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 [Formula: see text] and a free working distance of [Formula: see text], and an [Formula: see text] array of markers with a diameter of [Formula: see text] and a period of [Formula: see text], we obtain 2D localization errors as small as [Formula: see text] in [Formula: see text] measurement time ([Formula: see text]). 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.