  This work is concerned with a direct sampling method (DSM) for inverse
acoustic scattering problems using far-field data. The method characterizes
some unknown obstacles, inhomogeneous media or cracks, directly through an
indicator function computed from the measured data. Using one or very few
incident waves, the DSM provides quite reasonable profiles of scatterers in
time-harmonic inverse acoustic scattering without a priori knowledge of either
the physical properties or the number of disconnected components of the
scatterer. We shall first derive the DSM using far-field data, then carry out a
systematic evaluation of the performances and distinctions of the DSM using
both near-field and far-field data. The numerical simulations are shown to
demonstrate interesting and promising potentials of the DSM: a) ability to
identify not only medium scatterers, but also obstacles, and even cracks, using
measurement data from one or few incident directions, b) robustness with
respect to large noise, and c) computational efficiency with only inner
products involved.
