Electron holography is holography

Holography

Holography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that when an imaging system is placed in the reconstructed beam, an image of the object will be seen even when the object is no longer present...

 with electron waves. Dennis Gabor

Dennis Gabor

Dennis Gabor CBE, FRS was a Hungarian-British electrical engineer and inventor, most notable for inventing holography, for which he later received the 1971 Nobel Prize in Physics....

 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 Muley in 1952; they demonstrated recorded with 60keV electrons holograms of zinc oxide crystals and their reconstructions at about 1nm resolution. In 1955 G. Möllenstedt and H. Düker invented biprism for electrons and recording of electron holograms in off-axis scheme became possible. Cowley has described 20 configurations for electron holography. Usually, high spatial and temporal coherence (i.e. energy spread) of 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 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. 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.

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 (50-1000eV) can be realized in in-line scheme.

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

Aharonov-Bohm effect

The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic field , despite being confined to a region in which both the magnetic field B and electric field E are...

. 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.

The principle of electron holography can also be applied to interference lithography

Interference lithography

Interference lithography is a technique for patterning regular arrays of fine features, without the use of complex optical systems or photomasks.-Basic principle:...

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