A New Approach to Calculating Spatial Impulse Responses

Using linear acoustics the emitted and scattered ultrasound field can be found by using spatial impulse responses as developed by Tupholme and Stepanishen. The impulse response is calculated by the Rayleigh integral by summing the spherical waves emitted from all of the aperture surface. The evaluation of the integral is cumbersome and quite involved for different aperture geometries. This paper re-investigates the problem and shows that the field can be found from the crossings between the boundary of the aperture and a spherical wave emitted from the field point onto the plane of the emitting aperture. Summing the angles of the arcs within the aperture readily yields the spatial impulse response for a point in space. The approach makes is possible to make very general calculation routines for arbitrary, flat apertures in which the outline of the aperture is either analytically or numerically defined. The exact field can then be found without evaluating any integrals by merely finding the zeros of the either the analytic or numerically defined functions. This makes it possible to describe the transducer surface using an arbitrary number of lines for the boundary. The approach can also be used for finding analytic solutions to the spatial impulse response for new geometries of, e.g. ellipsoidal shape. The approach also makes it easy to incorporate any apodization function and the effect from different transducers baffle mountings. Examples of spatial impulse responses for a shape made from lines bounding the aperture is shown along with solutions for Gaussian apodized round transducer.