  Cold-atom experiments in optical lattices offer a versatile platform to
realize various topological quantum phases. A key challenge in those
experiments is to unambiguously probe the topological order. We propose a
method to directly measure the characteristic topological invariants (order)
based on the time-of-flight imaging of cold atoms. The method is generally
applicable to detection of topological band insulators in one, two, or three
dimensions characterized by integer topological invariants. Using detection of
the Chern number for the 2D anomalous quantum Hall states and the Chern-Simons
term for the 3D chiral topological insulators as examples, we show that the
proposed detection method is practical, robust to typical experimental
imperfections such as limited imaging resolution, inhomogeneous trapping
potential, and disorder in the system.
