Electron holography - basics and applications

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.