Tempering Rayleigh's curse with PSF shaping

It has been argued that, for a spatially invariant imaging system, the information one can gain about the separation of two incoherent point sources decays quadratically to zero with decreasing separation, an effect termed Rayleigh's curse. Contrary to this belief, we identify a class of point spread functions with a linear information decrease. Moreover, we show that any well-behaved symmetric point spread function can be converted into such a form with a simple nonabsorbing signum filter. We experimentally demonstrate significant superresolution capabilities based on this idea.