A new Calculation Procedure for Spatial Impulse Responses in Ultrasound

A new procedure for the calculation of spatial impulse responses for linear sound fields is introduced. This calculation procedure uses the well known technique of calculating the spatial impulse response from the intersection of a circle emanating from the projected spherical wave with the boundary of the emitting aperture.

This general result holds for all aperture boundaries for a flat transducer surface, and this is used in the procedure to yield the response for all types of flat transducers. An arbitrary apodization function over the aperture can be incorporated through a simple one-dimensional integration. The case of a soft baffle mounting of the aperture is also included.

Specific solutions for transducer boundaries made from lines are given, so that any polygon transducer can be handled. Specific solutions for circles are also given. Finally, a solution for a general boundary is stated, and all these boundary elements can be combined to, e.g., handle annular arrays or semi-circle transducers.

Results from an implementation of the approach are given and compared to previously developed solutions for a simple aperture, a complex aperture, and a Gaussian apodized circular transducer.