Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T19:03:02.727Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic Artifact Reduction in Fourier Transforms of Full Field Atomic Resolution Images

Published online by Cambridge University Press:  19 January 2015

Robert Hovden ,
Yi Jiang ,
Huolin L. Xin  and
Lena F. Kourkoutis
Robert Hovden*
Affiliation:
School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA
Yi Jiang
Affiliation:
Department of Physics, Cornell University, Ithaca, NY 14853, USA
Huolin L. Xin
Affiliation:
Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
Lena F. Kourkoutis
Affiliation:
School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA
*
*Corresponding author. E-mail: [email protected]
Get access

Abstract

The discrete Fourier transform is among the most routine tools used in high-resolution scanning/transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp discontinuities between the edges of an image cause a cross patterned artifact along the reciprocal space axes. This artifact can interfere with the analysis of reciprocal lattice peaks of an atomic resolution image. Here we demonstrate that the recently developed Periodic Plus Smooth Decomposition technique provides a simple, efficient method for reliable removal of artifacts caused by edge discontinuities. In this method, edge artifacts are reduced by subtracting a smooth background that solves Poisson’s equation with boundary conditions set by the image’s edges. Unlike the traditional windowed Fourier transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal lattice peaks from the image’s entire field of view.

Keywords

STEMFourier transformdata processingatomic imagingdiffractionaberration correction
Type
Materials Applications
Information
Microscopy and Microanalysis , Volume 21 , Issue 2 , April 2015 , pp. 436 - 441
Copyright
© Microscopy Society of America 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batson, P.E., Dellby, N. & Krivanek, O.L. (2002). Sub-ångstrom resolution using aberration corrected electron optics. Nature 418, 617–620.Google Scholar
Beaudoin, N. & Beauchemin, S.S. (2001). “An Accurate Discrete Fourier Transform for Image Processing” Proceedings of the 16th International Conference on Pattern Recognition (ICPR 02), Quebec City, Canada, pp. 935–939, Aug. 11-15 2002.Google Scholar
Braidy, N., Le Bouar, Y., Lazar, S. & Ricolleau, C. (2012). Correcting scanning instabilities from images of periodic structures. Ultramicroscopy 118, 67–76.Google Scholar
Cowley, J.M. & Smith, D.J. (1987). The present and future of high-resolution electron microscopy. Acta Crystallographica Section A Foundations of Crystallography 43, 737–751.Google Scholar
Gibbs, J.W. (1899). Fourier’s series. Nature 59, 606.CrossRefGoogle Scholar
Harris, F.J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proc IEEE 66, 51–83.Google Scholar
Hashimoto, H., Yokota, Y., Takai, Y., Tomita, M., Kori, T., Fujino, M. & Endoh, H. (1980). Dynamic and simultaneous observation of electron microscopic image and diffraction patterns of crystal lattice structure. Proceedings. 7th European Congress on Electron Microscopy, The Hague 268pp.Google Scholar
Hewitt, E. & Hewitt, R.E. (1979). The Gibbs-Wilbraham phenomenon: an episode in Fourier analysis. Arch Hist Exact Sci 21, 129.Google Scholar
Jones, L. & Nellist, P.D. (2013). Identifying and correcting scan noise and drift in the scanning transmission electron microscope. Microsc Microanal 19, 1050–1060.Google Scholar
Kirkland, E.J. & Thomas, M.G. (1996). A high efficiency annular dark field detector for STEM. Ultramicroscopy 62, 79–88.Google Scholar
Moisan, L. (2010). Periodic Plus Smooth Image Decomposition. J Math Imaging Vision 39, 161–179.Google Scholar
Muller, D.A. (2009). Structure and bonding at the atomic scale by scanning transmission electron microscopy. Nat Mater 8, 263–270.Google Scholar
Muller, D.A., Kirkland, E.J., Thomas, M.G., Grazul, J.L., Fitting, L. & Weyland, M. (2006). Room design for high-performance electron microscopy. Ultramicroscopy 106, 1033–1040.Google Scholar
Rust, H.P. (1974). Real time Fourier analysis by electronic means. Proceedings. Eighth International Congress on Electron Microscopy, Canberra.Google Scholar
Saito, N. & Remy, J.-F. (2006). The polyharmonic local sine transform: A new tool for local image analysis and synthesis without edge effect. Appl Comput Harmonic Anal 20, 41–73.Google Scholar
Sang, X. & LeBeau, J.M. (2014). Revolving scanning transmission electron microscopy: Correcting sample drift distortion without prior knowledge. Ultramicroscopy 138, 28–35.Google Scholar
Thomson, G.P. & Reid, A. (1927). Diffraction of cathode rays by a thin film. Nature 119, 890–890.CrossRefGoogle Scholar
Voyles, P.M., Grazul, J.L. & Muller, D.A. (2003). Imaging individual atoms inside crystals with ADF-STEM. Ultramicroscopy 96, 251–273.Google Scholar
Wall, J., Langmore, J., Isaacson, M. & Crewe, A.V. (1974). Scanning transmission electron microscopy at high resolution. Proc Natl Acad Sci 71, 1–5.Google Scholar
Wilbraham, H. (1848). On a certain periodic function. Cambridge Dublin Math J 3, 198–201.Google Scholar
Yankovich, A.B., Berkels, B., Dahmen, W., Binev, P., Sanchez, S.I., Bradley, S.A., Li, A., Szlufarska, I. & Voyles, P.M. (2014). Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts. Nat Commun 5, 4155.CrossRefGoogle ScholarPubMed
Zhang, H., Hu, B., Sun, L., Hovden, R., Wise, F.W., Muller, D.A. & Robinson, R.D. (2011). Surfactant Ligand Removal and Rational Fabrication of Inorganically Connected Quantum Dots. Nano Lett 11, 5356–5361.Google Scholar
Supplementary material: File

Hovden supplementary material

Hovden supplementary material

Download Hovden supplementary material(File)
File 72.8 KB