  We demonstrate differential dynamic microscopy and particle tracking for the
characterization of the spatiotemporal behavior of active Janus colloids in
terms of the intermediate scattering function (ISF). We provide an analytical
solution for the ISF of the paradigmatic active Brownian particle model and
find striking agreement with experimental results from the smallest length
scales, where translational diffusion and self-propulsion dominate, up to the
largest ones, which probe effective diffusion due to rotational Brownian
motion. At intermediate length scales, characteristic oscillations resolve the
crossover between directed motion to orientational relaxation and allow us to
discriminate active Brownian motion from other reorientation processes, e.g.,
run-and-tumble motion. A direct comparison to theoretical predictions reliably
yields the rotational and translational diffusion coefficients of the
particles, the mean and width of their speed distribution, and the temporal
evolution of these parameters.
