Murray Drew A, McGough Robert J
Department of Computer Science and Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA.
Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA.
J Acoust Soc Am. 2022 May;151(5):3104. doi: 10.1121/10.0009351.
Exact analytical expressions for the spatial impulse response are available for certain transducer geometries. These exact expressions for the spatial impulse response, which are only available for lossless media, analytically evaluate the Rayleigh integral to describe the effect of diffraction in the time domain. To extend the concept of the spatial impulse response by including the effect of power law attenuation in a lossy medium, time-domain Green's functions for the Power Law Wave Equation, which are expressed in terms of stable probability density functions, are computed numerically and superposed. Numerical validations demonstrate that the lossy spatial impulse for a circular piston converges to the analytical lossless spatial impulse response as the value of the attenuation constant grows small. The lossy spatial impulse response is then evaluated in different spatial locations for four specific values of the power law exponent using several different values for the attenuation constant. As the attenuation constant or the distance from the source increases, the amplitude decreases while an increase in temporal broadening is observed. The sharp edges that appear in the time-limited lossless impulse response are replaced by increasingly smooth curves in the lossy impulse response, which decays slowly as a function of time.
对于某些换能器几何形状，空间脉冲响应的精确解析表达式是可用的。这些仅适用于无损介质的空间脉冲响应的精确表达式，通过解析评估瑞利积分来描述时域中的衍射效应。为了通过纳入有损介质中幂律衰减的影响来扩展空间脉冲响应的概念，以稳定概率密度函数表示的幂律波动方程的时域格林函数通过数值计算并叠加。数值验证表明，随着衰减常数的值变小，圆形活塞的有损空间脉冲收敛到解析无损空间脉冲响应。然后使用几个不同的衰减常数值，针对幂律指数的四个特定值在不同空间位置评估有损空间脉冲响应。随着衰减常数或与源的距离增加，幅度减小，同时观察到时间展宽增加。在限时无损脉冲响应中出现的尖锐边缘在有损脉冲响应中被越来越平滑的曲线所取代，该曲线随时间缓慢衰减。
