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