摘要
The coherent interaction between an electromagnetic field and a 3D weakly scattering medium results in a simple Fourier transform relationship between the object’s structure and the complex scattered field1.As a result,knowledge about the phase of the scattered field is necessary for solving this inverse problem with a unique solution.However,in applications,such as X-ray crystallography,typically one only has experimental access to the amplitude of the diffracted field,which results in ambiguities of the reconstruction.This century-old challenge,known as“the phase problem”2 motivated the development of computational algorithms combined with a priori knowledge about the object of interest to limit the solution space.While generally successful,this approach sometimes led to multiple solutions,i.e.,different inferred object structures for the same set of data:“Not all the guesses have been successful.This is clear,for example,from the following:Two different structures were predicted for the mineral bixbyite,one by L.Pauling,the other by W.H.Zachariasen.It is not known which,if either,is correct.”(Chapter 7 in ref.2).
