Modulation enhanced multi-emitter localization microscopy

Abstract

For a long time, scientists believed that it is not possible to achieve a better microscopic resolution than half the wavelength of light (~ 200 nm). During the last decades, various super-resolution fluorescence microscopy techniques have been developed, offering high-resolution imaging beyond the diffraction limit. It has been established as one of the major tools currently available for the study and analysis of biological tissues. The observation of, previously limited and unclear, cellular structures has demonstrated the great promise of super-resolution fluorescence microscopy in exemplifying biological processes at the cellular level. Inherently, single-molecule localization microscopy (SMLM) is based upon acquiring a sequence of diffraction-limited images, consisting of localizations of sparsely distributed emitting fluorophores. Next, precise and accurate estimates of the spatial coordinates of the fluorophores, placed on the structures of interest, are made. Subsequently, all recovered emitter positions from each frame are combined, and a super-resolution image is generated. One of the most crucial questions in SMLM concerns the precision with which the location of a single molecule can be determined. The Cramér–Rao lower bound (CRLB) is used to quantify the estimation performance in terms of localization precision. Recently, several modulation enhanced methods have shown resolution improvement by combining structured patterned illumination with SMLM techniques, such as MINFLUX and SIMFLUX. However, the analysis of images by SMLM and these modulation enhanced methods requires sparse activation regions to prevent overlap between active emitters. Recently, several methods have been developed with the ability to analyze higher density data, allowing partial overlap between emitters. In this work, we propose a maximum likelihood-based, modulation enhanced SMLM method able to localize multiple active emitters within a single region of interest (ROI), which we refer to as Multi- SIMFLUX. The mathematical framework of the algorithm is comprehensively built up throughout this work. The performance of the algorithm has been evaluated, and validated under a wide range of realistic imaging conditions. This involves various active-emitter densities, different emitter- and background intensities, numerous emitter configurations, a multitude of ROI-sizes and point spread function widths. As theoretically expected, our approach significantly outperforms conventional 2DGaussian SMLM with a twofold improvement factor in terms of localization precision for various emitter densities and intensities. At higher active emitter imaging densities, the extension from a single to a multi-emitter approach showed a clear improvement in recall fraction.