Nonlinear Ultrasound Fields Generated by an Annular Array with Electronic and Geometric Adjustment of its Focusing Angle

Linear and nonlinear fields produced by a twelve-ring annular array with varied axial electronic focus steering distances and varied number of activated elements were simulated using wide-angle parabolic representation of the Westervelt equation. The effects of electronic adjustment of the focusing angle and/or switching off the array elements were investigated with regard to the shock-forming conditions at the focus and in the grating lobes in water. Prefocal steering was shown to result in shock formation in the postfocal grating lobe, which can occur at lower array power than that required for shock formation at the main focus. Postfocal steering resulted in shock formation at the main focus and no shock in the prefocal grating lobe at any power considered. To decrease focusing angle, switching off the outer rings was more favorable than postfocal steering with all rings enabled: a fully developed shock of the same amplitude formed at the same source pressure amplitude but with lower pressure level in the prefocal grating lobe. To increase focusing angle, prefocal steering with the outer rings switched off was less favorable than using all array elements with no steering: higher source pressure amplitude was required for a fully developed shock formation at the focus, with additional shock fronts forming in the postfocal grating lobe.