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Single molecule localization microscopy (SMLM) detects and locates sparsely luminous single fluorescent molecules to achieve super-resolution imaging at nanoscale spatial resolution. In order to improve the temporal resolution, it is necessary to increase the density of the simultaneously emitting molecules. However, with the increase of the density, the point spread function (PSF) of different molecules will overlap severely on the detector, resulting in reduced spatial resolution, especially for three-dimensional (3D) SMLM. To solve this problem, a high density 3D-SMLM imaging method based on orthogonal astigmatism is proposed. Analysis and numerical simulation study for the method are carried out and presented. The main idea of the proposed orthogonal astigmatic method is to split the collected fluorescence in a SMLM microscope into two beams, each of which paths through a separate channel with a cylindrical lens and arrives at a specific region on the same detector. The two cylindrical lenses have the same optical parameters, but their orientations are set to be orthogonal to each other. They are used to obtain both positive and negative astigmatic PSF images of the same fluorescent molecule. Then, a linear projection model of the imaging process is established, and the 3D localization of the fluorescent molecules is realized using a compression sensing algorithm. The results show that, the two orthogonal cylindrical lenses produce a pair of astigmatic PSFs for one single molecule so that different PSF pairs between different molecules have lower mutual correlation, and thus the 3D localization accuracy for high density imaging can be significantly improved compared to traditional astigmatic method using one single cylindrical lens, and the larger the defocusing degree, the greater the shape difference between the two astigmatic PSFs, the more obvious this advantage is.

Numerical simulation study of three-dimensional high-density single molecule localization microscopy based on orthogonal astigmatism