A method to determine acoustic hologram of an intricate object

为了在预测物体周围的声场中对具有复杂形状和元素的物体施加边界条件，我们尝试引入阻抗全息图，该阻抗全息图描述具有简单形状的适当界面（M平面表面元素）上的声学特性，而不是实际物体表面。为了表征阻抗全息图，我们采用由全息图和子全息图表面（N个元件）包围的全息图子区域，并且在M个声场条件下对全息图子区域中的2（M+N）个点进行压力测量。通过使用这些压力和基尔霍夫-亥姆霍兹积分定理，我们确定的压力和正常的速度的每个表面元素作为一个反问题。通过由这些元素值构成的M × M线性方程，可以确定阻抗全息图的M × M未知分量。我们对二维座位的全息图（M=4）进行了边界元子程序、全尺寸数值实验和物理实验，并能精确求解出全息图。4个扬声器和124个麦克风分别嵌入在全息图子区域的外部和内部。研究发现，在阻抗全息图中，要获得最大精度的全息图子区域的麦克风位置是在全息图表面元素的中心和边缘附近。它被证实，从60 dB精度的子区域压力测量获得的阻抗全息图预测的声场在3 dB的幅度误差和10度的相位误差的实际精度内。然而，物理实验在预测精度上还没有达到数值实验的水平。我们仍在研究振膜面积效应和每个麦克风的灵敏度校准。

To impose the boundary condition for an object with intricate shape and elements in prediction of a sound field surrounding the object, we make an attempt to introduce an impedance hologram which describes the acoustic property on an appropriate interface (of M plane surface elements) with simple shape instead of the actual object surface. To characterize the impedance hologram we employ a hologram sub-region enclosed by the hologram and a sub-hologram surface (of N elements), and make pressure measurements of 2(M+N) points in the hologram sub-region under M sound field conditions. By using these pressures and the Kirchhoff-Helmholtz integral theorem, we determine the pressure and normal velocity of each surface element as an inverse problem. By MxM linear equations made of these element values, MxM unknown components of the impedance hologram can be determined. We made BEM subroutines, full scale numerical and physical experiments on the hologram (M=4) of a 2 dimensional seat of which we can solve the exact one. Four loudspeakers and 124 microphones were embedded respectively outside and inside the hologram sub-region. It is found that the microphone positions of the hologram sub-region to give the maximal precision in the impedance hologram are around the centers and edges of the hologram surface elements. It is confirmed that the impedance hologram obtained from the sub-region pressure measurement of 60 dB precision predicts the sound field within the practical precision of 3 dB error in magnitude and 10 degree error in phase. However the physical experiment has not reached the numerical one in the prediction accuracy. We are still studying on diaphragm area effects and sensitivity calibration of each microphone.