Fast and accurate nonlinear pressure field simulation: A finite-difference scheme into the Fourier domain

The linear propagation of ultrasound in tissues is an approximation of the reality because harmonics are induced during the propagation. Various nonlinear pressure simulation tools exist in the literature but still require a long computation time. A previous published tool, based on a generalized angular spectrum method, quickly computes the fundamental and second-harmonic component in media with an inhomogeneous coefficient of nonlinearity. However, such tools did not take into account the possible nonlinear interaction between the transmitted waves. In this paper, a fast simulation tool based on a finite-difference scheme into the Fourier domain is proposed in order to consider this nonlinear interaction. Based on the previous mathematical background, the method remains effective in term of computation time and handles media with an inhomogeneous coefficient of nonlinearity.