Sheu Yae-Lin, Li Pai-Chi
Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan 106, Taiwan.
J Acoust Soc Am. 2008 Dec;124(6):3471-80. doi: 10.1121/1.3003087.
This study developed a numerical solution of the general photoacoustic generation equations involving the heat conduction theory and the state, continuity, and Navier-Stokes equations in 2.5D axisymmetric cylindrical coordinates using a finite-difference time-domain scheme. The numerical techniques included staggered grids and Berenger's perfectly matched layers (PMLs), and linear-perturbation analytical solutions were used to validate the simulation results. The numerical results at different detection angles and durations of laser pulses agreed with the theoretical estimates to within an error of 2% in the absolute differences. It was also demonstrated that the simulator can be used to develop advanced photoacoustic imaging methods. The performance of Berenger's PMLs was also assessed by comparisons with the traditional first-order Mur's boundary condition. At the edges of the simulation domain, a ten-layer PML medium with polynomial attenuation coefficient grading from 0 to 5 x 10(6) m(3)/kg s was designed to reduce the reflection to as low as -60 and -32 dB in the axial and radial directions, respectively. The reflections at the axial and radial boundaries were 32 and 7 dB lower, respectively, for the ten-layer PML absorbing layer than for the first-order Mur's boundary condition.
本研究采用有限差分时域方法，在二维半轴对称圆柱坐标系中，基于热传导理论以及状态方程、连续性方程和纳维 - 斯托克斯方程，对一般光声产生方程进行了数值求解。数值技术包括交错网格和贝伦格完全匹配层（PML），并使用线性微扰解析解对模拟结果进行验证。不同探测角度和激光脉冲持续时间下的数值结果与理论估计值的绝对差值误差在2%以内。研究还表明，该模拟器可用于开发先进的光声成像方法。通过与传统一阶穆尔边界条件进行比较，对贝伦格PML的性能进行了评估。在模拟域边缘，设计了一种十层PML介质，其多项式衰减系数从0到5×10⁶ m³/(kg·s)渐变，以使轴向和径向的反射分别降低至-60 dB和-32 dB。对于十层PML吸收层，轴向和径向边界处的反射分别比一阶穆尔边界条件低32 dB和7 dB。
