Electron holography

Last updated

Electron holography is holography with electron matter waves. It was invented by Dennis Gabor in 1948 when he tried to improve image resolution in electron microscope. [1] The first attempts to perform holography with electron waves were made by Haine and Mulvey in 1952; [2] 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 [3] 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. [4] Usually, high spatial and temporal coherence (i.e. a low energy spread) of the electron beam are required to perform holographic measurements.

Contents

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 (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.

An illustration to off-axis electron holography in transmission electron microscope. Off axis in TEM.jpg
An illustration to off-axis electron holography in transmission electron microscope.

Reconstruction of off-axis holograms is done numerically and it consists of two mathematical transformations. [5] 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

The 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. [6]

Inline electron holography scheme. InlineHolography.jpg
Inline electron holography 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. 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

At this image one can see the electron hologram of a latex sphere on a carbon coating with gold particles (black dots), at the lower part of the image is vacuum. The biprism is approx above the vacuum edge; parallel to this edge one can see the phase planes of the interferogram, which is part of the image and from which the phase information can be extracted. Elektronenhologramm.jpg
At this image one can see the electron hologram of a latex sphere on a carbon coating with gold particles (black dots), at the lower part of the image is vacuum. The biprism is approx above the vacuum edge; parallel to this edge one can see the phase planes of the interferogram, which is part of the image and from which the phase information can be extracted.

Electron holography is commonly used to study electric and magnetic fields in thin films, [7] [8] as magnetic and electric fields can shift the phase of the interfering wave passing through the sample. [9]

The principle of electron holography can also be applied to interference lithography. [10]

Related Research Articles

<span class="mw-page-title-main">Microscopy</span> Viewing of objects which are too small to be seen with the naked eye

Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye. There are three well-known branches of microscopy: optical, electron, and scanning probe microscopy, along with the emerging field of X-ray microscopy.

<span class="mw-page-title-main">Holography</span> Recording to reproduce a three-dimensional light field

Holography is a technique that enables 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 interferometry. In principle, it is possible to make a hologram for any type of wave.

<span class="mw-page-title-main">Electron diffraction</span> Bending of electron beams due to electrostatic interactions with matter

Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes.

<span class="mw-page-title-main">High-resolution transmission electron microscopy</span>

High-resolution transmission electron microscopy is an imaging mode of specialized transmission electron microscopes that allows for direct imaging of the atomic structure of samples. It is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp2-bonded carbon. While this term is often also used to refer to high resolution scanning transmission electron microscopy, mostly in high angle annular dark field mode, this article describes mainly the imaging of an object by recording the two-dimensional spatial wave amplitude distribution in the image plane, similar to a "classic" light microscope. For disambiguation, the technique is also often referred to as phase contrast transmission electron microscopy, although this term is less appropriate. At present, the highest point resolution realised in high resolution transmission electron microscopy is around 0.5 ångströms (0.050 nm). At these small scales, individual atoms of a crystal and defects can be resolved. For 3-dimensional crystals, it is necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron tomography.

Holographic interferometry (HI) is a technique which enables static and dynamic displacements of objects with optically rough surfaces to be measured to optical interferometric precision. These measurements can be applied to stress, strain and vibration analysis, as well as to non-destructive testing and radiation dosimetry. It can also be used to detect optical path length variations in transparent media, which enables, for example, fluid flow to be visualised and analyzed. It can also be used to generate contours representing the form of the surface.

Digital holography refers to the acquisition and processing of holograms with a digital sensor array, typically a CCD camera or a similar device. Image rendering, or reconstruction of object data is performed numerically from digitized interferograms. Digital holography offers a means of measuring optical phase data and typically delivers three-dimensional surface or optical thickness images. Several recording and processing schemes have been developed to assess optical wave characteristics such as amplitude, phase, and polarization state, which make digital holography a very powerful method for metrology applications .

Computer-generated holography (CGH) is a technique that uses computer algorithms to generate holograms. It involves generating holographic interference patterns. A computer-generated hologram can be displayed on a dynamic holographic display, or it can be printed onto a mask or film using lithography. When a hologram is printed onto a mask or film, it is then illuminated by a coherent light source to display the holographic images.

<span class="mw-page-title-main">Low-energy electron microscopy</span>

Low-energy electron microscopy, or LEEM, is an analytical surface science technique used to image atomically clean surfaces, atom-surface interactions, and thin (crystalline) films. In LEEM, high-energy electrons are emitted from an electron gun, focused using a set of condenser optics, and sent through a magnetic beam deflector. The “fast” electrons travel through an objective lens and begin decelerating to low energies near the sample surface because the sample is held at a potential near that of the gun. The low-energy electrons are now termed “surface-sensitive” and the near-surface sampling depth can be varied by tuning the energy of the incident electrons. The low-energy elastically backscattered electrons travel back through the objective lens, reaccelerate to the gun voltage, and pass through the beam separator again. However, now the electrons travel away from the condenser optics and into the projector lenses. Imaging of the back focal plane of the objective lens into the object plane of the projector lens produces a diffraction pattern at the imaging plane and recorded in a number of different ways. The intensity distribution of the diffraction pattern will depend on the periodicity at the sample surface and is a direct result of the wave nature of the electrons. One can produce individual images of the diffraction pattern spot intensities by turning off the intermediate lens and inserting a contrast aperture in the back focal plane of the objective lens, thus allowing for real-time observations of dynamic processes at surfaces. Such phenomena include : tomography, phase transitions, adsorption, reaction, segregation, thin film growth, etching, strain relief, sublimation, and magnetic microstructure. These investigations are only possible because of the accessibility of the sample; allowing for a wide variety of in situ studies over a wide temperature range. LEEM was invented by Ernst Bauer in 1962; however, not fully developed until 1985.

A holographic display is a type of 3D display that utilizes light diffraction to display a three-dimensional image to the viewer. Holographic displays are distinguished from other forms of 3D displays in that they do not require the viewer to wear any special glasses or use external equipment to be able to see the image, and do not cause the vergence-accommodation conflict.

<span class="mw-page-title-main">Ptychography</span>

Ptychography is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function moving laterally by a known amount with respect to another constant function. The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" into one another as shown in the figure.

Electronic quantum holography is an information storage technology which can encode and read out data at unprecedented density storing as much as 35 bits per electron.

<span class="mw-page-title-main">Contrast transfer function</span>

The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.

<span class="mw-page-title-main">Digital holographic microscopy</span>

Digital holographic microscopy (DHM) is digital holography applied to microscopy. Digital holographic microscopy distinguishes itself from other microscopy methods by not recording the projected image of the object. Instead, the light wave front information originating from the object is digitally recorded as a hologram, from which a computer calculates the object image by using a numerical reconstruction algorithm. The image forming lens in traditional microscopy is thus replaced by a computer algorithm. Other closely related microscopy methods to digital holographic microscopy are interferometric microscopy, optical coherence tomography and diffraction phase microscopy. Common to all methods is the use of a reference wave front to obtain amplitude (intensity) and phase information. The information is recorded on a digital image sensor or by a photodetector from which an image of the object is created (reconstructed) by a computer. In traditional microscopy, which do not use a reference wave front, only intensity information is recorded and essential information about the object is lost.

Electron magnetic circular dichroism (EMCD) is the EELS equivalent of XMCD.

A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.

Holographic interference microscopy (HIM) is holographic interferometry applied for microscopy for visualization of phase micro-objects. Phase micro-objects are invisible because they do not change intensity of light, they insert only invisible phase shifts. The holographic interference microscopy distinguishes itself from other microscopy methods by using a hologram and the interference for converting invisible phase shifts into intensity changes.

<span class="mw-page-title-main">Quantitative phase-contrast microscopy</span>

Quantitative phase contrast microscopy or quantitative phase imaging are the collective names for a group of microscopy methods that quantify the phase shift that occurs when light waves pass through a more optically dense object.

The time-domain counterpart of spatial holography is called time-domain holography. In other words, the principles of spatial holography is surveyed in time domain. Time-domain holography was inspired by the theory known as space-time duality which was introduced by Brian H. Kolner in 1994.

Joanne Etheridge is an Australian physicist. She is Director of the Monash Centre for Electron Microscopy and Professor in the Department of Materials Science and Engineering at Monash University.

4D scanning transmission electron microscopy is a subset of scanning transmission electron microscopy (STEM) which utilizes a pixelated electron detector to capture a convergent beam electron diffraction (CBED) pattern at each scan location. This technique captures a 2 dimensional reciprocal space image associated with each scan point as the beam rasters across a 2 dimensional region in real space, hence the name 4D STEM. Its development was enabled by evolution in STEM detectors and improvements computational power. The technique has applications in visual diffraction imaging, phase orientation and strain mapping, phase contrast analysis, among others.

References

  1. Gabor, D. (1948). "A New Microscopic Principle". Nature. Springer Science and Business Media LLC. 161 (4098): 777–778. doi: 10.1038/161777a0 . ISSN   0028-0836.
  2. Haine, M. E.; Mulvey, T. (1952-10-01). "The Formation of the Diffraction Image with Electrons in the Gabor Diffraction Microscope". Journal of the Optical Society of America. The Optical Society. 42 (10): 763. doi:10.1364/josa.42.000763. ISSN   0030-3941.
  3. Möllenstedt, G.; Düker, H. (1956). "Beobachtungen und Messungen an Biprisma-Interferenzen mit Elektronenwellen". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 145 (3): 377–397. doi:10.1007/bf01326780. ISSN   1434-6001.
  4. Cowley, J.M. (1992). "Twenty forms of electron holography". Ultramicroscopy. Elsevier BV. 41 (4): 335–348. doi:10.1016/0304-3991(92)90213-4. ISSN   0304-3991.
  5. Lehmann, Michael; Lichte, Hannes (2002). "Tutorial on Off-Axis Electron Holography". Microscopy and Microanalysis. Cambridge University Press (CUP). 8 (6): 447–466. doi:10.1017/s1431927602020147. ISSN   1431-9276.
  6. Fink, Hans-Werner; Stocker, Werner; Schmid, Heinz (1990-09-03). "Holography with low-energy electrons". Physical Review Letters. American Physical Society (APS). 65 (10): 1204–1206. CiteSeerX   10.1.1.370.7590 . doi:10.1103/physrevlett.65.1204. ISSN   0031-9007.
  7. Lichte, Hannes (1986). "Electron holography approaching atomic resolution". Ultramicroscopy. Elsevier BV. 20 (3): 293–304. doi:10.1016/0304-3991(86)90193-2. ISSN   0304-3991.
  8. Tonomura, Akira (1987-07-01). "Applications of electron holography". Reviews of Modern Physics. American Physical Society (APS). 59 (3): 639–669. doi:10.1103/revmodphys.59.639. ISSN   0034-6861.
  9. R. E. Dunin-Borkowski et al., Micros. Res. and Tech. 64, 390 (2004).
  10. Ogai, Keiko; Matsui, Shinji; Kimura, Yoshihide; Shimizu, Ryuichi (1993-12-30). "An Approach for Nanolithography Using Electron Holography". Japanese Journal of Applied Physics. Japan Society of Applied Physics. 32 (Part 1, No. 12B): 5988–5992. doi:10.1143/jjap.32.5988. ISSN   0021-4922.