A New Approach to Calculating Spatial Impulse Responses Based on X-wave

X-wave is a particular case of limited diffracting waves which have great application potential for field focus depth enlargement in acoustic imaging systems. In practice, we have experimentally produced a zeroth-order band-limited X-wave, it needs annular array transducer. Because X-wave have complicated theory background, so the simulation calculation is very complicated. The calculation of X-wave acoustic fields is most often based on the spatial impulse response approach as suggested by field is found from a convolution between the acceleration of Tupholme and Stepanishen. The impulse response is calculated by the Rayleigh integral by summing the spherical waves emitted from the entire aperture surface. The evaluation of the integral is cumbersome and quite involved for different aperture geometries. This paper shows the X-wave acoustic 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. We sum the angles of the arcs within the aperture readily yields the spatial impulse response for a point in space. The new approach can be used for finding analytic solutions to the spatial impulse response for new geometries of, e.g. annular shape, X-wave uses the annular array transducer. The approach also makes it easy to calculate of X-wave acoustic fields.