摘要：Abstract For analyzing displacement-vector fields in mechanics, for example to characterize the properties of 3D printed mechanical metamaterials, routine high-precision position measurements are indispensable. For this purpose, nanometer-scale localization errors have been achieved by wide-field optical-image cross-correlation analysis. Here, we bring this approach to atomic-scale accuracy by combining it with well-defined 3D printed marker arrays. By using an air-lens with a numerical aperture of $$0.4$$ 0.4 and a free working distance of $$11.2\, \mathrm{mm}$$ 11.2 mm , and an $$8\times 8$$ 8 × 8 array of markers with a diameter of $$2\, \upmu\mathrm{m}$$ 2 μ m and a period of $$5\,\upmu \mathrm{ m}$$ 5 μ m , we obtain 2D localization errors as small as $$0.9\, \AA$$ 0.9 Å in $$12.5\, \mathrm{ms}$$ 12.5 ms measurement time ( $$80\, \mathrm{frames}/\mathrm{s}$$ 80 frames / s ). The underlying experimental setup is simple, reliable, and inexpensive, and the marker arrays can easily be integrated onto and into complex architectures during their 3D printing process.
其他摘要：Abstract For analyzing displacement-vector fields in mechanics, for example to characterize the properties of 3D printed mechanical metamaterials, routine high-precision position measurements are indispensable. For this purpose, nanometer-scale localization errors have been achieved by wide-field optical-image cross-correlation analysis. Here, we bring this approach to atomic-scale accuracy by combining it with well-defined 3D printed marker arrays. By using an air-lens with a numerical aperture of $$0.4$$ 0.4 and a free working distance of $$11.2\, \mathrm{mm}$$ 11.2 mm , and an $$8\times 8$$ 8 × 8 array of markers with a diameter of $$2\, \upmu\mathrm{m}$$ 2 μ m and a period of $$5\,\upmu \mathrm{ m}$$ 5 μ m , we obtain 2D localization errors as small as $$0.9\, \AA$$ 0.9 Å in $$12.5\, \mathrm{ms}$$ 12.5 ms measurement time ( $$80\, \mathrm{frames}/\mathrm{s}$$ 80 frames / s ). The underlying experimental setup is simple, reliable, and inexpensive, and the marker arrays can easily be integrated onto and into complex architectures during their 3D printing process.
