The Relation Between the Phase of the Electron Wave (Which is Lost When an Em Image is Recorded) and the Preserved Crystallographic Structure Factor Phases

Abstract

The phase problem in X-ray crystallography is one of the most interesting and most studied mathematical problems that exist. There is still today no general solution of the phase problem, but partial solutions have resulted in at least 8 Nobel Prizes, even though one of the most prominent solutions, the Patterson function, was not awarded the Prize.It has frequently been claimed that there should be a phase problem also in electron microscopy. It may be more correct to say that there is no phase problem, only a phase confusion problem in electron microscopy. The phase confusion problem has arisen since the word phase is used for (at least) two very different physical entities in the field of electron microscopy. When crystallographers speak about phases, they mean the crystallographic structure factor phases, while physicists mean the wave front phases. In order to resolve the phase confusion problem, it is necessary to define clearly which phases are meant.