The development of a coherent field-emission electron beam has facilitated practical applications of electron holography. This paper reviews this field of growing importance, making special reference to the application of electron holography to current technological problems. It is seen that the phase distribution of an electron wave function transmitted through a specimen can be observed as an interference micrograph, thus providing considerable information about the microscopic distribution of electromagnetic potentials. For example, a magnetic sample's contour fringes directly indicate its magnetic lines of force. These fringes can also show the equipotential lines of an electric sample and thickness contours of a homogeneous specimen. Holographic techniques can be effectively employed to improve the accuracy of phase measurements up to an order of $\frac{2\ensuremath{\pi}}{100}$. This opens the way for use of electron holography as a high-precision measurement method that can cast light on wide regions of the microscopic world pertinent to both basic science and practical industry.

Applications of electron holography

Despite the huge progress achieved recently by means of the corrector for aberrations, allowing now a true atomic resolution of 0.1 nm, hence making it an unrivalled tool for nanoscience, transmission electron microscopy (TEM) suffers from a severe drawback: in a conventional electron micrograph only a poor phase contrast can be achieved, i.e. phase structures are virtually invisible. Therefore, conventional TEM is nearly blind for electric and magnetic fields, which are pure phase objects. Since such fields provoked by the atomic structure, e.g. of semiconductors and ferroelectrics, largely determine the solid state properties, hence the importance for high technology applications, substantial object information is missing.Electron holography in TEM offers the solution: by superposition with a coherent reference wave, a hologram is recorded, from which the image wave can be completely reconstructed by amplitude and phase. Now the object is displayed quantitatively in two separate images: one representing the amplitude, the other the phase. From the phase image, electric and magnetic fields can be determined quantitatively in the range from micrometre down to atomic dimensions by all wave optical methods that one can think of, both in real space and in Fourier space.Electron holography is pure wave optics. Therefore, we discuss the basics of coherence and interference, the implementation into a TEM, the path of rays for recording holograms as well as the limits in lateral and signal resolution. We outline the methods of reconstructing the wave by numerical image processing and procedures for extracting the object properties of interest. Furthermore, we present a broad spectrum of applications both at mesoscopic and atomic dimensions.This paper gives an overview of the state of the art pointing at the needs for further development. It is also meant as encouragement for those who refrain from holography, thinking that it can only be performed by specialists in highly specialized laboratories. In fact, a modern TEM built for atomic resolution and equipped with a field emitter or a Schottky emitter, well aligned by a skilled operator, can deliver good holograms. Running commercially available image processing software and mathematics programs on a laptop-computer is sufficient for reconstruction of the amplitude and phase images and extracting desirable object information.

https://iopscience.iop.org/article/10.1088/0034-4885/71/1/016102/pdf

Electron holography?basics and applications

A state-of-the-art review of electron interferometry and interference electron microscopy is given. The various types of interferometry device, interferometers and interference microscopes, which have been proposed and/or constructed are reviewed and commented upon. The electron biprism, by far the most successful interferometry device, is treated in some detail from both the experimental and theoretical (geometric and wave optics) points of view. The applications of electron interferometry are presented with particular reference to off-axis electron holography. Finally the future perspectives are indicated.

https://iopscience.iop.org/article/10.1088/0022-3735/14/6/001/pdf

Electron interferometry and interference electron microscopy

In the 1970s the prominent goal was to overcome the limitations of electron microscopy caused by aberrations of electron lenses by the development of electron holography. In the meantime this problem has been solved, not only in the roundabout way of holography, but directly by correcting the aberrations of the lenses. Nevertheless, many quantitative electron microscopical measurement methods?e.g. mapping and visualization of electric and magnetic fields?were developed within the context of holography and have become fields of their own. In this review we focus on less popular electron interferometric experiments which complement the field of electron holography. The paper is organized as follows. After a short sketch of the development of electron biprism interferometry after its invention in 1954, recent advances in technology are discussed that made electron biprism interferometry an indispensable tool for solving fundamental and applied questions in physics: the development and preparation of conventional and single-atom field electron and field ion sources with their extraordinary properties. Single- and few-atom sources exhibit spectacular features: their brightness at 100?keV exceeds that of conventional field emitters by two orders in magnitude. Due to the extremely small aberrations of diode field emitter extraction optics, the virtual source size of single-atom tips is on the order of 0.2?nm. As a consequence it illuminates an area 7?cm in diameter on a screen at a distance of 15?cm coherently. Projection electron micrographs taken with these sources reach spatial resolutions of atomic dimensions and in-line holograms are?due to the absence of lenses with their aberrations?not blurred. Their reconstruction is straightforward. By addition of a carbon nanotube biprism into the beam path of a projection microscope a lensless electron interferometer has been realized. In extremely ultrahigh vacuum systems flicker noise is practically absent in the new sources. In the context of holography, methods have been developed to record holograms without modulation of the biprism fringes by waves diffracted at the edges of the biprism filament. This simplifies the reconstruction of holograms and the evaluation of interferograms (taken, e.g. to extract a spectrum by Fourier analysis of the fringe system) significantly. A major section is devoted to the influence of electromagnetic and gravito-inertial potentials and fields on the quantum mechanical phase of matter waves: the Aharonov?Bohm effect, the inertial Aharonov?Bohm effect and its realization, the Sagnac effect and Sagnac experiments with atoms, superfluid helium, Bose?Einstein condensates, electrons and ions and their potential as rotation sensors are discussed. M?llenstedt and Wohland discovered in a crossed beam analyzer (Wien filter) an optical element for charged particles that shifts wave packets longitudinally that transverse a Wien filter on laterally separated paths. This new optical element rendered it possible to measure coherence lengths and the spectrum of charged particle waves by visibility- and Fourier-spectroscopy, to perform a 'Welcher Weg' experiment, to re-establish seemingly lost longitudinal coherence in an interferometer for charged particles and to realize a decoherence free quantum eraser. A precision test of decoherence according to a proposal from Anglin and Zurek and biprism interferences with helium atoms close the section on first-order coherence experiments. The topics of the last section are Hanbury Brown?Twiss correlations and an antibuching experiment of free electrons.

Progress in electron- and ion-interferometry

Through recent years, off-axis electron holography has helped us to understand and to overcome some experimental restrictions in transmission electron microscopy. With development of powerful electron microscopes, slow-scan CCD cameras, and computers, holography is not an academic technique anymore used by specialized laboratories. Holography has proven its wide range of applications in solving real-world problems in materials science and biology. At medium resolution, that is, on nanometer scale, holography allows access to large area phase contrast produced by magnetic fields and electric potentials. In the high-resolution domain, holography unveils its power by unscrambling amplitude and phase of the electron wave, resulting in an improved lateral resolution up to the information limit. Holography is a thoroughly quantitative method, and, in combination with the perfect zero-loss filtering inherent to this method, the interpretation of the reconstructed data is strongly simplified. After outlining the basics of holography, in this tutorial we focus on development of a step-by-step procedure for recording and reconstruction of holograms. At the end, some recent applications are discussed.

Tutorial on off-axis electron holography.

The numer i ca l eva l ua t i on of Eq. (2) for 152Sm gives Re 3\" 109/sec (with n ~ 4). This is fas te r t h a n t h e nuc lea r y ra te [8~ of R~, = 5' 10S/se c ( t22 keV level). Similar re la t ions are f ound in o the r de fo rmed nucle i because t h e p h e n o m e n a are collective, w i th increas ing t e n d e n c y for Re a t larger Z. If on ly one c o m p o n e n t of t he hfs doub le t is seen t he experim e n t a l i somer sh i f t h a s to be correc ted b y a b o u t ha l f t he sp l i t t ing ene rgy [Eq. (1)? (for s impl ic i ty egrounds ta te=0 is a s s u m e d ) :

https://link.springer.com/content/pdf/10.1007/BF00600454.pdf

H. Wahl

Papers

Elektronenholographie und Rekonstruktion mit Laserlicht