AI 中文总结
本文提出Sparse Delta Integration方法，实现了超声压力场模拟的高效计算，在保持高精度的同时，相对于Field II获得了显著加速，相关成果已集成至开源Python包eSDIva。
AI 中文摘要
超声压力场与脉冲回波响应的精确高效模拟对换能器设计、波束形成优化及基于模型的成像研究至关重要。传统空间脉冲响应（SIR）方法通过对每个矩形孔径细分的梯形脉冲响应进行显式采样来计算声场，这对于大孔径、密空间网格和高采样频率会导致高计算成本。本文提出Sparse Delta Integration（稀疏δ积分），这是一种用于矩形孔径远场SIR的数学框架，将梯形空间脉冲响应表示为稀疏狄拉克δ分布集的双重积分。该公式给出了时域和频域SIR的紧凑表达式，并支持向量化实现，其计算成本与梯形持续时间无关。我们进一步推导了用于脉冲回波模拟的频谱公式，该公式移除了传统傅里叶域卷积流水线的部分环节。这些方法在开源Python包eSDIva中实现，相对于Field II，它们在时域SIR计算上实现了高达180倍的加速，在脉冲回波射频（RF）模拟上实现了高达20倍的加速，同时保持了高数值精度，均方误差低于1e-5，相关系数接近1。
英文摘要
Accurate and efficient simulation of ultrasound pressure fields and pulse-echo responses is essential for transducer design, beamforming optimization, and model-based imaging research. Conventional Spatial Impulse Response methods compute acoustic fields by explicitly sampling trapezoidal impulse responses for each rectangular aperture subdivision, which leads to high computational cost for large apertures, dense spatial grids, and high sampling frequencies. We introduce Sparse Delta Integration, a mathematical framework for the far-field SIR of rectangular apertures that expresses the trapezoidal spatial impulse response as the double integration of a sparse set of Dirac delta distributions. This formulation yields compact expressions for time-domain and frequency-domain SIRs and enables vectorized implementations whose computational cost is independent of the trapezoid duration. We further derive a spectral formulation for pulse-echo simulation that removes part of the conventional Fourier-domain convolution pipeline. Implemented in the open-source Python package eSDIva, these methods achieve speedups of up to 180x for temporal SIR computation and up to 20x for pulse-echo RF simulation relative to Field II, while maintaining high numerical accuracy with mean squared errors below 1e-5 and correlation coefficients close to unity.
