A spline-based spatial impulse response simulator

TL;DR

This paper introduces a novel spline-based method for simulating the spatial impulse response of transducers, offering high accuracy and efficiency by leveraging NURBS surfaces and advanced quadrature rules.

Contribution

It presents a new approach using NURBS surfaces and B-spline bases for precise and efficient SIR simulation, improving over traditional discretization methods.

Findings

Allows sampling SIR at low rates without errors

Achieves high accuracy with fewer quadrature points

Enables exact transducer element representations

Abstract

The spatial impulse response (SIR) method is a well-known approach to calculate transient acoustic fields of arbitrary-shape transducers. It involves the evaluation of a time-dependent surface integral. Although analytic expressions of the SIR exist for some geometries, numerical methods based on the discretization of transducer surfaces have become the standard. The proposed method consists of representing the transducer as a non-uniform rational B-spline (NURBS) surface, and decomposing it into smooth B\'ezier patches onto which quadrature rules can be deployed. The evaluation of the SIR can then be expressed in B-spline bases, resulting in a sum of shifted-and-weighted basis functions. Field signals are eventually obtained by a convolution of the basis coefficients, derived from the excitation waveform, and the basis SIR. The use of NURBS enables exact representations of common transducer elements. High-order Gaussian quadrature rules enable high accuracy with few quadrature points. High-order B-spline bases are ideally suited to exploit efficiently the bandlimited property of excitation waveforms. Numerical experiments demonstrate that the proposed approach enables sampling the SIR at low sampling rates, as required by the excitation waveform, without introducing additional errors on simulated field signals.