DeRosier D J
W.M. Keck Institute for Cellular Visualization, Rosenstiel Basic Medical Sciences Research Center, Brandeis University, Waltham, MA 02454, USA.
Ultramicroscopy. 2000 Mar;81(2):83-98. doi: 10.1016/s0304-3991(99)00120-5.
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 coefficients 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.
在足够高的分辨率下（这取决于电子的波长），样品的厚度超过了显微镜的景深。在这种分辨率下，围绕入射光束以对称角度散射的光束对不再受弗里德定律的约束；也就是说，描述它们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，从图像中提取的傅里叶系数是对应于三维（3-D）结构的独立（与弗里德相关相对）傅里叶系数的线性组合。为了重建三维散射密度，必须从每个图像的傅里叶系数中恢复对应于该结构的傅里叶系数。仍然需要对结构的不同视图以收集完整的三维数据集。使用计算机模拟来确定在何种分辨率、电压和样品厚度下，提取的系数与三维结构所需的傅里叶系数有显著差异。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不同层以不同程度的散焦成像来处理。本文提出了几种提取三维重建所需傅里叶系数的方法。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，只需要一张图像。
