An error reduction algorithm for numeric calculation of the spatial impulse response

Abstract

The most frequently used method for calculation of the pulsed pressure field of ultrasonic transducers is the spatial impulse response (SIR) method. This paper presents a numeric approach that reduce the numeric error by weighting the contribution of each source element into the SIR time array, by considering the exact time of arrival of each contribution. The resolution of the time array Δt must be finite. This results in an error in travel time of ±Δt/2. However, knowledge of the exact travel time can be used to share the contribution from each source element between the two closest time elements so that the average time corresponds to the exact travel time and thereby reduce the numeric error. This study compares the standard and the proposed numeric algorithm with the analytic solution for a planar circular disc because it has a simple analytic solution. The paper presents calculations of the SIR for selected points in space and calculations of the RMS-error between the numeric algorithms and the analytic solution. The proposed numeric algorithm decreases the numeric noise or error with a factor of five compared to the standard numeric algorithm.