Supplementary Figure 3: The axial localization precision determined from the Cramér–Rao lower bound.

The data from Fig. 1L is presented here containing a total of nine beads at different depths. A) The best axial localization precision is plotted for each PSF with the shaded regions representing the average localization precision calculated from CRLB at ±500 nm from the axial position of the optimal localization precision. The lines correspond to the axial localization precision for the imaged beads with no AO correction (short dashed line, cyan shade), AO correction (long dashed line, magenta shade), and AO with AA (solid line, yellow shade). Constant astigmatism was used for no AO and AO, while adaptive astigmatism was used to preserve the PSF modulation at each depth. B) Astigmatic PSF cutouts from depths of 14.4 µm (green outline), 120 µm (blue outline) and 170 µm (red outline) recorded at three different focal positions (top panel: +480 nm, middle: in focus and bottom: -480 nm) illustrate the difference in PSF quality. PSFs beyond the coverslip and not corrected with AO feature suppressed stretching when out of focus, limiting the precision of axial localization. Number of photons of bead and background used in simulation: 1000 photons and 10 background for AO and AO+AA. Photon numbers decrease without AO and were estimated as described in Methods.