Experimental application of high precision k-space filters and stopping rules for fully automated near-field acoustical holography

Abstract

In general, inverse acoustics problems are ill-posed. Without proper regularization action taken noisy measurements result in an increasingly disturbed solution of the inverse acoustics wave equation as the distance from the measurement plane to the desired source grows. Two distinctive steps take place in the regularization process for planar near-field acoustical holography (PNAH): first, a low-pass filter function is defined and secondly a stopping rule is applied to determine the parameter settings of the filter. In acoustical imaging practice, it turns out to be very hard to determine the right filter for a certain case, ideally by means of an automatic search for the (near-) optimal parameters. This paper presents the practical application of a novel automated method that combines fitted filters for a broad number of possible experimental sources combined with highly efficient stopping rules by taking advantage of k-space. Also, a number of well-known and newly developed filter functions and stopping rules are discussed and compared with one another. Results based on actual measurements demonstrate the effectiveness, applicability, and precision of the fully implemented and automated regularization process for PNAH. Practical results even show acoustic source visualization below one millimeter primarily by successful application of k-space regularization. Implementations include modifications of Tikhonov, exponential and truncation low-pass filters, L-curve Generalised Cross-Validation (GCV) and the novel Cut-Off and Slope (COS) parameter selection methods for PNAH COS iteration in combination with either a modified exponential or Tikhonov low-pass filter results in an automated selection of the regularization parameters and eventually a fully automated PNAH system.