  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: the "static" errors come from signal noise, and the "dynamic" errors
arise from the motion blur due to finite frame acquisition time. We show that
these errors result in systematic and non-trivial biases in the measured energy
landscapes. We derive a relationship between the true and the measured
potential that elucidates, among other aberrations, the presence of false
double-well minima in the apparent potentials reported in recent studies. We
further assess several canonical trapping and pair-interaction potentials, by
using our analytically derived results and Brownian dynamics simulations. In
particular, we show that the apparent spring stiffness of harmonic potentials
(such as optical traps) is increased by dynamic errors, but decreased by static
errors. Our formula allows for the development of efficient corrections
schemes, which we also present in this paper.
