  We deal with the stability issue for the determination of outgoing
time-harmonic acoustic waves from their far-field patterns. We are especially
interested in keeping as explicit as possible the dependence of our stability
estimates on the wavenumber of the corresponding Helmholtz equation and in
understanding the high wavenumber, that is frequency, asymptotics.
  Applications include stability results for the determination from far-field
data of solutions of direct scattering problems with sound-soft obstacles and
an instability analysis for the corresponding inverse obstacle problem.
  The key tool consists of establishing precise estimates on the behavior of
Hankel functions with large argument or order.
