High-Resolution Localization with Arbitrary Point Spread Functions

We present a method of three dimensional localization of particles which is agnostic to point spread functions and which achieves high localization resolution. By learning the spatial variation of the imaging system's point spread function using computationally efficient spline surfaces it is possible to utilize convex expectation-maximization localization methods with any imaging system. Perhaps more importantly, this methodology allows for the use of common localization point spread functions (Astigmatism, Double-Helix, Bessel Beam among others) but where strong aberrations might have precluded measurements. In addition to the method we will present experimental results comparing the resolution of this technique to localization where the point spread function is well known.