Fig. 2

Three-dimensional super-resolution imaging over an adjustable axial range. a, b 3D super-resolution images of the nucleoporin Nup133 in HeLa cells reconstructed by ZOLA for a saddle point PSF with oil immersion objective and a tetrapod PSF with water immersion objective, respectively. Color indicates depth z. The axial range is 2 μm in a, showing the bottom portion of the nucleus, and 5 μm in b, allowing to visualize almost the entire nucleus. The (x′, z) view shows a projection from the region of interest enclosed by the violet dashed rectangle. Magnified views of pink boxed regions show nuclear pores visible as ring-like structures. Scale bars are 5 μm for the main images, and 0.5 μm for insets and (x′, z) projections. c, e 3D super-resolution images of microtubules in a U-373 MG cell. The same cell was imaged first with an astigmatic PSF (c), then with a saddle point PSF (e). The astigmatic PSF enables an axial range of 1 μm, allowing to visualize the bottom of the cell. The saddle point PSF enables an axial range of 2.5 μm, allowing to visualize the full cell. The (x′, z) view shows a projection from the region of interest enclosed by the violet dashed rectangle. Scale bars are 5 μm for the main images, 0.5 μm for insets and (x′, z) projections. d, f Histograms (2D and 1D) show the distribution of lateral and axial (z) coordinates of localizations across microtubule filaments at the three positions indicated by the pink rectangles in images c and e above. The number of localizations (N) and the mean z-coordinate (\(\bar z_{}^{}\)) are indicated. Black curves show the probability densities of axial and lateral coordinates expected for optimal precision, based on the average theoretical precision limits (Cramér–Rao lower bounds \(\bar \sigma _{xy}^{\mathrm {CR}}\) and \(\bar \sigma _z^{\mathrm {CR}}\) of lateral and axial localization errors are indicated) and the diameter of immunolabeled tubulin filaments (see Supplementary Fig. 8). Full width at half maxima of the probability densities are indicated below double arrows. The good match between the theoretical probability densities and the experimental histograms indicates that ZOLA achieves optimal precision at all depths