Tempering Rayleigh's curse with PSF shaping

TL;DR

This paper challenges the traditional view of Rayleigh's curse by introducing a class of PSFs with linear information decay and demonstrates superresolution using a simple signum filter, improving imaging resolution.

Contribution

It shows that symmetric PSFs can be transformed to mitigate Rayleigh's curse, enabling superresolution with simple filtering techniques.

Findings

Identified PSFs with linear information decay

Implemented signum filter to enhance resolution

Experimentally demonstrated superresolution capabilities

Abstract

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.