  The wave equation on a bounded domain of $\R^{n}$ with non homogeneous
boundary Dirichlet data or sources supported on a subset of the boundary is
considered. We analyze the problem of observing the source out of boundary
measurements done away from its support.
  We first show that observability inequalities may not hold unless an infinite
number of derivatives are lost, due to the existence of solutions that are
arbitrarily concentrated near the source.
  We then establish observability inequalities in Sobolev norms, under a
suitable microlocal geometric condition on the support of the source and the
measurement set, for sources fulfilling pseudo-differential conditions that
exclude these concentration phenomena.
  The proof relies on microlocal arguments and is essentially based on the use
of microlocal defect measures.
