Angular spectrum approach for fast simulation of pulsed non-linear ultrasound fields

The paper presents an Angular Spectrum Approach (ASA) for simulating pulsed non-linear ultrasound fields. The source of the ASA is generated by Field II, which can simulate array transducers of any arbitrary geometry and focusing. The non-linear ultrasound simulation program - Abersim, is used as the reference.

A linear array transducer with 64 active elements is simulated by both Field II and Abersim. The excitation is a 2-cycle sine wave with a frequency of 5 MHz. The second harmonic field in the time domain is simulated using ASA. Pulse inversion is used in the Abersim simulation to remove the fundamental and keep the second harmonic field, since Abersim simulates non-linear fields with all harmonic components.

ASA and Abersim are compared for the pulsed fundamental and second harmonic fields in the time domain at depths of 30 mm, 40 mm (focal depth) and 60 mm. Full widths at -6 dB (FWHM) are f0.97, 0.95g mm at the focal depth for the fundamental fields for ASA and Abersim, and f0.56, 0.55g mm for the second harmonic fields.

Full widths at -12 dB are f1.27, 1.26g mm for the fundamental fields for ASA and Abersim, and f0.77, 0.73g mm for the second harmonic fields. The calculation time, for the second harmonic fields, using ASA is 12 minutes and for all harmonic fields using Abersim is 14 hours. Compared to Abersim, the error of ASA for calculating the second harmonic fields is 1.5% at -6 dB and 6.4% at -12 dB, and the calculation time is reduced by a factor of 70.