  Point-spread-function (PSF) engineering is a well-established computational
imaging technique that uses phase masks and other optical elements to embed
extra information (e.g., depth) into the images captured by conventional CMOS
image sensors. To date, however, PSF-engineering has not been applied to
neuromorphic event cameras; a powerful new image sensing technology that
responds to changes in the log-intensity of light.
  This paper establishes theoretical limits (Cram\'er Rao bounds) on 3D point
localization and tracking with PSF-engineered event cameras. Using these
bounds, we first demonstrate that existing Fisher phase masks are already
near-optimal for localizing static flashing point sources (e.g., blinking
fluorescent molecules). We then demonstrate that existing designs are
sub-optimal for tracking moving point sources and proceed to use our theory to
design optimal phase masks and binary amplitude masks for this task. To
overcome the non-convexity of the design problem, we leverage novel implicit
neural representation based parameterizations of the phase and amplitude masks.
We demonstrate the efficacy of our designs through extensive simulations. We
also validate our method with a simple prototype.
