Electron holography is

holography Holography is a technique that allows a wavefront to be recorded and later reconstructed. It is best known as a method of generating three-dimensional images, and has a wide range of other uses, including data storage, microscopy, and interfe ...

with

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

matter wave Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...

s. It was invented by

Dennis Gabor Dennis Gabor ( ; ; 5 June 1900 – 9 February 1979) was a Hungarian-British physicist who received the Nobel Prize in Physics in 1971 for his invention of holography. He obtained British citizenship in 1946 and spent most of his life in Engla ...

in 1948 when he tried to improve

image resolution Image resolution is the level of detail of an image. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies ...

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 Zinc oxide is an inorganic compound with the Chemical formula, formula . It is a white powder which is insoluble in water. ZnO is used as an additive in numerous materials and products including cosmetics, Zinc metabolism, food supplements, rubbe ...

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

hologram Holography is a technique that allows a wavefront to be recorded and later reconstructed. It is best known as a method of generating three-dimensional images, and has a wide range of other uses, including data storage, microscopy, and interf ...

s is done numerically and it consists of two mathematical transformations. First, a

Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

of the hologram is performed. The resulting complex image consists of the

autocorrelation Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a random variable at differe ...

(center band) and two mutually conjugated sidebands. Only one side band is selected by applying a

low-pass filter A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filt ...

(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

The original holographic scheme by Dennis Gabor is inline scheme, which means that reference and object wave share the same

optical axis An optical axis is an imaginary line that passes through the geometrical center of an optical system such as a camera lens, microscope or telescopic sight. Lens elements often have rotational symmetry about the axis. The optical axis defines ...

. 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 The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanics, quantum-mechanical phenomenon in which an electric charge, electrically charged point particle, particle is affected by an elect ...

. 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 Interference lithography (or holographic lithography) is a technique that uses coherent light (such as light from a laser) for patterning regular arrays of fine features without the use of complex optics, optical systems or photomasks. Basic prin ...

References

{{Authority control Electron microscopy techniques Holography