We introduce a new approach to the numerical simulation of Scanning Transmission Electron Microscopy images. The Lattice Multislice Algorithm (LMA) takes advantage of the fact that electron waves passing through the specimen have limited bandwidth and therefore can be approximated very well by a low-dimensional linear space spanned by translations of a well-localized function $u$. Just like in the PRISM algorithm recently published by C. Ophus, we utilize the linearity of the Schr\"odinger equation, but perform the approximations with functions that are well localized in real space instead of Fourier space. This way, we achieve a similar computational speedup as PRISM, but at a much lower memory consumption and reduced numerical error due to avoiding virtual copies of the probe waves interfering with the result. Our approach also facilitates faster recomputations if local changes are made to the specimen such as changing a single atomic column.

翻译：我们提出了一种用于扫描透射电子显微镜图像数值模拟的新方法。晶格多层切片算法（LMA）利用了电子波穿过样品时带宽有限的特点，因此可以通过一个高度局域化的函数 $u$ 的平移所张成的低维线性空间进行良好近似。与C. Ophus近期发表的PRISM算法类似，我们利用了薛定谔方程的线性特性，但在实空间而非傅里叶空间中采用高度局域化的函数进行近似。通过这种方式，我们实现了与PRISM相当的计算加速效果，同时内存消耗大幅降低，并且由于避免了探针波的虚拟副本对结果产生干扰，数值误差也有所减小。此外，我们的方法在样品发生局部变化（如改变单个原子列）时，还能实现更快速的重计算。