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In this article, we propose a strategy for the active manipulation of scalarHelmholtz fields in bounded near field regions of an active source whilemaintaining desired radiation patterns in prescribed far field directions. Thiscontrol problem is considered in two environments: free space and respectively,homogeneous ocean of constant depth. In both media, we proved the existence ofand characterized the surface input, modeled as Neumann data (normal velocity)or Dirichlet data (surface pressure) such that the radiated field satisfies thecontrol constraints. We also provide a numerical strategy to construct thispredicted surface input by using a method of moments-approach with a Morozovdiscrepancy principle-based Tikhonov regularization. Several numericalsimulations are presented to demonstrate the proposed scheme in scenariosrelevant to practical applications.

Active manipulation of Helmholtz scalar fields: Near field synthesis with directional far field control