# Localizing axial dense emitters based on single-helix point spread function and compressed sensing

## TL;DR

This paper introduces a new method for 3D single molecule localization microscopy that improves temporal resolution while maintaining accuracy.

## Contribution

The novel SH-CS method combines light needle excitation, single helix PSF, and compressed sensing for axial localization.

## Key findings

- SH-CS achieves axial localization accuracy between 12.1–73.5 nm for 1–15 molecules in a 4 μm depth range.
- The method is validated using a 3D sample of fluorescent beads.
- SH-CS is suitable for relatively dense molecule distributions.

## Abstract

Among the approaches in three-dimensional (3D) single molecule localization microscopy, there are several point spread function (PSF) engineering approaches, in which depth information of molecules is encoded in 2D images. Usually, the molecules are excited sparsely in each raw image. The consequence is that the temporal resolution has to be sacrificed. In order to improve temporal resolution and ensure localization accuracy, we propose a method, SH-CS, based on light needle excitation, detection system with single helix-point spread function (SH-PSF), and compressed sensing (CS). Although the SH-CS method still has a limitation about the molecule density, it is suited for relatively dense molecules. For each light needle scanning position, an SH image of excited molecules is processed with CS algorithm to decode their axial information. Simulations demonstrated, for random distributed 1–15 molecules in depth range of 4 μm, the axial localization accuracy is 12.1–73.5 nm. The feasibility of this method is validated with a designed 3D sample composed of fluorescent beads.