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

Abstract

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.