Sound field separation for planar sources facing a parallel reflector

We consider the problem of separating and reconstructing the sound field radiated by a planar source, e.g. a vibrating plate, that faces a parallel reflector. For this purpose we propose a Fourier-based technique to process near-field microphone array measurements that are performed on a single plane between the plate and the reflector. A closed-form expression is derived in the wavenumber domain to recover the free-space sound field radiated by the plate. The fundamental assumption is that the plate scatters sound in a locally-reacting fashion. Overall, provided the admittances of the plate and the reflecting surface are known, the results demonstrate that it is possible to recover the free-field sound radiated by the plate with a reasonable accuracy.