Angular Spectrum Simulation of Pulsed Ultrasound Fields

The optimization of non-linear ultrasound imaging should in a first step be based on simulation, as this makes parameter studies considerably easier than making transducer prototypes. Such a simulation program should be capable of simulating non-linear pulsed fields for arbitrary transducer geometries for any kind of focusing and apodization.

The Angular Spectrum Approach (ASA) is capable of simulating monochromatic non-linear acoustic wave propagation. However, for ultrasound imaging the time response of each specific point in space is required, and a pulsed ASA simulation with multi temporal frequencies must be performed. Combining it with Field II, the generation of non-linear simulation for any geometry with any excitation array transducer becomes feasible.

The purpose of this paper is to make a general pulsed simulation software using the modified ASA. Linear and phased array transducers are used to create the source plane, which is 2 mm from the transducer surface. Field II generates pulses for all the points in the source plane, and the 3D matrix data (1D time, 2D space) are obtained.

The pulses in the simulated plane are calculated by the modified ASA, which is the 3D inverse Fourier transform of the values in a series of planes corresponding to each temporal frequency. The values in the planes are the multiplications between the 2D spatial Fourier transform of the pressure in the source plane and the ASA propagator for every temporal frequency components.

The beam focusing is produced by Field II in the source plane. A rectangular plane matched to the shape of the transducer surface is chosen as the source. The plane covering 12.7?156.3 mm2 has 33?407 points with a spatial sampling interval of 1/2 wavelength. A comparison of ASA to Field II at the focal point (0, 0, 64) mm for a 64-element, 2 MHz linear array transducer has been made in the paper, and the root mean square (RMS) error is 2.7%.

For further validation, 3 randomly selected points in - - the simulated plane have RMS errors of 12.5%, 13.3%, 23.4% at the positions (3.9, -1.5, 64), (-1.9, 1.9, 64), (6.2, -4.2, 64) mm. The RMS error of the pulses for all points in the simulated plane is 10.9%. The good agreement between ASA and Field II simulation for the pulsed ultrasound fields obtained in this paper makes it possible to expand Field II to non-linear pulsed fields.