Equivalent Source Arrays for the Accurate Modeling of Acoustic Finite-Size Transducer Radiation Patterns

We present a method to retrieve virtual point-source time histories that reproduce the recorded wavefields of an arbitrary acoustic source in the linear regime. The method uses recorded acoustic records around the source and a set of virtual point sources covering the area of the actual source. By means of an inverse problem, the wavelets obtained reproduce accurately the wavefields generated by the actual source. We test the method for simple configurations as well as for numerical models of actual transducers and finally real recordings from an ultrasound tomography device, both in 2D and 3D. The time histories found by means of our method are shown to reproduce accurately the recorded wavefields without prior knowledge about the actual source’s radiation pattern. Our results further imply that our method is equivalent to the application of the Moore-Penrose inverse but without requiring the assembly of the full Green’s function system.