Single-Photon Single-Particle Tracking

Mobile biological particles, ranging from biomolecules to viral capsids, often diffuse faster than 1 {micro}m2/s, resulting in severe motion blur in conventional millisecond-scale imaging. While shorter exposures may help provide the data needed to capture faster dynamics, quantization of signal intensity per pixel at such exposures eventually interferes with our ability to track. In the extreme case of binary (1-bit-per-pixel) output-- where going from 8-bit conventional grayscale imaging to 1-bit directly corresponds to a 255-fold faster acquisition rate--no existing tracking methods can be used, as these methods fundamentally rely on intensity-based localization, which does not leverage the binary output. For this reason, we introduce single-photon single-particle tracking (SP2T), a framework that bypasses localization and linking by estimating particle numbers and trajectories directly by jointly considering 1-bit image stacks. While cameras capable of microsecond-scale exposures, typically based on scientific CMOS (sCMOS) sensors or single-photon detectors (SPDs), are increasingly central to this effort, in this work, we focus on single-photon avalanche diode (SPAD). Single-photon detector (SPD) arrays offer microsecond exposures over large fields of view (512x512 pixels). SP2T accounts for detector-specific artifacts such as hot and cold pixels and is validated with programmed fluorescent bead trajectories and biological systems (aerolysin and ganglioside). These experiments, in addition to simulations, reveal that analysis performed with longer exposures can bias diffusion coefficient estimates (up to 70% for particles with diffusion coefficients of 5 {micro}m2/s) and distort jump-distance distributions, underscoring the need for photon-by-photon tracking in fast-diffusion regimes. Moreover, SP2T delivers substantial computational gains--achieving more than a 50-fold GPU speedup over CPU-based likelihood tracking methods that assume continuous intensity, when compared on datasets with the same frame size and number of frames. Together, these advances establish SP2T as a robust, data-efficient solution for unbiased particle tracking with millisecond-to-microsecond temporal resolution.