Splicing exponential point spread function design for localization of nanoparticles.

We propose a point spread function for three-dimensional localization of nanoparticles. The axial detection range of the point spread function can be simply changed by adjusting the design parameters. In addition, the spatial extent of the point spread function can also be changed by adjusting the design parameters, which is an advantage other point spread functions do not have. We used our point spread functions and the existing point spread functions for dense multi-particle imaging, which proved the advantage that the point spread function with a smaller spatial extent we designed can effectively reduce the overlap between the point spread functions. The three-dimensional process of the fluorescent microsphere penetrating HT-22 cell membrane was successfully recorded, which verified the effectiveness of this method.

Particles 3D tracking with large axial depth by using the 2π-DH-PSF.

We propose a 2π-double-helix point spread function (2π-DH-PSF) using the Fresnel zone approach that can rotate 2π rad. When 16 Fresnel zones are used, the particles can be tracked in the axial range of 10 µm in a 100× microscopy imaging system (NA=1.4, λ=514nm). We measured the diffusion coefficient of nanospheres in different concentrations of glycerol with the 2π-DH-PSF, and the error between the measured results and theoretical value was within 10%, indicating the superior performance of 2π-DH-PSF in 3D localization imaging of nanoparticles. When combined with the defocus phase, the rotation angle can reach 4π rad, four times that of the conventional DH-PSF.

Three-dimensional diffusion coefficient measurement by a large depth-of-field rotating point spread function.

A prominent challenge in single-molecule localization microscopy is the real-time, fast, and accurate localization of nano-objects moving in three-dimensional (3D) samples. A well-established method for 3D single-molecule localization is the double-helix pointspread-function (DH-PSF) engineering, which uses additional optical elements to make the PSF exhibit different rotation angles with different nanoparticle depths. However, the compact main lobe size, effective detection depth, and precise conversion between rotation angle and depth are necessary, posing challenges to the DH-PSF generation method. Here we generate a more compact DH-PSF using Fresnel-zone-based spiral phases, and the pure phase mask achieves high transmission efficiency. The final generated DH-PSFs have a linear rotation rate at each axial position, showing a more accurate rotation angle and depth conversion. The Cramer-Rao lower limit calculation results show that the axial depth of DH-PSF extends to ∼11µm with an axial localization precision of ∼45nm at 3000 photons and average background noise of 15. We measured the diffusion coefficient of nanospheres in different concentrations of glycerol using the generated DH-PSF. The measured results are within 6% error from the theoretical values, indicating the superior performance of the DH-PSF for nanoparticle diffusion coefficient measurements.