Analysis of the ultrasonic field radiated by time-delay cylindrically focused linear arrays

The ultrasonic field at the scanning central plane of a linear array whose driving delays are quadratically varied for cylindrical focusing is studied. An efficient and accurate algorithm based on the classical time domain convolution-impulse response methodology is applied for calculations. The method takes into account the full size of the array elements and does not use any paraxial or far-field approximations. The cases of linear and sector scanning are studied. Patterns of array impulse responses h(A)(x ,t) at selected field zones, including the main propagation axis and the focal line, are described for different steering conditions. In order to facilitate the analysis of h(A)(.) curves, a set of temporal and spatial parameters are defined. In particular, the concepts of "elements" times of arrival vectors" and "virtual aperture" are shown to be helpful in achieving a simple interpretation of array fields. Plots of pressure under wide-band and continuous-wave radiations are also presented and discussed. In particular, several discrepancies with classical approaches are mentioned, as well as other aspects of the focused held such as the location of the point of maximum amplitude, and the lateral deterioration and asymmetries caused by steering.