Electron Holography: phases matter

Essentially, all optics is wave optics, be it with light, X-rays, neutrons or electrons. The information transfer from the object to the image can only be understood in terms of waves given by amplitude and phase. However, phases are difficult to measure: for slowly oscillating waves such as sound or low-frequency electromagnetic waves, phases can be measured directly; for high frequencies this has to be done by heterodyne detection, i.e. superposition with a reference and averaging over time. In optics, this is called interferometry. Because interference is mostly very difficult to achieve, phases have often been considered 'hidden variables' seemingly pulling the strings from backstage, only visible by their action on the image intensity. This was almost the case in conventional Electron Microscopy with the phase differences introduced by an object. However, in the face of the urgent questions from solid state physics and materials science, these phases have to be determined precisely, because they encode the most dominant object properties, such as charge distributions and electromagnetic fields. After more than six decades of very patient advancement, electron interferometry and holography offer unprecedented analytical facilities down to an atomic scale. Akira Tonomura has prominently contributed to the present state.