Practical Limits of the Parabolic Approximation for Focused Ultrasound Beams

Applying the parabolic approximation to the wave equation results in a far simpler and more tractable model for ultrasound propagation. The approximate (Kuznetsov) model assumes that sound propagates predominantly in the axial direction and that the pressure amplitude is a slowly varying function of the axial coordinate. Since the terms "predominantly" and "slowly" ar far from quantitative descriptors, and since recent work shows excellent agreement between simulation and experiment at surprisingly low F-numbers, the present work seeks to more firmly establish the region of validity of this approximation for focused ultrasound sources. To this end, the focused beam of a flat panel transducer is modeled using both the full wave equation and its parabolic approximation. The simulation results are compared as a function of focusing depth and beam steering angle.