Background The contrast transfer function (CTF) is an important principle in the field of transmission electron microscopy (TEM) imaging. It provides information on how the electron wave that interacted with a sample (in frequency domain) in an objective lens is transferred to the imaging system (in real space domain) depending on the effects of lens aberrations. Based on the CTF calculation, various useful results, such as the TEM instrumental information limit and optimal imaging condition, can be estimated. Recently, aberration-corrected TEM (AC-TEM) has been widely applied in various research fields for imaging at the nanoscale or atomic scale. To use AC-TEM effectively, a deep understanding of the complicated CTF with an electron wave controlled via an aberration corrector is required. Unfortunately, this complicated CTF is difficult to understand for most microscopists without the use of computational tools. In this study, we develop the extended CTF (exCTF) simulator to perform the full as well as simple CTF calculation. Findings We successfully developed the exCTF simulator, which can obtain more information than previously reported software. The exCTF simulator not only calculates the CTF for basic optical information that can be obtained in conventional TEM, but also can calculate the extended CTF with various aberrations (up to fifth order) for more detailed information obtained in advanced high-performance AC-TEM in one-dimensional and two-dimensional formats. The user interface of the simulator includes CTF calculation, saving, and edit functions for five graphs for different conditions, allowing for detailed comparative analysis. Conclusion We confirmed that the exCTF simulator produced reliable calculation data for various applications. The exCTF simulator made it easy to obtain instrumental performance information and demonstrated the influence of optical aberrations on the actual resolution of AC-TEM. Consequently, the proposed exCTF simulator is expected to be useful to microscopists as a simulation tool for electron microscopy and as a training tool for electron optics.

中文翻译：

---

exCTF 模拟器：用于像差校正透射电子显微镜的相差传递函数的模拟工具

背景 对比传递函数 (CTF) 是透射电子显微镜 (TEM) 成像领域的重要原理。它提供了有关如何根据镜头像差的影响将与物镜中的样本（在频域中）相互作用的电子波传输到成像系统（在实空间域中）的信息。基于CTF计算，可以估计各种有用的结果，例如TEM仪器信息限制和最佳成像条件。最近，像差校正 TEM (AC-TEM) 已广泛应用于各种研究领域，用于在纳米级或原子级成像。为了有效地使用 AC-TEM，需要深入了解具有通过像差校正器控制的电子波的复杂 CTF。很遗憾，如果不使用计算工具，大多数显微镜专家很难理解这种复杂的 CTF。在这项研究中，我们开发了扩展 CTF (exCTF) 模拟器来执行完整和简单的 CTF 计算。结果 我们成功开发了 exCTF 模拟器，它可以获得比以前报道的软件更多的信息。exCTF 模拟器不仅可以计算常规 TEM 中可以获得的基本光学信息的 CTF，还可以计算具有各种像差（高达五阶）的扩展 CTF，以便在高级高性能 AC-TEM 中获得更详细的信息。一维和二维格式。模拟器的用户界面包括针对不同条件的五个图形的CTF计算、保存和编辑功能，可以进行详细的对比分析。结论 我们证实，exCTF 模拟器为各种应用程序生成了可靠的计算数据。exCTF 模拟器使获取仪器性能信息变得容易，并演示了光学像差对 AC-TEM 实际分辨率的影响。因此，所提出的 exCTF 模拟器有望作为电子显微镜的模拟工具和电子光学的培训工具对显微镜学家有用。