Optimization of Fresnel-zones-based Double Helix Point Spread Function and measurement of particle diffusion coefficient

Abstract In the field of microscopic imaging, the double-helix point spread function (DH-PSF) based on the Fresnel zones is often used to locate the three-dimensional position of particles. The lower transfer function efficiency makes it difficult to track the trajectory of moving particles in real-time, especially when the particles are far from the initial focal plane. We proposed a method based on the iterative Fourier transform algorithm and the Fresnel approximate imaging to optimize the phase which is used to generate the DH-PSF. The optimized DH-PSF has been significantly improved throughout the rotation process, and the maximum peak intensities of some positions have been increased by 82.31%. The main lobe strength of the optimized DH-PSF has been significantly improved, which was proved in vector diffraction simulation and practical experiments. After that, the optimized DH-PSF was used to track the 3D motion trajectories of nanoparticles with different shapes, and their diffusion coefficients were calculated. Experiments show that the optimized DH-PSF can quickly and accurately obtain the 3D motion trajectories of nanoparticles of various shapes and accurately calculate their diffusion coefficients in various solutions, which is important for the development of nanomedicine.