Tracking Without Linking or Localization: Single-Photon Tracking

Abstract

Mobile biological particles, ranging from biomolecules to viral capsids, often diffuse faster than 1m2/s, resulting in severe motion blur in conventional millisecond-scale imaging. Shorter exposures capture faster dynamics, but quantizing the per-pixel signal at such exposures eventually degrades our ability to localize particles at all. In the extreme case of binary (1-bit-per-pixel) output--where moving from 8-bit grayscale to 1-bit corresponds to a 255-fold faster acquisition rate--no existing tracking method applies, since all of them rely on intensity-based localization that binary data cannot supply. We therefore introduce single-photon single-particle tracking (SP2T), a framework that bypasses localization and linking by estimating particle numbers and trajectories directly from the full 1-bit image stack. We demonstrate SP2T on single-photon avalanche diode (SPAD) arrays, which deliver microsecond exposures over a large field of view (512x512 pixels) and explicitly account for detector-specific artifacts such as hot and cold pixels. We validate the method against programmed fluorescent bead and organic dye trajectories, and apply it to two biological systems, aerolysin and ganglioside GM1. Together with simulation, these experiments reveal that longer exposures bias diffusion coefficient estimates (by up to 70% for particles diffusing at 5m2/s) and distort jump-distance distributions, underscoring the need for photon-by-photon tracking in fast-diffusion regimes. Evaluating the likelihood on a GPU further delivers more than a 50-fold speedup over a CPU implementation when compared on datasets of the same frame size and number of frames, enabling multiplexed tracking for crowded particles. Together, these advances establish SP2T as a robust, data-efficient route to unbiased particle tracking at microsecond temporal resolution.