Journal: Scientific Reports

Article Title: Atomic scale displacements detected by optical image cross-correlation analysis and 3D printed marker arrays

doi: 10.1038/s41598-021-81712-8

Figure Lengend Snippet: Scheme of the simple optical setup used to determine two-dimensional displacement vectors of a macroscopic sample with atomic-scale localization errors. The surface of a sample is illuminated by unpolarized visible white light from a filtered incandescent source impinging onto the sample under an angle. An objective lens (with focal length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=8.25\, \mathrm{mm}$$\end{document} f = 8.25 mm ) together with a tube lens (with focal length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=200\, \mathrm{mm}$$\end{document} f = 200 mm ) images the sample surface onto a digital black/white camera. The objective lens has a numerical aperture of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NA}=0.4$$\end{document} NA = 0.4 and a free working distance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$11.2\,\mathrm{ mm}$$\end{document} 11.2 mm . The images acquired by the camera are processed using image cross-correlation analysis. We can displace the sample in the plane normal to the optical axis by a precision piezoelectric stage. The setup is located on a vibration-isolated optical table and enclosed in a box to reduce vibrations and drifts between the sample and the camera position.

Article Snippet: This microscope images the sample plane onto a silicon complementary metal–oxide–semiconductor (CMOS) black/white camera chip (Sony IMX264, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2448\times 2048\,\mathrm{ pixels}$$\end{document} 2448 × 2048 pixels ), which is connected to a computer.

Techniques: Isolation

Journal: Scientific Reports

Article Title: Atomic scale displacements detected by optical image cross-correlation analysis and 3D printed marker arrays

doi: 10.1038/s41598-021-81712-8

Figure Lengend Snippet: Top-view electron micrographs of four of the five investigated samples. ( a ) Sample #1 is a sandblasted copper surface. ( b ) Sample #2 is a glass substrate with randomly distributed micrometer-sized gold grains on top. Sample #3 (not depicted) is a glass substrate with a square array of polymer markers with period \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a=10\,\upmu \mathrm{m}$$\end{document} a = 10 μ m on top, fabricated by 3D laser printing. Without metal coating, this sample cannot easily be imaged by electron microscopy. ( c ) Sample #4 is as sample #3, but coated with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$54\,\mathrm{ nm}$$\end{document} 54 nm thin film of gold. ( d ) Sample #5 is as sample #4, but with a period of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a=5\, \upmu \mathrm{m}$$\end{document} a = 5 μ m .

Article Snippet: This microscope images the sample plane onto a silicon complementary metal–oxide–semiconductor (CMOS) black/white camera chip (Sony IMX264, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2448\times 2048\,\mathrm{ pixels}$$\end{document} 2448 × 2048 pixels ), which is connected to a computer.

Techniques: Polymer, Electron Microscopy

Journal: Scientific Reports

Article Title: Atomic scale displacements detected by optical image cross-correlation analysis and 3D printed marker arrays

doi: 10.1038/s41598-021-81712-8

Figure Lengend Snippet: Summary of data obtained from five different samples #1 to #5 (cf. Fig. ). Column ( a ) exhibits an example optical image with the used regions of interest (ROI) indicated by the blue squares. Each ROI comprises \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$30\times 30$$\end{document} 30 × 30 camera pixels. The ROI lie in a footprint of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left(40\, \upmu\mathrm{m}\right)}^{2}$$\end{document} 40 μ m indicated by the dashed white square. Column ( b ) shows results obtained from the optical-image cross-correlation approach for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document} x -component (red) and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y$$\end{document} y -component (blue). For comparison, the read-out signal from the capacitive sensor of the piezoelectric actuator is shown in gray. This signal has been shifted vertically for clarity. For each of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$800$$\end{document} 800 data points, we obtain localization errors \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{x}$$\end{document} σ x and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{y}$$\end{document} σ y . The mean values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {\sigma }_{x}\rangle$$\end{document} ⟨ σ x ⟩ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {\sigma }_{x}\rangle$$\end{document} ⟨ σ x ⟩ over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$800$$\end{document} 800 measurements are indicated. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {\sigma }_{x}^{^{\prime}}\rangle$$\end{document} ⟨ σ x ′ ⟩ is the corresponding value for the capacitive sensor, for the same measurement time of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$12.5\, \mathrm{ms}$$\end{document} 12.5 ms . In column ( b ), the piezoelectric actuator has not been moved intentionally. In contrast, in column ( c ), the piezoelectric actuator has been moved in a staircase manner with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\,\mathrm{nm}$$\end{document} 1 nm high steps each \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5\, \mathrm{s}$$\end{document} 0.5 s .

Article Snippet: This microscope images the sample plane onto a silicon complementary metal–oxide–semiconductor (CMOS) black/white camera chip (Sony IMX264, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2448\times 2048\,\mathrm{ pixels}$$\end{document} 2448 × 2048 pixels ), which is connected to a computer.

Techniques: Comparison