Algorithm for Atomic Resolution Holography Using Modified L1‐Regularized Linear Regression and Steepest Descent Method

• Published in: physica status solidi (b) Vol. 255; no. 11
• Main Author: Matsushita, Tomohiro
• Format: Journal Article
• Language: English
• Published: 01.11.2018
• Subjects: atomic resolution holography; atomic structure; dopants; neutron holography; photoelectron holography; X‐ray fluorescence holography
• ISSN: 0370-1972; 1521-3951
• DOI: 10.1002/pssb.201800091

Atomic resolution holography techniques, including X‐ray fluorescence holography, photoelectron holography, and neutron holography, provide new knowledge about the local atomic structure around dopants in crystals and adsorbates on crystals. Three‐dimensional atomic images can be reconstructed from atomic resolution holograms using reconstruction calculation techniques. The development of appropriate algorithms is a critical first step in the reconstruction process. Barton's method, which is based on the Fourier transformation, is typically used. However, that approach requires multiple‐energy holograms, and it sometimes results in images with unexpected artifacts. This report presents the details of an algorithm developed on the basis of an iterative approach with regularized linear regression and a modified steepest descent method. Atomic resolution holography techniques, including X‐ray fluorescence holography, photoelectron holography, and neutron holography, provide three‐dimensional local atomic structure around dopants in crystals and adsorbates on crystals. The details of an atomic image reconstruction algorithm, developed on the basis of an iterative approach with L1‐regularized linear regression and a modified steepest descent method, are presented.