Beam-forming using multidimensional sigma-delta modulation

A new beam-forming technique for an ultrasonic transmitting array using multidimensional sigma-delta (ΣΔ) modulation is described. Waveforms required for driving the array are converted to binary streams which are oversampled spatially and temporally. The ultrasonic wavefront generated by the binary streams is approximately equal to the one generated by the original driving waveforms. The shapes and the levels of the transmitted beams are controlled precisely with simple electrical circuits since the large dynamic range waveforms are replaced with binary ones. In this paper, various array geometries are presented. Computer simulation and experimental results using a linear array made of VDF-TrFe copolymer are presented for evaluation and demonstration of the applicability of the proposed method