Propagation and backpropagation for ultrasonic wavefront design

TLDR

Wave backpropagation enables calculation of array excitation signals to generate a specified field devoid of evanescent components and to predict far‑field patterns from aperture measurements, with three primary methods—diffraction integral, angular spectrum, and shift‑and‑add—applicable in uniform media. The study analyzes implicit boundary conditions of these propagation methods, explores their interrelations, and demonstrates how the angular‑spectrum approach can be extended to alternative boundaries, using backpropagation to design excitation signals for a ring transducer that generates a localized pulsatile plane wave.

Abstract

Wave backpropagation is a concept that can be used to calculate the excitation signals for an array with programmable transmit waveforms to produce a specified field that has no significant evanescent wave components. This concept can also be used to find the field at a distance away from an aperture based on measurements made in the aperture. For a uniform medium, three methods exist for the calculation of wave propagation and backpropagation: the diffraction integral method, the angular spectrum method, and the shift-and-add method. The boundary conditions that are usually implicitly assumed by these methods are analyzed, and the relationship between these methods are explored. The application of the angular spectrum method to other kinds of boundary conditions is discussed, as is the relationship between wave backpropagation, phase conjugation, and the time-reversal mirror. Wave backpropagation is used, as an example, to calculate the excitation signals for a ring transducer to produce a specified pulsatile plane wave with a limited spatial extent.