P1C045-07. Feasibility of Non-Linear Simulation for Field II Using an Angular Spectrum Approach

Simulation of non-linear fields is most often restricted to single element, circularly symmetric sources, which is not used in clinical scanning. To obtain a general and valuable simulation, array transducers of any geometry with any excitation, focusing, and apodization should be modeled. Field II is restricted to simulate these for the linear case and the purpose of this paper is to develop a general frame work for extending it to non-linear simulation. The extension to the non-linear domain is made by using the angular spectrum approach (ASA), where the field is calculated in a plane close to the transducer surface. This calculation is performed using Field II and, thus, includes modeling array transducers of any geometry with any excitation, focusing, and apodization. The propagation in the linear or nonlinear medium is then performed using the angular spectrum approach. The first step in deriving this procedure is to find the accuracy of the approach for linear propagation, where the result can be validated using Field II simulations. The ASA calculations are carried out by 3D fast Fourier transform using Matlab, where λ/2 is chosen as the spatial sampling rate to reduce aliasing errors. Zero-padding is applied to enlarge the source plane to a (4N-1)(4N-1) matrix to overcome artifacts in terms of the circular convolution. The source plane covering an area of 99 mm with N = 61 samples along both side, is 0.05 mm away from a 5 MHz planar piston transducer, which is simulated by Field II. To determine the accuracy, different sampling intervals and zero-paddings are compared and the errors are calculated with Field II as a reference. It can be seen that zero-padding with 4N1 and λ/2 sampling can both reduce the errors from 25.7% to 12.9% for the near-field and from 18.1% to 5.8% for the far-field, and improve the price of an increase in computation time. The angular spectrum approach in combination with Field II opens for the possibility of simulating the non-linear acoustic propagation for any kind of array transducers.