Astigmatism-based superresolution microscopy is widely used to determine the position of individual fluorescent emitters in three-dimensions (3D) with subdiffraction-limited resolutions. This point spread function (PSF) engineering technique utilizes a cylindrical lens to modify the shape of the PSF and break its symmetry above and below the focal plane. The resulting asymmetric PSFs at different z-positions for single emitters are fit with an elliptical 2D-Gaussian function to extract the widths along two principle x- and y-axes, which are then compared with a pre-measured calibration function to determine its z-position. While conceptually simple and easy to implement, in practice, distorted PSFs due to an imperfect optical system often compromise the localization precision; and it is laborious to optimize a multi-purpose optical system. Here we present a methodology that is independent of obtaining a perfect PSF and enhances the localization precision along the z-axis. By utilizing multiple calibration images of fluorescent beads at varying z-planes and characterizing experimentally measured background distributions, we numerically approximated the probability of observing a certain signal in a given pixel from a single emitter at a particular z-plane. We then used a weighted maximum likelihood estimator (WLE) to determine the 3D-position of the emitter. We demonstrate that this approach enhances z-axis localization precision in all conditions we tested, in particular when the PSFs deviate from a standard 2D Gaussian model.

Improved single-molecule localization precision in astigmatism-based 3D superresolution imaging using weighted likelihood estimation