What is resolution? A statistical minimax testing perspective on superresolution microscopy

As a general rule of thumb the resolution light microscope (i.e., ability to discern objects) is predominantly described by full width at half maximum (FWHM) its point spread function (psf)—the diameter blurring density maximum. Classical wave optics suggests linear relationship between FWHM and also manifested in well-known Abbe Rayleigh criteria, dating back end 19th century. However, during last two decades conventional microscopy has undergone shift from microscopic scales nanoscales. This increase comes with need incorporate random nature observations (light photons) challenges classical view discernability, as we argue this paper. Instead, suggest statistical description obtained such data. Our notion discernability based on testing whether one or objects same total intensity are present. For Poisson measurements, get dependence (minimax) detection boundary FWHM, whereas for homogeneous Gaussian model nonlinear. Hence, small physical modeling gaussians inadequate, although often implicitly assumed many reconstruction algorithms. In contrast, variance stabilized approximation seem provide statistically sound nanoscale. theory applicable other imaging setups, telescopes.