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.
Bibliographical noteFunding Information:
We thank Ethan Rosenthal and Erick Andrade for help with STM data acquisition, and Andrew Millis and Rafael Fernandes for discussions. M.A.M. and I.M.E. are thankful to Sergey Borisenko for providing the tight-binding parametrization of the ARPES data in NaFe1−xCoxAs. This work is supported by the National Science Foundation Bigdata program (Grant number IIS-1546411). Support for STM equipment and operations is provided by the Air Force Office of Scientific Research (Grant number FA9550-16-1-0601). The work of I.M.E. was carried out with financial support from the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST MISiS Grant No. K2-2017-085.
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