Fig. 1: Intrinsic aberrations enable accurate localization microscopy in six degrees of freedom.
From: Accurate localization microscopy by intrinsic aberration calibration

a–c Fluorescence micrographs showing images of a particle at z positions of (a) 2 µm above, (b) near, and (c) 2 µm below best focus. The particle diameter is 1 μm and the resolution limit is 0.7 µm. Two aberration effects are apparent – symmetry variation from astigmatism and intensity variation from defocus. Dots indicate asymmetry in (a, c). Vertical positions correspond to white boxes in (d). d Schematic showing (red) fluorescent particles on part of a complex microsystem. We localize single particles in three dimensions and fit a rigid transformation to measure motion with six degrees of freedom – translations Δx, Δy, and Δz, intrinsic rotation γ about the axis of rotation \(\overrightarrow{{\boldsymbol{u}}}\), nutation β, and precession α. White arrows indicate play due to clearances in the microsystem. (d) Lateral dimensions are nearly to scale. Vertical dimensions are not to scale.