Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: signal noise (or "static" errors) and motion blur ("dynamic" errors). We derive an equation for the measured energy landscape contaminated by these errors, which notably elucidates the presence of false double-well minima in the apparent potentials reported in recent studies. Our formula also allows for the development of post-measurement corrections schemes for reconstructing true potentials from the measured ones.