| An investigation is undertaken to validate the Helmholtz Equation-Least Squares (HELS) method, a novel approach in acoustic holography. The HELS method, like other acoustic holography methods, allows for 3-D reconstruction of the radiated sound field based on 2-D measurements of acoustic pressure signals. It does so by assuming the pressure field to be written as a series expansion in spherical wave functions and uses the collocation method to solve for the expansion coefficients. This expansion is shown to be valid for non-spherical objects as long as the aspect ratio is not very high. Also, the parameters of the expansion are investigated, namely the number of functions used and the number and locations of measurements. It is found that the number of expansion functions is dependent on the frequency, size of object and measurement distance. Meanwhile, the number of measurements must exceed the number of functions by more than half for the reconstruction to be accurate. Also, the HELS method is found to be able to accurately reconstruct the pressure field based on partial planar measurements. The HELS method is validated experimentally on a bowling ball, a vehicle front end and an engine block. In the vehicle front end case, the pressure is measured on two planes parallel to the object surfaces. The coefficients obtained from employing the HELS method on the data from the plane farther away are used to reconstruct the acoustic pressure on the plane nearer to the surface where a comparison takes place with very good results. The intensity and the far field pressure are calculated for the case of the engine block and shown to be accurate. A prototype of a holography system based on this method is developed and validated. This prototype uses a 16 microphone array and a data acquisition and processing modules interfaced with the HELS algorithm. This holography system based on the HELS method is found to improve efficiency and functionality of the holography procedure. |
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