Modeling of received signals from annular array ultrasound transducers due to extended reflectors

This paper describes a computationally efficient numerical technique for calculating the received signal from a broadband annular array transducer operating in pulse-echo mode, due to a specified reflector. The technique is referred to as the Diffraction Response from Extended Area Method (DREAM) and operates by tessellating the reflector into planar tiles with a dimension of several wavelengths (at the highest frequency of interest) and finding the contribution from a given tile by a temporal low-pass filtering rather than spatial integration. In particular, this paper formulates the theory for the DREAM for tessellation into triangular tiles and demonstrates the improved performance with triangular tiles relative to square tiles. This paper also analyzes the mean square error of the received signal as a function of the diameters of the transmitting and the receiving transducers and the radial position and orientation of the tile. Based on this, a set of rules for the optimal tile size is developed. The power of the modeling technique is demonstrated by calculating the received signal from an annular array transducer due to three given extended reflectors in which the effect of the focal point location on the received signal is readily demonstrated.