Fluorescence phase-shifting interferometry for axial single particle tracking: a numerical simulation study

Tracking of single fluorescent probes along the axial (depth) dimension is an important task in the biological and physical sciences. In this paper, we propose and analyze the use of fluorescence phase-shifting interferometry (FPSI) for axial single particle tracking (SPT) along 1 μm-depth (z) trajectories. FPSI is a photon-efficient, self-interference method that collects and coherently combines the 4π steradian emission wavefronts of a single fluorescent particle while introducing multiple phase shifts between the wavefronts to axially localize the particle with high precision over an extended depth-of-field. We employ vectorial imaging analysis and Monte-Carlo simulations of diffusive and directed motions to present a detailed comparative study of spatial and temporal FPSI for axial SPT based on simultaneous and time sequential collection of four phase-shifted interferograms using a single camera, respectively. The results of the numerical simulations show that for ≤0.105 μm2/s diffusion, spatial FPSI attains a maximal twofold improvement in the trajectory reconstruction precision at the expense of a fourfold reduced field-of-view compared to temporal FPSI. Furthermore, the analysis predicts that for sufficiently slow random linear motions, temporal FPSI is superior to spatial FPSI and achieves a smaller trajectory reconstruction error.