It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed.

有人认为，在稀疏弱散射结构（例如小生物分子）的原子分辨率透射电子显微镜（TEM）中，多重电子散射通常只有很小的影响，而分子内菲涅耳衍射可能是显着的，因为本质上是浅景深。这些事实表明，使用不相干的第一波恩近似，可以有效地分别为每个原子分别有效地执行从在分子的多个旋转方向收集的散焦图像系列的这种结构的三维重建。相应的重建方法，这里称为差分全息断层扫描，在理论上得到了发展，并在几个生物分子的数值模型上进行了计算证明。结果表明，该方法能够根据在分子的少量随机方向上收集的 TEM 数据准确重建分子中原子的位置，每个方向具有一个或多个散焦图像。简要讨论了低温电子显微镜和其他领域的可能应用。