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.

在显微成像领域，常使用基于菲涅耳区的双螺旋点扩散函数（DH-PSF）来定位粒子的三维位置。较低的传递函数效率使得很难实时跟踪运动粒子的轨迹，尤其是当粒子远离初始焦平面时。我们提出了一种基于迭代傅里叶变换算法和菲涅耳近似成像的方法来优化用于生成DH-PSF的相位。优化后的DH-PSF在整个旋转过程中得到了显着提升，部分位置的最大峰值强度提高了82.31%. 优化后的 DH-PSF 的主瓣强度得到了显着提高，这在矢量衍射模拟和实际实验中得到了证明。之后，使用优化后的 DH-PSF 跟踪不同形状纳米粒子的 3D 运动轨迹，并计算它们的扩散系数。实验表明，优化后的 DH-PSF 可以快速准确地获得各种形状纳米粒子的 3D 运动轨迹，并准确计算其在各种溶液中的扩散系数，这对纳米医学的发展具有重要意义。