Fourier-Bessel Field Calculation and Tuning of a CW Annular Array

A 1-D Fourier-Bessel series method for computing and tuning the linear lossless field of flat continuous wave (CW) annular arrays is given and discussed with both numerical simulation and experimental verification. The technique provides a new method for modelling and manipulating the propagated field by linking the quantized surface pressure profile to a set of limited diffraction Bessel beams propagating into the medium. In the limit, these become a known set of nondiffracting Bessel beams satisfying the lossless linear wave equation, which allow us to derive a linear matrix formulation for the field in terms of the ring pressures on the transducer surface. Tuning (beamforming) of the field then follows by formulating a least squares design with respect to the transducer ring pressures. Results are presented in the context of a 10-ring annular array operating at 2.5 MHz in water.