正负交替反转法解析电子衍射相位问题

与X射线晶体学中存在的相位问题类似,在电子衍射中也存在相位问题:在电子衍射实验中只能收集到衍射强度而丢失了相位.最近,衍射重构成像方法(diffractive imaging),即直接从衍射重构出晶体结构的方法,从理论和实验都有了重大进展.从理论上,人们提出和发展许多有效的相位解析方法.从实验上,高强度的X射线源,场发射电子枪以及高灵敏度的记录媒介的发展都对此有贡献.直接从衍射重构出晶体结构有许多的优点:首先在重构像中,物镜球差的影响很小.这是由于物镜传递函数对衍射强度的影响远远小于对相位的影响;其次,从同一晶体收集的电子衍射有更多的高阶衍射斑,使得衍射重构能得到较高的分辨率(小于0.1 nm);同时,在同样辐射条件下晶体的电子衍射比其高分辨像具有更高的信噪比.这对于用电镜解析对辐射损伤敏感的有机物和生物蛋白晶体是有用的.本文叙述了一个解决电子衍射相位的新方法.在本文的程序中,同时使用了Oszlányi和Süto提出的正负交替反转法(charge-flipping algorithm)和Fienup的重构方法(hybrid input-output algorithm).作者用模拟数据来验证该方法的有效性.在程序中输入计算的运动学电子衍射强度,模拟晶体的二维静电势场分布能被重构出来.使用归一化结构因子可以提高正空间的重构像衬度;这对解决相位问题是有利的.使用Fienup的重构方法可以有效地解决由局域最小值而引起程序停滞问题.在正负交替反转法中通常会有停滞问题而不能找到全局最小值.正负交替反转法会逐步地在正空间中产生较大的零值电势区域,从而减小了正空间中未知数的数目.当未知数数目小于或等于从傅立叶变换建立起来的等式数目时,晶体的相位就可以解决了.

Iterative phase retrieval for electron diffraction patterns by the charge flipping algorithm

We have combined the charge-flipping algorithm of Oszlányi and Süto with the Fienup hybrid input-output algorithm for solving the phase problem. We demonstrate the reconstruction of the 2-dimensional projected potential of a thin crystal, by retrieving the phases from atomic-resolution simulated kinematic electron diffraction patterns. The use of normalized structure factors as input is shown to enhance image contrast (atomicity) in real space. This combination of the dynamic Fienup Hybrid input-output algorithm with the flipping algorithm has the advantage of solving the stagnation problem. The charge-flipping algorithm can be used to solve the phase problem for conventional Bragg diffraction patterns from thin crystalline specimens because it reduces the number of unknowns in real space, so as to fulfil the requirement for having as many unknowns as constraint equations.