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

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 and a free working distance of 11.2mm, and an 8×8 array of markers with a diameter of 2μm and a period of 5μm, we obtain 2D localization errors as small as 0.9Å in 12.5ms measurement time (80frames/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.