On the application of the Rayleigh integral to the calculation of the field of a concave focusing radiator

The acoustic field of a focusing radiator made in the form of a spherical b owl is studied both theoretically and experimentally. Special attention is paid to the diffraction effects related to the concavity of the surface and the presence of protrusions at the edge of the radiator. In the geometric approximation, the aforementioned effects are related to multiple reflectio ns of waves from the radiating surface and the scattering of these waves by the edge. Theoretically, it is shown that in the case of a weakly focusing radiator, the Rayleigh integral adequately describes the acoustic held awa y from the radiating surface, but near the surface it leads to considerable errors. At large focusing angles, noticeable deviations from the true acou stic field occur also at greater distances from the radiator. However, the diffraction effects can be adequately described when a single reflection of waves from the concave surface is taken into account. To estimate the edge effects, experimental studies of the field of a concave piezoceramic trans ducer with the curvature radius 100 mm, the aperture radius 50 mm, and the operating frequency 1 MHz have been performed. Different edge conditions ar e obtained by mounting thick metal rings of different shapes over the trans ducer perimeter. It is found that these conditions have practically no effe ct on the axial acoustic field. The results of the theoretical and experime ntal studies lead to the conclusion that the Rayleigh integral can be used for calculating the fields of real concave transducers even at large focusi ng angles.