reconstructions with approximately 1 nm resolution. In 1955, G. Möllenstedt and H. Düker 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. 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 (80-200 keV) can be realized in a

transmission electron microscope Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a gr ...

(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. Off axis in TEM

Reconstruction of off-axis holograms is done numerically and it consists of two mathematical transformations. First, a Fourier transform of the

hologram Holography is a technique that enables a wavefront to be recorded and later re-constructed. Holography is best known as a method of generating real three-dimensional images, but it also has a wide range of other applications. In principle, i ...

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.

Electron holography in in-line scheme

Original holographic scheme by Dennis Gabor is inline scheme, which means that reference and object wave share the same optical axis. This scheme is also called ''point projection holography''. An object is placed into divergent electron beam, part of the wave is scattered by the object (object wave) and it interferes with the unscattered wave (reference wave) in detector plane. The spatial coherence in in-line scheme is defined by the size of the electron source. Holography with low-energy electrons (50-1000 eV) can be realized in in-line scheme. InlineHolography

Electromagnetic fields

It is important to shield the interferometric system from electromagnetic fields, as they can induce unwanted phase-shifts due to the Aharonov–Bohm effect. Static fields will result in a fixed shift of the interference pattern. It is clear every component and sample must be properly grounded and shielded from outside noise.

Applications

Electron holography is commonly used to study electric and magnetic fields in thin films, as magnetic and electric fields can shift the phase of the interfering wave passing through the sample.R. E. Dunin-Borkowski et al., Micros. Res. and Tech. 64, 390 (2004). The principle of electron holography can also be applied to interference lithography.

References

{{Authority control Electron microscopy techniques Holography