Fig. 4: Comparison with astigmatic 4Pi PSF-based approaches.

Previously reported 4Pi-SMLM microscopes use a shaped astigmatic 4Pi PSF, together with an analysis that measures both the ellipticities and the interference phases of the fluorophore images, to help avoid localization artifacts. a, Side-by-side comparison of simulated astigmatic 4Pi and symmetric 4Pi PSFs, rendered as four-color isosurfaces at 35% and 8% of maximum intensity. b, Localization precision comparison for the astigmatic 4Pi PSF using the ellipticity-phase analysis^13,22 and the symmetric 4Pi PSF using the dynamic spline analysis. Simulated fluorophore images were generated on the basis of the two PSFs, using realistic photon counts (mean 8,000 photons) and signal-to-noise ratio (10 background photons per pixel), and the data were analyzed with the indicated method. The results show that while both approaches reached a similar localization precision at the focal plane (z = 0), for the astigmatic case the precision falls off sharply for positions further than 300 nm from focus. By contrast, the dynamic spline fit maintains a relatively constant precision over the full z range of the simulation. The frequency of localization artifacts for the two methods is evaluated in Supplementary Fig. 20.