Experimental study of the mapping relationship based near-field acoustic holography with spherical fundamental solutions

This paper is a consequent work of the previously proposed mapping relationship based near-field acoustic holography (MRS-based NAH), [H.J.Wu W.K. Jiang and H.B. Zhang, JSV, 373:66-88, 2016]. It is devoted to the performance study of its practical application with error analysis and experimental validation. Two types of errors, the truncation errors due to the limited number of participant modes, and the inevitable measurement errors caused by uncertainties in the experiment, are considered in the analysis. The influences of the errors on the performance of MRS-based NAH are systematically investigated. First of all, expression of the relative reconstruction error of the pressure energy is derived based on the two types of errors. An approach is developed to estimate the lower and upper bounds of the relative error. It gives a guide to predict the error for a reconstruction under the condition that the truncation error and the signal-to-noise ratio are given. Then, the condition number of the inverse operator is investigated to measure the sensitivity of the reconstruction to the input errors. Asymptotic expressions of the condition number for a special case, conformal spherical model and hologram, are obtained, which indicates the condition number has a geometric growth with the number of participant modes. Numerical examples with different kinds of errors are elaborately designed to validate the stability as well as the correctness of the error analysis. At last, the MRS-based NAH is further examined and verified by a physical experiment, a vibrating cubic model reconstructed from measurement on a spherical hologram. A satisfied agreement with the directly measured pressure on a validation surface is observed for both quantity and distribution of the reconstructed pressure.