A complex virtual source approach for calculating the diffraction beam field generated by a rectangular planar source

In this paper, a complex virtual source approach for calculating the ultrasound field generated by a rectangular planar source is presented. Instead of using a real rectangular plane source, the equivalent sources that have complex amplitudes in complex space are used to compute the sound field distribution. The parabolic equation first is solved in the k-space domain by applying Fourier transform. The k-space domain source is then expressed as a set of Gaussian functions, and the related coefficients is determined by the optimization method. The analytic solution then is derived, and the effect of the parameters on the calculation accuracy is discussed. The comparison between the proposed fast numerical scheme and previous methods (Fresnel integral and Ocheltree´s method) and are given in an example. The numerical results reveal that the computation time in obtaining accurate calculations is greatly reduced by using the proposed method.