A method to determine acoustic hologram of an intricate object

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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.