Measurements of the stability of the effective apodization for the nonlinearly generated second harmonic as a function of propagation distance

Abstract

The concept of an effective apodization was introduced to approximate the nonlinearly generated second harmonic field pattern based solely on the linear propagation of a field transmitted at the frequency of the harmonic. We have previously demonstrated that transmitting with an effective apodization determined from measurements made only in the focal plane yields an accurate description of the nonlinearly generated field over a very wide range of depths. The goal of this work was to determine the stability of the effective apodizations obtained from measurements of the ultrasonic field in a series of planes before and beyond the focal zone. Transverse 2D scans of the transmitted fields were performed with a 0.6-mm-diam. hydrophone for both vascular and cardiac arrays. Linear angular spectrum backpropagation of the measured fields determined the effective apodizations. These measurements were compared with simulations based on a nonlinear Burgers equation enhanced angular spectrum approach. The resulting effective apodizations of the second harmonic field were remarkably constant (differing by typically a few percent and never by more than 9.4% from the mean) for ten axial positions ranging from 0.1 to 1.6 times the focal distance. [Work supported by NIH HL072761 and Philips Medical Systems.]