Correction of high-resolution data for curvature of the Ewald sphere
Correction of high-resolution data for curvature of the Ewald sphere
复制标题
DOI：
10.1016/s0304-3991(99)00120-5
复制
发表时间：
2000-03-01
期刊：
影响因子：
2.2
通讯作者：
DeRosier, DJ
中科院分区：
文献类型：
--
作者：
DeRosier, DJ
在取决于电子波长的足够高的分辨率下，样品的厚度超过显微镜的景深。在这个分辨率下，以对称角度散射的光束对不再与弗里德尔定律相关;也就是说，描述它们的振幅和相位的傅里叶系数不再是彼此的复共轭。在这些条件下，从图像中提取的傅立叶系数是对应于三维（3-D）结构的独立（与Friedel相关相反）傅立叶系数的线性组合。为了重新生成三维散射密度，必须从每个图像的傅立叶系数中恢复与结构相对应的傅立叶系数。为了收集完整的三维数据集，仍然需要对结构进行不同的观察。计算机模拟用于确定在什么分辨率，电压和试样厚度的提取系数显着不同的3-D结构所需的傅立叶系数。本文提出了描述这种情况的理论。它提醒我们，这个问题可以通过考虑埃瓦尔德球的曲率来处理，或者等效地通过考虑结构内的不同层以不同的散焦量成像来处理。本文介绍了几种提取三维重建所需傅立叶系数的方法。最简单的方法是拍摄具有不同散焦量的图像。然而，对于螺旋结构，仅需要一个图像。(C)2000 Elsevier Science B. V.保留所有权利。
at sufficiently high resolution, which depends on the wavelength of the electrons, the thickness of the sample exceeds the depth of field of the microscope. At this resolution, pairs of beams scattered at symmetric angles about the incident beam are no longer related by Friedel's law; that is, the Fourier coeffcients that describe their amplitudes and phases are no longer complex conjugates of each other. Under these conditions, the Fourier coefficients extracted from the image are linear combinations of independent (as opposed to Friedel related) Fourier coefficients corresponding to the three-dimensional (3-D) structure. In order to regenerate the 3-D scattering density, the Fourier coefficients corresponding to the structure have to be recovered from the Fourier coefficients of each image. The requirement for different views of the structure in order to collect a full 3-D data set remains. Computer simulations are used to determine at what resolution, voltage and specimen thickness the extracted coefficients differ significantly from the Fourier coefficients needed for the 3-D structure. This paper presents the theory that describes this situation. It reminds us that the problem can be treated by considering the curvature of the Ewald sphere or equivalently by considering that different layers within the structure are imaged with different amounts of defocus. The paper presents several methods to extract the Fourier coefficients needed for a 3-D reconstruction. The simplest of the methods is to take images with different amounts of defocus. For helical structures, however, only one image is needed. (C) 2000 Elsevier Science B.V. all rights reserved.