Any imaging technique is limited by its field of view. As objects or particles move in and out of the observation field, tracking their motion, especially over long periods, becomes challenging. In addition, available analysis techniques face challenges in reconstructing trajectories in dense and heterogeneous systems where accurately labeling particles is difficult. Here, we shift this paradigm by introducing a broadly applicable technique that probes dynamics simply by counting particles in finite observation boxes.
Using colloidal experiments, simulations, and theory, we demonstrate that statistical properties of fluctuating counts can be used to determine self-diffusion coefficients. Our framework alleviates the hurdles associated with trajectory reconstruction. We subsequently show that by increasing the observation box size, counting naturally enables the study of collective dynamics.
We extend our technique to various suspensions, such as ions or active particles. The "Countoscope'' offers the unique possibility to systematically link individual and collective behavior, opening up broad soft matter and statistical physics perspectives.