Cheung Sky C, Shin John Y, Lau Yenson, Chen Zhengyu, Sun Ju, Zhang Yuqian, Müller Marvin A, Eremin Ilya M, Wright John N, Pasupathy Abhay N
Department of Physics, Columbia University, New York, NY, 10027, USA.
Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA.
Nat Commun. 2020 Feb 26;11(1):1081. doi: 10.1038/s41467-020-14633-1.
Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.
现代高分辨率显微镜通常用于研究具有密集且非周期性空间结构的标本。从这类显微镜获取的图像中提取有意义的信息仍然是一项艰巨的挑战。傅里叶分析通常用于分析此类图像的结构。然而，傅里叶变换应用于非周期性图像时从根本上会遭受严重的相位噪声。在此，我们报告了一种基于非凸优化的算法的开发，该算法能直接揭示实空间图像中存在的基本图案。除了在定量上优于传统傅里叶分析外，我们还表明该算法还能揭示有关底层图案结构的相位敏感信息。我们通过研究钴掺杂砷化铁超导体的扫描隧道显微镜图像来证明其有用性，并证明该算法的应用能够完全恢复这种材料中的准粒子干涉。
