Hybridization of Off-Axis and In-line High-Resolution Electron Holography

Abstract

Reconstruction of the complex-valued wave function that gives rise to the probability density of fast electrons in transmission electron microscopy (TEM) seems, at first glance, to be a solved problem. However, it is still challenging when considered more closely. In conventional TEM experiments, only the intensity (i.e., the square of the amplitude) of the wave function can be measured. Direct information about the phase of the wave, which carries information about electrostatic and magnetic fields that the electron has passed through, is lost during detection. In order to recover the phase information, it is necessary to interfere the electron wave function with a reference wave, in order to create an interference pattern. Denis Gabor introduced an approach that could be used to solve this problem 66 years ago [1]. In Gabor s original setup, which is the pioneering scheme for in-line holography, the wave that has been scattered by the specimen (the object wave) interferes with a reference wave propagated along the same axis. Using laser light, Leith and Upatnieks [2] showed that separation of the axes of propagation of the reference and object waves could be used to solve the twin-image problem. Mollenstedt later translated this idea back to electron microscopy, creating the field of off-axis electron holography [3,4].