Phase stretch transform for super-resolution localization microscopy.

Super-resolution localization microscopy has revolutionized the observation of living structures at the cellular scale, by achieving a spatial resolution that is improved by more than an order of magnitude compared to the diffraction limit. These methods localize single events from isolated sources in repeated cycles in order to achieve super-resolution. The requirement for sparse distribution of simultaneously activated sources in the field of view dictates the acquisition of thousands of frames in order to construct the full super-resolution image. As a result, these methods have slow temporal resolution which is a major limitation when investigating live-cell dynamics. In this paper we present the use of a phase stretch transform for high-density super-resolution localization microscopy. This is a nonlinear frequency dependent transform that emulates the propagation of light through a physical medium with a specific warped diffractive property and applies a 2D phase function to the image in the frequency domain. By choosing properly the transform parameters and the phase kernel profile, the point spread function of each emitter can be sharpened and narrowed. This enables the localization of overlapping emitters, thus allowing a higher density of activated emitters as well as shorter data collection acquisition rates. The method is validated by numerical simulations and by experimental data obtained using a microtubule sample.